We study deterministic multi-user identification over bosonic channels using coherent-state signatures. Each user is assigned a coherent product state under an average energy constraint, and identification is performed by a user-specific binary quantum test. In contrast to classical multi-user identification models based on shared codebooks, this formulation associates each receiver with a geometric signature in high-dimensional phase space. Using metric entropy bounds, we show that the identification capacity exhibits a near-k log k scaling behavior.

Bell inequalities play a central role in certifying quantum correlations and underpin protocols such as device-independent quantum key distribution. However, enumerating all Bell inequalities for a given scenario remains intractable beyond the simplest cases, as it requires solving a computationally hard facet enumeration problem on the associated Bell polytope. We propose the Adjacency Sampling method, which builds on the Adjacency Decomposition method but sacrifices completeness for speed. On previously solved Bell polytopes, the method reproduces every known class of inequalities. For scenarios where no complete enumeration exists, it greatly exceeds existing partial results: in $\mathcal{L}_{3,3,3,3}$ we obtain over $1.29 \times 10^8$ classes, more than 25 times the previous count; in $\mathcal{L}_{4,5,2,2}$ we nearly triple the known list to 49\,358 classes; and for $\mathcal{L}_{4,6,2,2}$ we report over 4.3 million classes.

GBM is a highly aggressive primary malignancy in adults, necessitating personalized therapeutic strategies due to its inherent molecular heterogeneity. MGMT promoter methylation is a pivotal prognostic biomarker for anticipating response to temozolomide-based chemotherapy. Although various AI frameworks have been developed for non-invasive MGMT prediction, spatial heterogeneity of methylation status and the high-dimensional and correlated nature of MRI data frequently constrain discriminative feature learning and generalizability of classical models. To circumvent these limitations, a specialized IA-QCNN architecture is proposed, based on the principles of quantum mechanics, including superposition and entanglement, and enabling more efficient representation learning in high-dimensional Hilbert space. The framework establishes a methodological bridge between GBM radiogenomics and quantum deep learning by integrating energy-based slice selection, importance-aware weighting, ring-topology quantum convolution, and folding-based pooling layers. When the model predicts MGMT promoter methylation status using both mpMRI and T1Gd images, experimental results demonstrate that the IA-QCNN achieves high accuracy despite its low number of trainable parameters while effectively minimizing the overfitting problem observed in classical models. Quantitative analyses reveal that the T1Gd modality possesses higher discriminative power than mpMRI, establishing a clinically significant sequence preference. Furthermore, the model exhibits exceptional robustness in hybrid noise environments, effectively utilizing noise as a regularization mechanism to enhance predictive performance. Consequently, the specialized IA-QCNN architecture provides a robust and computationally efficient alternative to classical approaches in the analysis of heterogeneous radiogenomic data.

While the spatial arrangement of individual units is essential for the physical implementation of quantum batteries, geometry-dependent interactions are rarely explicitly incorporated into existing theoretical models. To address this, we propose a planar many-body quantum-battery architecture consisting of coupled resonators. By introducing a distance-dependent function to modulate both the inter-battery coupling and tunneling, we investigate the open-system charging dynamics in the strong-coupling regime using a Redfield master-equation approach. Using ergotropy as the primary figure of merit, we demonstrate that the charging performance is highly sensitive to the inter-battery distance, nearest-neighbor coupling strength, and environmental conditions. Specifically, decreasing the inter-battery distance within an optimal window suppresses charging fluctuations and accelerates the system's approach to a steady charged state. However, an excessively short distance amplifies environmental dissipation, thereby degrading the overall performance. Furthermore, while overly strong inter-battery coupling induces post-charging instability, moderate coupling achieves a favorable balance between maximum stored energy and stability. We also establish that the system-bath coupling and bath cutoff frequency predominantly govern the charging timescale, and that the planar architecture maintains its robustness against thermal fluctuations over a broad temperature range. These results highlight the critical role of geometry-controlled interactions in many-body quantum batteries, providing a theoretical foundation for the design and optimization of two-dimensional quantum energy-storage devices.

We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU(1,1)$ group. In order to obtain the exact energy spectrum of this problem, we write its Hamiltonian in terms of the Dunkl creation and annihilation operators, which close the $su(1,1)$ Lie algebra. This allows us to exactly solve this Hamiltonian and obtain its parity-dependent energy spectrum. Then, we investigate the quantum dynamics of the system, particularly the collapse and revival phenomena, by using an initial state given by a superposition of even and odd Dunkl coherent states. We compute the field quadrature and the survival probability, showing that the Dunkl parameter $\mu$ modulates the fractional revivals and produces perfect state reconstructions at half-periods for specific deformation values. We analyze the quadrature variance to show that the Dunkl deformation generates interference-induced squeezed states around $t \approx \pi$. The standard Kerr medium dynamics are exactly recovered in the limit $\mu \rightarrow 0$.

It is known that the classical information like strings of bits can be copied. In 1982, Wootters and Zurek proposed the quantum no-cloning principle [1]. No-cloning principle says that it is impossible to make an identical copy of an arbitrary unknown quantum pure state by using unitary evolution. In this paper, we propose a general no-cloning principle. We call U|psi>, where U is any unitary operator, a U-copy of the state |psi>. The general no-cloning principle states that it is impossible to make a U-copy of an arbitrary unknown quantum pure state by using unitary evolution.

We propose a protocol that transfers entanglement from an entangled atomic two-level-system (TLS) resource to a pair of free electrons in an energy-sideband ladder via local electron-TLS interactions. In a controlled rotating-wave regime, closed-form reduced states are derived. TLS heralding then prepares a maximally entangled electron state in a two-dimensional single-excitation manifold, with a simple dependence on the initial TLS resource entanglement. Numerical integration of the full bilinear Hamiltonian quantifies the impacts of detuning and pulse shaping and identifies the leading beyond-rotating-wave corrections. The results establish a heralded route to entangled free electrons and will facilitate further advances in quantum electron optics.

Szegedy's quantum walk gives a generic quadratic speedup for reversible classical Markov chains, but extending this mechanism to quantum Gibbs sampling has remained challenging beyond special cases. We present a walk-free quantum algorithm for preparing purified Gibbs states with a quadratic improvement in spectral-gap dependence for a broad class of quantum Gibbs samplers that satisfy exact Kubo-Martin-Schwinger detailed balance. Our main structural result is an explicit factorization of the corresponding parent Hamiltonian into noncommutative first-order operators. This turns purified Gibbs-state preparation into a singular-value filtering problem and enables a quantum singular value transformation algorithm with quadratically improved gap dependence under standard coherent-access assumptions. The framework applies to several efficiently implementable Gibbs samplers beyond the Davies setting. We also introduce an auxiliary dissipative dynamics based on the same factorization, which can be used to generate warm starts in the doubled Hilbert space in metastable regimes.

Environmental noise can enhance transport, an effect known as environmental noise-assisted quantum transport. Most theoretical studies focus on optimizing system parameters under spatially uniform system-environment coupling. Here, instead, we optimize the environmental noise itself by allowing for site-dependent dephasing. We investigate steady-state transport in one-dimensional lattices with either ramped or disordered energy landscapes, considering both short- and long-range coherent tunneling. In the absence of environmental effects, in the thermodynamic limit these systems can exhibit localization, and thus suppressed transport, arising from destructive interference. Using a Lindblad master equation framework, we implement local dephasing optimized to maximize steady-state population flux. We find that for ramp potentials, short-range tunneling favors selective dephasing on alternating sites, whereas long-range tunneling benefits from a dephasing profile that increases with distance from the injection site. In energetically disordered systems, strongly detuned sites require enhanced local dephasing under short-range tunneling to facilitate transport. In all cases, we find that site-optimized dephasing allows higher transport efficiency than uniform dephasing, and it is accompanied by increased spatial delocalization of the steady state. Our results provide microscopic insight into the interplay between coherent dynamics and environmental noise. Dephasing broadens energy levels locally, helping to overcome detuning and destructive interference. More generally, we establish spatially-structured environmental noise as a strategy for controlling both quantum transport and state coherence in open systems.

We develop an angular momentum representation and implementation of the Clifford+T set of unitaries for qutrits. We show that local gates from this set can be realized by the sole use of suitable rotations and one-axis-twisting operations, which are at most quadratic in the angular momentum operators and thus can be experimentally realized in many quantum systems. Controlled rotations are shown to only require linear angular momentum couplings and, as a consequence, the full qutrit Clifford+T set is shown to be expressed solely in terms of two-body angular momentum couplings, rotations and one-axis-twisting operations. By employing the Jordan-Schwinger map, we show an analogous implementation in terms of bosonic modes, improving on the number of modes with regard to a previous scheme. Moreover, we employ the cross-Kerr interaction in order to obtain any qutrit Clifford+T gate for bosonic modes. We illustrate our findings with simple schemes for preparing entangled states of interest.

The speed of quantum evolution is limited under finite energy resources. While most quantum speed limits (QSLs) are formulated in terms of quantum states, they can be extended to the evolution operator itself, and thus impose fundamental limits on how quickly logical gate operations can be implemented on a quantum computer. Here, we derive a general, tight QSL that holds for any unitary evolution under the constraint that the spectral width of the Hamiltonian is bounded. We apply this result to obtain QSLs for several standard quantum gates, including Hadamard, CNOT, and Toffoli gates, finding that the QSL can vary significantly across different gates, including ones with the same entangling power. These findings can be understood geometrically using the Space Curve Quantum Control formalism, which maps unitary evolution to space curves in Euclidean space. In this formalism, the problem of finding QSLs is recast as the problem of finding minimal-length curves obeying a curvature bound. We find that time-optimal gates map to helices of varying dimensions, and that QSLs can be understood from the perspective of a bottleneck principle in which the operator that evolves the slowest governs the minimal gate time.

In this paper, we study the non-Gaussianity of the eigenstates of the Pegg-Barnett phase observable. By computing the Wigner functions of the eigenstates, we confirm that they take negative values in specific regions of the phase space. The Pegg-Barnett phase-operator eigenstates lie on a finite-dimensional Hilbert space. Thus, we examine how their negativity volumes depend on the dimension of the Hilbert space. Moreover, we present a quantum-optical circuit that generates these eigenstates and identify single-photon detection as the origin of their non-Gaussianity. To investigate a more realistic experimental implementation, we introduce imperfect single-photon detectors with non-unit efficiency into the circuit and evaluate the dependence of the detection probability, the output-ideal fidelity, and the negativity volume of the approximate eigenstate output from the circuit on the detector efficiency. Finally, as a practical application, we consider a phase-estimation experiment of an arbitrary unknown state by injecting both the unknown state and a known Pegg-Barnett eigenstate into a 50-50 beam splitter and individually counting the numbers of photons emitted from its two output ports.

Trotterization is a technique that allows one to approximate a time evolution of a Hamiltonian by repeatedly evolving the individual terms of the Hamiltonian one-at-a-time for small time durations. Bounds on the error of this approximation exist; however, they are typically loose and moreover, it is known that the true error can be greatly influenced by the order in which the terms of the Hamiltonian are evolved. In this work, we consider various ordering strategies that exploit the commutation structure of the Hamiltonian, in addition to a few other baseline ordering strategies. These commutation-based strategies involve dividing the terms of the Hamiltonian into groups where all the terms within each group commute with one another. These groupings can be obtained by using graph coloring techniques on what we call the "commutation graph" of the Hamiltonian. We prove various results regarding the structure and properties of such commutation graphs for certain classes of Hamiltonians. We also empirically calculate the (true) Trotter error using these ordering strategies on various 1D and 2D Heisenberg-style systems.

Any protocol to process quantum information has to conclude with a measurement, aimed at producing a specific set of probabilities of measurement outcomes. In this work, we investigate the time, energy and importantly the genuine quantum resources necessary for transforming a set of measurement probabilities generated by a positive-operator-valued measure (POVM), to a target set of measurement probabilities. To this end, we first show that the speed of measurement probabilities, defined as the average rate of the surprisal of measurement outcomes, is constrained by the genuine quantum fluctuations contained in the measurement probabilities. Interestingly, this quantum speed limit can act as a witness for bipartite quantum correlations by selecting an optimal local projective measurement. Furthermore, we obtain a minimum time to transform an initial measurement probabilities to a target measurement probabilities, and apply this result to analyzing the cost of generating a local athermality in terms of genuine quantum uncertainty.

Spectral collapse in the two-photon quantum Rabi model (tpQRM) has long been regarded as incompatible with quantum criticality due to the absence of a vanishing excitation gap. We show that, in the anisotropic tpQRM, spectral collapse constitutes a genuine continuous quantum phase transition governed by a single soft mode. The excitation gap within the same parity closes as $\epsilon_{sp} \sim |g - g_c|^{z\nu}$ with $z\nu = 1/2$, placing the system in the same universality class as the standard QRM, while the gap between different parities reflects symmetry-induced level splitting rather than a critical excitation. This soft mode defines a unique energy scale that controls both equilibrium and nonequilibrium properties, including macroscopic observables, quantum Fisher information, and Kibble-Zurek dynamics. These results establish spectral collapse as an experimentally accessible realization of quantum criticality in a few-body system and demonstrate that universality is fully determined by the soft-mode structure rather than by microscopic details.

We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences both globally, via the participation entropy, and locally, via the relative entropy of coherence. Combining exact vector evolution, matrix product state simulations, and replica tensor networks methods, we find that conservation laws replace the logarithmic saturation of unconstrained circuits with slow hydrodynamic relaxation of the global coherence measures. Locally, symmetry-constrained circuits show a clean rise-peak-fall structure whose peak time grows algebraically with subsystem size. In contrast, ergodic Hamiltonians broaden the peak into an extended plateau at larger subsystems, highlighting a qualitatively distinct mechanism. Coherence thus emerges as a sensitive probe of symmetry-constrained thermalization, linking quantum resource dynamics to many-body transport.

We investigate the performance of Grover's algorithm on three different generations of IBM Heron QPUs. On Heron family of IBM QPUs the success probabilities for three, four and five qubits without dynamical decoupling is better than results reported for previous generations of QPUs. The success probability as function of number of iterations of Grover operator is considered. A study of the improvement of results of Grover's algorithm for five qubit case with the help of topological dynamical decoupling is considered. For a six qubit case on Heron r3 QPU a clear result for finding the sought-after bitstring is reported for theoretically suboptimal number of iterations of Grover operator with the help of dynamical decoupling.

This paper introduces a conceptual framework of technology-dependent ternary quantum gates that could be implemented and fabricated into various superconducting and photonic quantum systems for operating 3-valued quantum bits (qutrits). The "technology-dependent" term means that such ternary quantum gates are on-purpose designed analogy to the contemporary binary quantum gates. Conceptually, the final built technology-dependent one-qutrit and two-qutrit ternary quantum gates are Chrestenson, Z3, 01, 02, 12, +1, +2, and their corresponding controlled gates, respectively.

In this paper, numerical simulations of four-mode continuous-variable cluster states with different topologies in the framework of measurement-based quantum computation are presented. By utilizing the symplectic representation and covariance matrix, the process of generating cluster states with linear, square, and T-shaped topologies has been systematically modeled. The simulation results show that the cluster graph structure is directly reflected in the pattern of quadrature correlations; in other words, the theoretical nullifier relations of the cluster states are reproduced in the final covariance matrices. Increasing the squeezing parameter leads to the strengthening of the target correlations and the suppression of unwanted components arising from anti-squeezing; such that the off-diagonal elements of the covariance matrix in the linear and square topologies increase to significant values, and in the T-shaped topology a stronger central correlation (similar to GHZ-like behavior in the continuous-variable domain) is observed. In order to quantitatively analyze these structural differences, a metric titled CCR (Correlation Concentration Ratio) is introduced that quantifies the concentration of effective correlations on the graph edges relative to the total correlations of the system. This index enables direct comparison of different topologies from the perspective of structural entanglement distribution and provides a framework for evaluating the efficiency of cluster graphs in MBQC architectures. The results show that CCR can be used as a practical tool for designing and selecting optimal topologies in larger clusters and more complex structures.

We develop a theory of quantum sufficiency on real *-subalgebras and real Jordan algebras. In contrast to the conventional formulation, which is based on families of states, complex completely positive coarse-grainings, and Radon-Nikodym cocycles associated with faithful reference states, our framework allows models consisting of general self-adjoint operators, including derivatives of states. Within this framework, square-root likelihood ratios and symmetric logarithmic derivatives arise naturally as fundamental self-adjoint likelihood-type objects. This makes it possible to treat ordinary quantum statistical models and local quantum statistical structures within a unified setting. We introduce sufficient real positive maps and show that sufficient complex *-subalgebras, sufficient real *-subalgebras, and sufficient real Jordan algebras correspond respectively to complex completely positive maps, real completely positive maps, and real positive maps. We characterize minimal sufficient real *-subalgebras by the likelihood-ratio set together with rho-modular invariance, and show that the real Jordan algebra generated by the likelihood-ratio set and the projected reference state is the minimal sufficient real Jordan algebra. We also obtain Koashi-Imoto type decompositions for sufficient real *-subalgebras and sufficient real Jordan algebras. Our formulation admits degenerate reference states and separates the likelihood-ratio aspect of sufficiency from its genuinely quantum modular aspect. These results suggest that real Jordan structure provides a natural framework for the statistical aspect of quantum theory beyond the conventional complex *-algebraic setting.

The irreversible emergence of classical behavior from a reduced quantum description via a canonical intrinsic decomposition of the density operator is analyzed. In the intrinsic reference basis (IRB), defined for a fixed physical conjugation K (determined by measurement convention, system symmetry, or secular approximation) by diagonalizing the real symmetric part of the state, the density operator separates into a diagonal population sector and a real antisymmetric coherence sector. For the class of Markovian open-system dynamics whose Lindblad operators are diagonal in the IRB, we prove that the quadratic coherence functional is a Lyapunov functional under pure-dephasing or interaction-picture evolution, with each intrinsic coherence component decaying exponentially at a computable rate. This yields a canonical state-dependent operational classicality criterion via the normalized cohesion index, an explicit logarithmic classicalization time controlled by the slowest dephasing rate, and a demonstration that the IRB projectors emerge as dynamically stable pointer sectors under IRB-selective evolution. Suppression of intrinsic coherences is exactly equivalent to suppression of fringe visibility in the corresponding interferometric sector; for a balanced two-path setup the cohesion index coincides with the fringe visibility, making the classicality criterion directly testable with standard interferometric equipment. The approach complements environment-induced einselection: it is applicable whenever a coarse-grained reduced description is available, independently of whether the microscopic system-environment coupling is known.

It is well known that bosons and fermions exhibit opposite behaviors when experiencing interference, in the sense that bosons have a tendency to bunch whereas fermions have a tendency to antibunch. Recently, this complementarity was mathematically characterized in [arXiv:2312.17709] by means of an identity relating the transition probabilities of both types of particles in a linear interferometer. Here, we show that such a complementarity still holds even when particles become partially distinguishable, for example, when they have slightly different polarizations or time delays. Namely, we establish a relation that combines bosonic and fermionic multiparticle interferences in an arbitrary linear interferometer, in the presence of partial distinguishability. Incidentally, this also provides a new mathematical identity relating the permanent and determinant of tensors of order 3. Importantly, this complementarity has direct operational consequences in quantum metrology. Indeed, we show that the correlation matrices for bosonic and fermionic particle number distributions at the output of the interferometer obey a simple sum rule: their sum equals twice the correlation matrix for classical particles. This, in turn, constraints the achievable quantum Fisher information in phase-estimation protocols, highlighting a trade-off whereby greater indistinguishability enhances bosonic sensitivity whereas reduced indistinguishability can benefit fermionic schemes.

Quantum optimization algorithms promise advantages for difficult problems but are costly to simulate and analyze on classical machines. Recently, constrained quantum optimization has been investigated through the lens of Quantum Zeno dynamics, an approach which constrains the search to a subspace by means of quantum measurements. Exploiting that quantum measurements are projections, we propose a model reduction approach and show that simulations can be conducted in a lower-dimensional space. As possible applications, we demonstrate exponential state-space reduction of constrained quantum optimization in case of random 3-SAT and agent coordination problems over graphs.

We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger rotation rather than small rotations in order polynomial times in the size $N$ of search space. We analyze the complexity of implementing the non-unitary operation and we observed that the price paid by performing this rotation is due the normalization. In Kraus operator approach we need $O(N)$ repetition of the algorithm to have a chance of measuring a solution in a post-selection, this is no better than the classical solution. However, the quantum singular value transform in addition with block encoding and Chebyshev polynomial approximation, we got complexity $O(\sqrt{N})$ and reach the Grover's bound with an extra resource of one single qubit, compared with the standard Grover's algorithm.

A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general form only in the non-relativistic approximation. It is shown that the auxiliary field is a superposition of Klein-Gordon fields, the parameters of which are related to singular points of the Fourier transform of the corresponding interatomic potential. The general form of the relativistic Hamiltonian system of interacting atoms is established. It is shown that the exact calculation of the relativistic partition function of a system of interacting atoms, taking into account the field degrees of freedom, reduces to renormalizing the parameters of the auxiliary field. It is established that the field degrees of freedom lead to a divergence in the total energy of a classical relativistic system - an analogue of the ultraviolet catastrophe. Quantization of the auxiliary field eliminates this divergence. The existence of a phase transition within the framework of relativistic quantum statistical thermodynamics has been proven.

Signal photons emitted by quantum nodes typically fall outside the low-loss telecom window of optical fibers, leading to severe transmission losses. Quantum frequency conversion (QFC) offers an effective optical interface that bridges quantum nodes with telecom-band channels, enabling long-distance quantum communication. In this work, we demonstrate a compact, fiber-integrated QFC system with low noise and a high signal-to-noise ratio (SNR). Using a periodically poled lithium niobate (PPLN) waveguide, input photons at 637.2 nm are down-converted to telecom photons at 1588.3 nm. Our system achieves a total conversion efficiency of approximately 9%, with pump-induced noise suppressed to 154 Hz. For input photon rates of 32.7, 118.0, and 327.7 kHz, the corresponding SNRs are 12.3, 43.9, and 117.8, respectively. We further develop a theoretical model to simulate the entanglement fidelity between nitrogen-vacancy (NV) center spins and the frequency-converted telecom photons. At the emission rate of an NV center, our QFC system maintains an expected fidelity exceeding 52% over a transmission distance of 100 km. These findings highlight the potential of our QFC system for scalable, long-distance quantum networking.

Causal discovery from observational data underpins applications in finance, climate modeling, and machine learning. Constraint-based causal discovery reduces structure learning to a sequence of conditional independence (CI) tests, where each test decides independence by estimating conditional mutual information $I(X;Y \mid Z)$ to additive precision $\tau$ and thresholding against it. Classically this requires $\Theta(1/\tau^{2})$ samples per test, a cost that dominates in the high-precision regime typical of weak dependencies. We present QKLA (Quantum Kullback--Leibler Amplitude estimation), a quantum algorithm that encodes a clipped log-density ratio as a bounded amplitude and applies amplitude estimation to recover the KL divergence. Given coherent oracle access to the joint distribution, QKLA achieves a quadratic precision improvement, needing only $\mathcal{O}((L/\tau)\log(1/\delta))$ queries, where $L$ is the log-ratio clip bound. Embedded in the PC algorithm, this compounds to an $\widetilde{\Omega}(1/(L\tau))$ reduction in total queries for the full causal discovery procedure. We validate the theory in three experiments. A gate-level state-vector simulation of the full QKLA circuit confirms the predicted $\mathcal{O}(1/M)$ error decay. Across $K=20$ random binary distributions, classical and quantum error scalings match theory to slope accuracy $\pm 0.005$. On two benchmark networks (\textsc{Asia}, 8 nodes; \textsc{Synthetic-12}, 12 nodes), quantum PC matches classical skeleton-recovery F1 while using $2.5$--$3.0\times$ fewer oracle queries at $\tau = 5\cdot 10^{-3}$ bits and up to $12\times$ fewer at $\tau = 10^{-3}$ bits.

High-precision quantum parameter estimation is fundamental to the advancement of quantum metrology. Although reservoir engineering provides a powerful approach to improve estimation by tailoring system-environment interactions, the role of the squeezing phase and correlations arising from the sequential utilization of the same squeezed reservoir remains inadequately explored. In this work, we employ a correlated squeezed-thermal reservoir to enhance the precision of estimating the phase parameter $\phi$ and the correlation factor $\mu$, both individually and simultaneously. We show that the squeezing phase $\Phi$ is crucial for achieving quantum-enhanced precision, with optimal phase-matching conditions that depend strongly on $\mu$. Specifically, we derive the near-optimal phase-matching relations aimed at maximizing the quantum Fisher information (QFI) for both $\phi$ and $\mu$, as well as minimizing the total variance $\Delta_{\rm sim}$ in joint estimation. Furthermore, we show that the joint estimation variance is dominated by $F_{\phi}$, which motivates our search for the phase-matching conditions that minimize $\Delta_{\text{sim}}$. Through the ratio $R$ of variances, we demonstrate that joint estimation conserves quantum resources and maintains high precision when the squeezing phase is optimized for $F_{\phi}$, despite the inherent incompatibility of the parameters. These findings provide practical insights into reservoir engineering strategies for high-precision quantum sensing and information processing.

Quantum fully homomorphic encryption (QFHE) promises secure delegated quantum computation but has been impeded by the prohibitive quantum resource demands of existing constructions. This paper introduces a unified framework that achieves an \textbf{exponential improvement} in efficiency by synergistically integrating three theoretical tools: \textbf{modular arithmetic programs (MAP)}, the \textbf{garden-hose model}, and \textbf{measurement-based quantum computation (MBQC)}. Our central innovation is a novel MAP tailored to the algebraic structure of Learning-with-Errors (LWE) decryption. Unlike generic approaches that incur exponential overhead, our MAP computes the inner product $\langle \boldsymbol{sk}, \boldsymbol{c} \rangle \bmod q$ by tracking a partial sum modulo $q$, requiring only $O(\log q)$ bits of state width. This yields branching programs of width $O(\log \lambda)$ and length $O(\lambda \log \lambda)$, thereby reducing the size of the essential quantum gadget from $O(\lambda^{2.58})$ to $O(\lambda \log^2 \lambda)$ EPR pairs -- a concrete improvement factor of $2^{15}$ to $2^{18}$ for standard security parameters. Critically, we demonstrate that LWE decryption is not a \textbf{symmetric function}, necessitating our specialized MAP design beyond prior symmetric-function optimizations. The framework provides a direct mapping from the MAP to an efficient gadget via the garden-hose model, with MBQC furnishing the deterministic control flow for homomorphic evaluation. The resulting QFHE scheme supports \textbf{fully classical clients}, relies solely on the \textbf{classical LWE assumption} (avoiding circular security or quantum hardness assumptions), and maintains compactness. This work dramatically lowers the quantum resource barrier for practical QFHE, paving the way for realistic privacy-preserving quantum cloud computing.

Flexible manipulation of quantum correlation resources enables the implementation of diverse quantum tasks based on hybrid quantum networks, where atom-magnon and optomagnonic entanglements and steerings play important roles. In this work, we propose an effective scheme to generate and manipulate quantum entanglements and steerings based on a hybrid optomagnomechanical system, which is composed of a polarizer, an optical cavity with YIG bridge as one end, and an atomic ensemble in it. According to the results of the parameter dependence of various quantum correlations, we can selectively generate bipartite and genuine tripartite entanglements and deterministically manipulate the concrete situation of bipartite, multipartite steerings, and collective pentapartite steering, by adjusting the polarization direction of the driving laser and the Tavis-Cummings coupling strength. Our all-optical controlled scheme is flexible, convenient, compact, and experimentally feasible, because multiple coupling channels can be tuned simultaneously. This work provides a new perspective for implementing specialized quantum tasks, such as hierarchical ultra-secure multi-user quantum communications.

This paper studies the quantification and structural properties of quantum average correlation based on average coherence. Motivated by two mathematically equivalent approaches to define average coherence: one by averaging over complete sets of mutually unbiased bases, and the other by integrating over all orthogonal bases under the Haar measure, we define an average correlation for bipartite systems as the difference between global and local skew information. This correlation measure is shown to satisfy essential properties including non negativity, contractivity under local quantum channels, and local unitary invariance. We further prove the equivalence between the average correlation defined via mutually unbiased bases and that defined via unitary groups. Finally, we derive a complementarity relation that connects wave-particle duality with the average correlation between a system and its environment.

We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information. Several natural averaging procedures are considered, including complete families of mutually unbiased bases, all orthonormal bases, operator orthonormal bases, and twirling channels induced by the unitary group. All these approaches lead to the same closed expression, which identifies the resulting average correlation as an intrinsic quantity independent of the averaging scheme. By defining measures of wave and particle features via metric-adjusted skew information, we establish complementarity relations among wave and particle features, quantum entropy, and average correlation. These results provide a unified framework for investigating quantum average correlations and complementarity relations in terms of metric-adjusted skew information.

We consider a generalization of the two-body contact interaction for nonrelativistic particles confined to a one-dimensional box, in which the interaction is decentered, i.e., the particles interact only when they are separated by a distance c. In contrast to the harmonically trapped system, this model is nonintegrable. Despite this, we demonstrate that the system exhibits partial solvability due to the presence of dark states, i.e., bosonic or fermionic states unaffected by the interaction. These states form exactly solvable subspaces embedded within an interacting spectrum. We characterize the stationary properties of the system, identify the conditions for the appearance of dark states, and show how they structure the spectrum and delineate interacting and noninteracting sectors.

Targeting entailment model checking, a recent study has pioneered an idea of Eigenmarking search, an improvement over Grover search using extra qubits. The extra qubits condition the quantum state evolution such that the answer states (if exist) are always in the minority. The minority criteria is essential to Grover probability-amplitude amplification and consequently the effectiveness of Grover search. In addition to enforce the minority criteria, Eigenmarking also employs complementary states (through well-orchestrated phase rotation) for easy identification of a no-answer case (related to a no-violation case in the context of model checking). Eigenmarking search has been shown effective in two-qubit simulations. The three Eigenmarking schemes have been previously proposed. Two schemes require two extra qubits. One scheme (called ``subtle marking'') requires one extra qubit with a multiple-qubit-controlled phase rotation. Our study refines the mechanism using only one extra qubit with only two-qubit-controlled phase rotation, commonly known as \texttt{ccz}, regardless of how many qubits the input has. Using a multiple-qubit-controlled phase rotation (as in subtle marking) associates with highly entangled states. Highly entangled states in a real quantum hardware are difficult (or in some cases may even be unachievable) particularly in a scaled up scenario involving many qubits. Our proposed new Eigenmarking scheme has lightened the burden for the hardware requirement. The new Eigenmarking search has been experimented in two-qubit-system simulations and shown viable, achieving the minimal relative local winning margin of W=3.17 and the worst-case distinguishability of D=0.769 (cf. W=0.67; D=0.19 from conventional marking and W=0.28; D=0.55 from subtle marking).

This work introduces a novel quantum algorithm for gradient-based edge detection that operates entirely within the quantum circuit model. Grayscale images are encoded using the Novel Enhanced Quantum Representation (NEQR), allowing exact arithmetic on pixel intensities. Directional gradients are computed by generating superpositions of neighboring pixels via cyclic shift operations and performing subtraction with an exact quantum arithmetic circuit. To refine accuracy, we introduce a direction-aware shifting mechanism that aligns edges with the darker side of intensity transitions. Our novel Quantum Partitioning Algorithm enables efficient in-place thresholding of edge candidates. This work exhibits polynomial-time improvements and optimizes the ancilla count compared to previous NEQR-based quantum edge detection algorithms. These results demonstrate a resource-efficient and fully quantum approach to edge detection, highlighting a practical quantum advantage in image processing.

Orbital angular momentum (OAM)-entangled states produced by spontaneous parametric down-conversion (SPDC) are considered ideal for realizing high-dimensional entangled states, which have several advantages for quantum technologies. However, the limited sensitivity of current two-photon OAM detectors is a major roadblock not only for realizing such technologies but also for resolving foundational questions, such as OAM conservation in SPDC. The current theoretical understanding is that OAM is not conserved in Type-II SPDC but is conserved in Type-I. Experimentally, although non-conservation in TypeII has not been demonstrated, conservation in Type-I has been reported frequently and has become an underlying assumption for techniques generating high-dimensional OAM entangled states. In this work, we experimentally demonstrate a high-sensitivity two-photon OAM detector, using which, contrary to the current understanding, we report non-conservation of OAM in Type-I SPDC. We attribute this to a spatial walk-off effect and prove it using a framework free of standard phase-matching approximations.

Calibrating the role of entanglement in quantum algorithms is a crucial task in the development of quantum computing. Most existing studies have primarily focused on how the static properties of entanglement-such as its magnitude and phase-affect key performance metrics. In this work, we instead explore the relationship between the dynamical behaviors of entanglement and the execution of variational quantum algorithms from a geometric perspective. We find that, in contrast to conventional Hamiltonian dynamics where the evolution process is dominated by the dynamical phase, quantum state evolution in quantum algorithms is primarily governed by the geometric phase with the trajectory determined by the parameter-dependent Hilbert space geometry. In the problem-agnostic Hardware-Efficient Ansatz (HEA), entanglement dynamics and state evolution are decoupled. Conversely, in the problem-inspired Hamiltonian Variational Ansatz (HVA), the dynamical phase contribution is enhanced, allowing entanglement to function as a dynamical resource: more entanglement consumption correlates directly with faster quantum state evolution.

We study the entanglement dynamics of $n=2,3,4$-qubit Bell- and GHZ-type states under an amplitude-damping channel (ADC). We quantify multipartite entanglement using the genuine multipartite concurrence (GMC) and evaluate its utility through the optimal teleportation fidelity. For $2$-qubit states, we analyze the standard (Bennett) teleportation protocol. For $3$- and $4$-qubit states, we study controlled quantum teleportation (CQT) with one and two \emph{controllers}, respectively. Entanglement sudden death (ESD) denotes the abrupt, finite-time disappearance of entanglement caused by decoherence in contrast to asymptotic decay. To counteract ESD, we apply local NOT ($\hat\sigma_x$) operations on $m$ of the $n$ qubits ($m \leq n$) and derive analytic formulae, revealing that a single-NOT operation often suffices to alter ESD into asymptotic decay when handling GMC. In contrast, teleportation fidelity can decay more rapidly for single-NOT flipped states, whereas flipping all qubits is more useful for preserving teleportation fidelity in certain regimes, highlighting that the amount of entanglement alone does not guarantee teleportation utility. Remarkably, in the case of GHZ-type states, ADC-evolved mixed biseparable states can be exploited successfully in the CQT protocol. Further, using the GHZ-symmetric parametrization, we map the 2- and 3-qubit ADC-evolved mixed states onto a $(x,y)$ plane, revealing their SLOCC (Stochastic Local Operations and Classical Communication) entanglement classes. We also explicitly check the Bell-CHSH nonlocality hierarchy in the 2-qubit teleportation alongside localizable-entanglement diagnostics for 3-qubit CQT. Our results clarify the distinct roles of global versus localizable bipartite correlations and suggest simple, experimentally accessible unitary controls for preserving useful quantum resources in noisy channels.

Topological quasiparticles of light, such as classical and quantum optical skyrmions, have so far relied on fully coherent or pure quantum states whose topology is encoded in the entanglement between polarization and two-dimensional spatial modes. Here we show that skyrmionic topology can emerge directly within the density matrix of a mixed quantum state. We introduce a framework in which a coherence-Stokes vector defines a topological texture over the density matrix, enabling the realization of quantum skyrmions using only a pseudospin and a real or synthetic one-dimensional space of modes. For a single photon, the density matrix is analogous to the coherence matrix of classical light, and can be encoded using partially coherent electromagnetic fields. We further analyze the topological texture encoded in a bipartite entangled photon pair, showing how skyrmions arise not only in the full bi-photon system, but also in its reduced subspaces with any pseudospin-mode combination simultaneously. We then explore the robustness of such skyrmions to environmental noise, and discover their persistence in mixed-quantum states of multiple photons. Finally, we propose a feasible experimental route to generate and measure such skyrmions using integrated photonic networks, and suggest avenues for similar implementations in other quantum systems. Our work paves the way for robustly encoding classical information on partially coherent light or on mixed quantum states and for encoding topological charges on many-body quantum systems.

This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. We begin by introducing the fundamental principles of chaotic ray dynamics in optical microcavities, where the transition from regular to fully chaotic dynamics fundamentally alters the underlying wavefunctions and lasing properties. A central focus is placed on "chaos-assisted light emission," which serves as a practical manifestation of "chaos-assisted tunneling" -- a hallmark phenomenon in the study of quantum chaos. We discuss both theoretical frameworks and experimental validations, demonstrating how chaotic orbits facilitate the coupling between evanescently localized modes and far-field emission. Furthermore, exploring how the presence of a gain medium influences established results from quantum chaos research remains a fundamental and intriguing problem in physics. To address this, we establish a rigorous and comprehensive derivation of the Maxwell-Bloch equations for two-dimensional microcavity lasers, specifically examining their application to fully chaotic, stadium-shaped billiard lasers. By bridging the gap between nonlinear lasing processes and chaotic wavefunctions, this chapter highlights the unique potential of chaotic billiards for controlling light-matter interactions and shaping the next generation of unconventional coherent light sources.

Ergodicity breaking in isolated systems has emerged as an important frontier in the study of quantum many-body physics. While generic Hamiltonians are expected to obey the eigenstate thermalization hypothesis (ETH), recent studies on Hilbert space fragmentation (HSF) have revealed possible robust nonthermal behavior even in disorder-free systems. Although numerous models exhibiting strong HSF are already known, existing analyses are typically model dependent, and a general organizing principle remains elusive. In this work, we introduce a simple mechanism for achieving strong HSF in one-dimensional integer spin chains, which we term "peak-valley (PV) fragmentation". The key idea is to devise a simple local rule which ensures the spin states in the computational basis can be labeled by a set of emergent good quantum numbers corresponding to the heights and depths of alternating peaks and valleys in a geometrical representation. We demonstrate that some known examples of strong HSF models, as well as their variants which break the HSF property, can be understood within the framework of PV fragmentation. Our approach also enables systematic construction of new fragmented models in higher-spin systems, and allows us to identify higher-order HSF models.

We study a one-dimensional non-Hermitian Stark chain in which nonreciprocal hopping, a linear potential, and linearly graded hopping act simultaneously. The central question is how boundary pumping and field-induced confinement are reorganized when the hopping amplitude itself grows with position. We show that the graded term separates the two localization channels at the level of the large-position asymptotics. An exact diagonal similarity transformation removes the bond asymmetry and converts the usual exponential skin factor into an algebraic boundary accumulation with exponent $\eta=\gamma/F_2$. The transformed symmetric chain then reduces asymptotically to a constant-coefficient recurrence, giving the Stark threshold $|F_1|=2|F_2|$. The original right eigenstates acquire the unified envelope $\psi_j^R\sim j^{\eta}\phi_j$, with oscillatory, double-root, and exponentially localized branches across the threshold. This form also yields two finite-size scales, one measuring the logarithmic screening of nonreciprocity and the other balancing the algebraic skin factor against the exponential Stark tail. A joint localization map in the $(\gamma,F_1/F_2)$ plane verifies this structure. The edge polarization bends near the Stark threshold and weakens on the localized side, while the inverse participation ratio of the most localized eigenstates rises rapidly for $F_1/F_2>2$. Using a normalized Gaussian projector appropriate for non-unitary evolution, we further show that the same threshold enhances half-chain entanglement growth after a charge-density-wave quench. These results identify graded hopping as a controlled mechanism for screening nonreciprocity, resetting Stark asymptotics, and organizing the finite-size crossover between algebraic skin accumulation and Stark localization.

We investigate the momentum-space entanglement between two Dirac quasiparticles in a double-layer honeycomb lattice coupled via a planar electromagnetic cavity. We model the low-energy excitations as massive Dirac fermions in $(1+2)$ dimensions and derive the Bethe-Salpeter equation using the ladder approximation. We use a Born-level approximation around a free two-body quasiparticle state, where the interaction is mediated by the cavity photon propagator. From the reduced sublattice density matrix, we compute a momentum-resolved von Neumann entropy. Within the perturbatively controlled regime, the entropy remains small, while phenomenological self-energy dressing drives a crossover to strong enhancement of the entanglement entropy. Stationary entanglement is obtained only when the quasiparticle coherence time exceeds the photon propagation time between the layers. The maximum-entropy regime appears to be a viable method for achieving Bell-like states. These results demonstrate how self-energy renormalization, virtual particle exchange, and spinor geometry combine to reshape the entanglement landscape of Dirac materials.

The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged as a promising tool. Recently, there has been significant research on methods for performing such cutting effectively. In this work, the duality between quantum circuits and classical graphs - specifically, directed acyclic graphs (dags) - is leveraged to analyze the complexity of finding an optimal circuit-cutting configuration that minimizes the number of cuts. After developing a rigorous graph-theoretic framework, the complexity of identifying cut locations that partition a given quantum circuit into smaller fragments is characterized. The corresponding graph-combinatorial task is then defined, and the resulting partition problem is shown to be NP-complete. Furthermore, even a simplified version of the problem, restricted to circuits composed only of one- and two-qubit gates, is shown to be NP-complete. Finally, based on these constraints, an algorithm grounded in satisfiability modulo theories (SMT) is proposed to find optimal cuts when the number of qubits per partition is bounded. This work therefore provides a complexity-theoretic characterization of cut placement and a practical solver for bounded-size decompositions.

Deploying quantum machine learning on NISQ devices requires architectures where training overhead does not negate computational advantages. We systematically compare two quantum approaches for chaotic time-series prediction on the Lorenz system: a variational Quantum Physics-Informed Neural Network (QPINN) and a Quantum Reservoir Computing (QRC) framework utilizing a fixed transverse-field Ising Hamiltonian. Under matched resources ($4$--$5$ qubits, $2$--$3$ layers), QRC achieves an $81\%$ lower mean-squared error (test MSE $3.2 \pm 0.6$ vs. $47.9 \pm 36.6$ for QPINN) while training $\sim 52,000\times$ faster ($0.2$\,s vs. $\sim 2.4$\,h per seed). Drawing on the classical delay-embedding principle, we formalize a temporal windowing technique within the QRC pipeline that improves attractor reconstruction by providing bounded, structured input history. Analysis reveals that QPINN instability stems from capacity limitations and competing loss terms rather than barren plateaus; gradient norms remained large ($10^3$--$10^4$), ruling out exponential suppression at this scale. These failure modes are absent by construction in the non-variational QRC approach. We validate robustness across three canonical systems (Lorenz, Rössler, and Lorenz-96), where QRC consistently achieves low test MSE ($3.1 \pm 0.6$, $1.8 \pm 0.1$, and $12.4 \pm 0.6$, respectively) with sub-second training. Our findings suggest the fixed-reservoir architecture is a primary driver of QRC's advantage at these scales, warranting further investigation at larger qubit counts and on hardware where quantum-specific advantages are expected to emerge.

The Barnett effect is usually understood through an effective magnetic field generated by mechanical rotation, while its reciprocal Einstein--de Haas effect describes the transfer of spin angular momentum to mechanical motion. We show that this effective-field picture changes qualitatively once the mechanical degree of freedom itself is quantized. To demonstrate this, we introduce an exactly solvable minimal spin-rotor model in which a spin-$1/2$ is coupled to a quantum rotor. In a fixed angular-momentum sector, the model reproduces the conventional Barnett splitting and remains formally equivalent to a Zeeman problem. For a superposition of rotor sectors, however, the Barnett field becomes operator-valued and the resulting dynamics generates coherent spin-rotor entanglement. This is directly visible in the reduced spin purity, rotor coherence, and entanglement entropy. Our results identify a minimal quantum setting in which the Barnett effective-field picture departs from its classical form and acquires a reciprocal manifestation through spin-dependent rotor coherence.

We present a novel architecture-aware transpilation method for exact general unitary gate synthesis on superconducting quantum hardware. Our approach is tightly integrated with the optimized block-ZXZ decomposition, exploiting its recursive structure to make hardware-aware decisions at each level of the recursion rather than treating transpilation as an independent post-processing step. The method introduces three key techniques: a greedy qubit mapping strategy that minimizes pairwise distances between physical qubits, an adaptive Gray code selection combined with qubit swapping that optimizes the construction of uniformly controlled Rz gates for the target topology, and a heuristic for reducing CNOT gates by exploiting the structure of long-range CNOT ladders. We benchmark our method against TKet, Qiskit, and Pennylane on the 20-qubit IQM Garnet (square lattice) and the 156-qubit IBM Marrakesh (heavy-hex) architectures with qubit counts ranging from 3 to 11. Our method achieves CNOT count reductions of up to 36 percent on the IQM Garnet and up to 34 percent on the IBM Marrakesh compared to the best competing transpiler, while simultaneously achieving transpilation speedups of up to 553x. Furthermore, our method is the only one capable of transpiling circuits beyond 10 qubits within a 30-minute time limit across both architectures.

Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a solution of the representability problem for quantum systems without particle-number conservation. The physically allowed set of 2-RDMs can be characterized from a geometrically `orthogonal' set, the polar cone. We derive explicit linear equations for the two-body operators in the polar cone -- the intersection of the $p$-positive cone with the two-body operator space -- to obtain a systematic hierarchy of representability conditions that do not depend on higher RDMs or the wave function. Moreover, by augmenting these conditions with the particle-number variance, we obtain a unified framework for treating both particle-number-conserving and nonconserving systems. We illustrate with a spin system and molecular H$_4$.

We place several known indicators of Kochen--Specker contextuality -- the KCBS correlator $\chi$, the contextual fraction $\CF$, the Shannon-entropic $n$-cycle inequality of Chaves and Fritz, and the operational commutator witness $D$ of Paper~I -- into a single projector-geometric framework organized around the overlap matrix $\Tcal_{ij} = d^{-1}\tr[(\hat P_i \hat Q_j)^2]$, where $\hat P_i$ and $\hat Q_j$ are the joint-eigenspace projectors of the two compatible observable pairs within a measurement context. The state-independent scalar content of $\Tcal$ is carried by two independent contractions: the mutual information energy $E = \sum_{ij}\Tcal_{ij}$ of Paper~I (equivalently, its logarithmic form $S_2 = -\log_2 E$), and the Maassen--Uffink extremal overlap $c_\MU = \max_{i,j}|\langle a_i,b_i | c_j,b_j\rangle|$. We prove that $S_2$ is non-increasing under coarse-graining, that $S_2(\Gcal) = 0$ is a necessary configuration-level condition for observable contextuality, and that the additive composition $S_2(\Gcal) = \sum_\alpha S_2(\Gcal_\alpha)$ is exact for the KCBS pentagon. We further show that in the spin-$1$ realization of the KCBS pentagon, a shared $m_s=0$ eigenstate in each context forces $c_\MU = 1$, rendering every Maassen--Uffink-type bound trivial -- a structural mechanism that makes explicit why outcome-entropic uncertainty relations based on $c_\MU$ are silent on KCBS contextuality, while $S_2 \approx 2.7266$~bits throughout. Applied to KCBS and CHSH, the framework identifies regimes in which every state-dependent witness considered here is silent yet $S_2(\Gcal) > 0$ by an amount set by the projector geometry alone.

Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96\% of the $R^2$ of attention-based VQCs while using 40-50\% fewer parameters, and consistently outperform equal-capacity MLPs (mean $R^2{=}0.829$ vs.\ MLP$_{720}$'s $0.753$ on Boston Housing, 3-seed average); \textbf{(ii)}~FC-VQC's Type~4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}~expressibility saturates at circuit depth~${\approx}\,3$, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.

We study when block-coupled regular graphs can realize prescribed complex quantum-like bit states as exact synchronized eigenstates. Two regular subgraphs $G_A$ and $G_B$ supply normalized all-ones eigenvectors $V_A$ and $V_B$, and algebraically regular bipartite couplings reduce the full graph-supported operator exactly to a $2\times 2$ effective block on $\mathcal S=\operatorname{span} \{ \lvert 0\rangle, \lvert 1\rangle \}$. Within this reduction we prove that two natural symmetric complexifications are not universal under a real-spectrum requirement: complex symmetric coupling with real diagonal regularities forces the target computational basis amplitude ratio $r=\omega_2/\omega_1$, for $\lvert \psi\rangle = \omega_1\lvert 0\rangle + \omega_2\lvert 1\rangle$, to satisfy $r^2\in\mathbb{R}$, while real symmetric coupling with complex diagonal regularities forces $r+1/r\in\mathbb{R}$. Replacing complex symmetry by Hermitian coupling removes this phase obstruction. For any nonbasis target state, any prescribed real eigenvalue, and any prescribed nonzero signed spectral gap, a Hermitian weighted coupling realizes the target exactly. Additionally, an independently tuned directed-coupling model gives a second universality mechanism. We then pass from continuous effective parameters to finite weighted graphs with entries in $\{0, \pm1, \pm i\}$ (the fourth roots of unity and zero), characterize the balanced discrete coupling lattice by perfect matchings, and show that exact discrete Hermitian realizations are dense in the synchronized pure-state space. These results give a universality taxonomy for complex QL-bits and identify Hermitian conjugate pairing as the robust structural mechanism that supports arbitrary complex amplitudes with real two-level spectra.

The Kerr-nonlinear parametric oscillator (KPO) provides a foundational semiclassical model for cat-state quantum hardware. Standard analyses of the KPO typically rely on autonomous, frozen-time approximations to describe the stabilization of macroscopic coherent states. However, state preparation and gate manipulation are driven by explicitly time-dependent microwave pulses, so the operational dynamics are inherently nonautonomous. In this paper, we show that static algebraic equilibrium pictures are incomplete for describing both state formation and gate-induced transport in the Kerr-cat qubit. For nonautonomous state preparation, we analyze the ramped resonant model by combining a linear nonautonomous stability analysis with a local invariant-graph reduction near the vacuum trajectory. This yields a quintic reduced normal form in the critical direction and identifies two symmetric post-threshold moving branches that organize the local state-formation dynamics. The associated diagnostics separate the reduced branch dynamics from the full two-dimensional phase-twist relaxation observed in the hardware coordinates. For gate execution, we model a fast pulse as a weak aperiodic perturbation of the conservative resonant figure-eight separatrix and apply Melnikov's method to derive a leading-order transport criterion. In this framework, transient lobe dynamics emerge as a semiclassical mechanism for non-adiabatic leakage, and the resulting amplitude-width threshold curve provides a leading-order geometric indicator for the onset of gate-pulse-induced transport.

Scalable quantum computing is fundamentally bottlenecked not by qubit count or fabrication yield, but by a rigid temporal mismatch: macroscopic classical coordination latency ($\tau_c$) inevitably grows with system diameter, while microscopic quantum coherence ($\tau_q$) remains strictly bounded. Beyond a critical scale, this mismatch breaches the classical control light cone, triggering a superlinear geometric penalty ($\epsilon > 0$) that renders monolithic synchronization physically impossible. We formalize the resulting structural phase transition through a governing scaling law, $1+\epsilon > \gamma$, which mandates modular decomposition and a shift from global unitaries to Local Operations and Classical Communication (LOCC). To manage the resulting resource contention under strict coherence budgets, we introduce a layered semantic architecture and a time-aware Reserve--Commit protocol. By embedding predictive temporal pre-validation, the protocol acts as an architectural semantic classifier: it preemptively aborts transactions that exceed the causal horizon and explicitly converts scheduling-induced failures into location-known erasure metadata, directly relaxing hardware fidelity thresholds for downstream QEC decoders. Under near-term transduction targets ($\eta_{\mathrm{trans}} \sim 0.1$), we project a crossover scale at $N_c \sim 10^5$--$10^6$ physical qubits. This threshold marks a profound architectural convergence: the footprint required for modularity aligns precisely with early fault-tolerant utility, establishing time-aware distributed orchestration, rather than monolithic expansion or centralized classical control, as the physical imperative for utility-scale quantum computing.

Magnetic clock transitions (CTs), defined by vanishing first-order sensitivity of the transition frequency to magnetic field fluctuations, provide a powerful route to suppress decoherence in donor spin systems. Here, we present the observation of magnetic field CTs from an ensemble of near-surface $^{75}$As ($I = 3/2$) spins in silicon using low-field ($< 10$~mT) continuous-wave electrically detected magnetic resonance (EDMR). As the CT condition is approached, pronounced linewidth broadening is observed, consistent with a donor Hamiltonian informed linewidth model. These results establish low-field EDMR as a sensitive probe of CTs in near-surface donor systems relevant to silicon-based quantum devices.

The quantization of superconducting transmission-line resonators is usually introduced phenomenologically by modeling the resonator as an effective LC circuit and imposing canonical commutation relations on macroscopic variables such as charge and flux. Although this approach is highly successful, it leaves open why these macroscopic variables should obey quantum commutation relations and how this behavior emerges from the superconducting state. In this work, starting from the microscopic pairing Hamiltonian underlying BCS superconductivity, we derive the low-energy effective Hamiltonian of a circuit-QED architecture containing a superconducting transmission line with distributed capacitive and inductive elements. We establish quantitative relations between macroscopic observables, including current and voltage, and the spatially local superconducting phase, as well as the microscopic parameters of the electron-phonon system. We then extend the third quantization of the superconducting order parameter, introduced in Paper (I) for the global phase, to the spatially local case. This gives a macroscopic field quantization of the superconducting phase. We show that, after restriction to the low-energy excitation subspace, the local superconducting phase becomes a genuine quantum dynamical variable. Thus, the quantum behavior of transmission-line resonators need not be postulated at the macroscopic level, but follows from the third quantization of the superconducting order parameter. These results suggest that capacitive and inductive superconducting circuit elements share the same microscopic origin, providing a unified framework for superconducting circuit quantization.

We study single-copy stabilizer learning, the problem of identifying a stabilizer group of dimension $n-t$ from an $n$-qubit quantum state $\rho$. We obtain two complementary results. First, in the average case, logarithmic-depth local Clifford circuits suffice to efficiently learn almost all stabilizer groups with $t=O(\log n)$, instead of the linear-depth measurements required in previous approaches. We support this result with numerical simulations for systems of up to 100 qubits. Second, we show that, in the worst case, any adaptive single-copy measurement scheme requires a number of samples that scales exponentially in $t$. Together with existing results on two-copy learning, our findings suggest that, for large $t$, identifying Pauli symmetries of a quantum system exhibits a quantum advantage in the learning setting.

Nonreciprocal relaxation matrices can have skin-localized right eigenmodes, but their imprint on a mixed steady state is not fixed by the density profile alone. We develop an exact steady-state theory for number-conserving Gaussian fermion chains and show that the dominant natural orbital of the correlation matrix provides a mode-resolved diagnostic of hidden skin order. The steady-state correlator admits a biorthogonal decomposition in terms of the left and right eigenmodes of the relaxation matrix $X$ and the source matrix $Y$. This formula separates three ingredients: slow rapidity denominators, source loading by left eigenmodes, and real-space geometry from right eigenmodes. For a local pump, the pump position is read by the left modes, whereas the selected profile is drawn by the right modes. In a single-slow-mode regime, the dominant natural orbital locks to the Euclidean-normalized slow right mode. The density can follow the same boundary trend, but it is a less selective incoherent sum over occupied natural orbitals. We verify this selection law in a nonreciprocal Hatano--Nelson chain and show that, in a nonreciprocal SSH chain, the selected natural orbital crosses over from a topological edge candidate to a slow bulk-skin candidate. These results identify natural-orbital locking as a steady-state diagnostic of nonreciprocal localization in Gaussian open fermion chains.

This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of $\mathbf{X}_t$, we generate quantum states that encode $\mathbf{X}_t$ in the amplitudes, while most of the existing quantum methods for SDEs employ binary encoding. A key challenge is the amplitude encoding of the noise term, and we address this by utilizing the quantum circuit implementation of a pseudorandom number generator (PRNG). We propose two methods: the Dyson series-based method and the Euler-Maruyama (EM)-based method. In the former, we express the noise term via the Dyson series approximation of the time evolution operator, while in the latter, it is approximated using the EM time discretization. Both methods use the quantum linear systems solver to generate the amplitude-encoding state of $\mathbf{X}_t$, making only ${\rm polylog}(N)$ queries to the PRNG circuit and the block-encodings of $A$ and $B$. Additionally, going beyond state preparation, we present methods to estimate expectations of functions of $\mathbf{X}_t$ using the state.

Currently, quantum computing and artificial intelligence are driving revolutionary advancements in computational science. This study pioneers the integration of quantum kernel networks on smoothed particle hydrodynamics (SPH). SPH has matured into a highly versatile meshfree/particle method, exceptionally suited for tracking spatiotemporal trajectories and dynamic modeling phenomena. We developed a hierarchy of Lagrangian quantum network models built upon an improved quantum multilayer perceptron (QMLP). Specifically, a sequential hybrid quantum-classical framework is constructed, utilizing Pauli-Z expectation values over traditional probability outputs to ensure robust gradient-based optimization and mitigate barren plateaus. It combines smoothing kernels with quantum learning, establishing a novel quantum intelligent SPH paradigm. The framework is validated through some continuous benchmarks on eurypalynous quantum neural networks, static multi-level nebula vortex interference reconstructions and transient scalar field advectional tests. Numerical results demonstrate that while pure elementary quantum circuits struggle with parameter-specific generalization in unstructured domains, the proposed hybrid crossed-QMLP seamlessly matches the fitting accuracy of classical SPH in quantum optimized space. Although this approach currently faces limitations in computational efficiency and hardware implementation, it nonetheless paves the way for a novel investigation into quantum SPH, by mapping unstructured Lagrangian particle topologies into integrated quantum circuits.

We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a quantum state, enabling a compact representation of high-dimensional distributions. Exploiting the circulant structure of finite-difference operators, the evolution is realized in the spectral domain using quantum Fourier transforms and phase rotations. A key result is that the drift component can be implemented exactly in amplitude space, leading to an accurate reproduction of the classical transport dynamics. In contrast, the diffusion term does not admit a linear representation in amplitude space due to the nonlinear relation between probability density and wave function. To enable a quantum implementation, we introduce a unitary surrogate based on a Wick rotation, transforming diffusion into a dispersive phase evolution. This yields a fully unitary propagation that can be implemented efficiently on a gate-based quantum computer. The proposed method is evaluated numerically for different scenarios and shows strong agreement with the exact solution of the Fokker-Planck equation. The approach demonstrates the potential of quantum computing for Bayesian state estimation, as the representable state space grows exponentially with the number of qubits. This allows the efficient representation and propagation of probability densities that would otherwise require complex tensor decompositions on classical hardware, making the method a promising candidate for high-dimensional filtering problems.

Two-mode squeezed states as paradigmatic entangled resources have broad applications in quantum information processing. Here, we study the generation of stable optical-microwave squeezing in structured environments within a hybrid electro-optomechanical system, where a mechanical oscillator is simultaneously coupled to an optical cavity mode and a microwave mode of an LC resonator. Specifically, an effective Hamiltonian that captures the optical-microwave squeezing interaction is constructed by combining strongly modulated driving fields applied to both photonic modes with a mechanical parametric amplifier. Based on this effective model, the dynamical evolution of two-mode squeezing in structured environments is analyzed. It is remarkably shown that the non-Markovian noise can substantially enhance the squeezing level in comparison to the Markovian case, and that two-mode squeezing can persist even in the absence of external driving fields under non-Markovian conditions, thereby mitigating the detrimental effects of anti-squeezing. Furthermore, the persistence of the two-mode squeezed state is enhanced when the environmental spectral densities of the microwave and optical modes are identical. Our work provides a theoretical framework for generating and persisting two-mode squeezing in structured environments.

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback is designed to engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable.

Configuring variational quantum algorithms for combinatorial optimization remains a difficult, expert-driven process requiring coordinated choices over solver family, ansatz, objective, and optimizer. We present AutoQResearch, an LLM-guided closed-loop experimentation framework that casts this task as sequential policy search over a curated design space. Instead of a single static configuration, the framework searches for adaptive solver-control policies that condition future decisions on diagnostics such as feasibility, optimality gap, and convergence stagnation. The system operates through a structured workflow: an LLM agent edits a small policy surface under a fixed evaluation harness, candidate policies are screened using cheap scout evaluations, and only the strongest candidates are promoted to full confirmation. This enables controlled autonomous exploration while guarding against proxy overfitting and unstable selection. We evaluate the framework on Maximum Independent Set (MIS) and the Capacitated Vehicle Routing Problem (CVRP). On MIS instances (16--64 vertices), discovered policies substantially outperform static baselines and reveal scale-dependent behavior: CVaR objectives are effective at small scale, while QRAO-based qubit compression provides the most effective explored scaling path. On CVRP curricula (8--12 customers) and a held-out E-n13-k4 benchmark, the framework discovers adaptations involving sampling budget, penalty design, and hybrid repair protocols, yielding high-quality solutions. Methodologically, we find that staged confirmation is essential: cheap proxy evaluations can materially misestimate policy quality and even invert candidate rankings. Overall, the paper positions AutoQResearch as a benchmarked quantum--GenAI co-design workflow for autonomous solver discovery in variational quantum optimization.

We study numerical integration on $[0,1]$ by quantum amplitude estimation (QAE), focusing on the cost of constructing the amplitude oracle. Although QAE improves the statistical component of the integration error, this advantage is relevant only when the integrand has low encoding complexity. We introduce a hierarchy of grid function classes $\mathcal{G}_n^{(d)}$, defined by requiring the angle map $\Theta_g:\{0,1\}^n\to[0,\pi]$ to be multilinear of degree at most $d$. Membership is classically checkable in $O(n2^n)$ time by the Walsh--Hadamard transform. For $g\in\mathcal{G}_n^{(d)}$, the encoding operator factorises into $\sum_{k=0}^d\binom{n}{k}$ multi-controlled $R_Y$ gates, interpolating between an affine $O(n)$ regime and the generic exponential regime. Combining this structure with classical discretisation estimates for $g\in C^\alpha[0,1]$, we obtain a depth-versus-accuracy trade-off: gate count $O((\log(1/\varepsilon))^d\varepsilon^{-1})$ suffices to achieve $\varepsilon$-accuracy with constant probability. For $d=1$ this becomes $O(\varepsilon^{-1}\log(1/\varepsilon))$, improving over classical Monte Carlo for every $\alpha\ge1$. We also prove an unconditional separation: $\mathcal{G}_n^{(1)}$ contains functions of Sobolev regularity $s<1/2$ for which the quantum oracle cost is $O(1/\varepsilon)$, whereas classical deterministic or randomised quadrature requires $\Omega(\varepsilon^{-1/s})$ evaluations. These results identify explicit integrand classes for which the full cost of QAE-based integration, including state preparation, is asymptotically better than classical methods. Experiments on SpinQ Triangulum and IBM Kingston illustrate the hierarchy at $n=2$: circuits inside $\mathcal{G}_n^{(d)}$ run successfully, while those exceeding the Triangulum coherence budget fail as predicted.

In realistic quantum information processing tasks, quantum states are inevitably affected by environmental noise, leading to decoherence and degradation of useful quantum resources. The coherence fraction, which serves as an important figure of merit for several quantum protocols, may decrease significantly after the action of a noisy channel. Such degradation can result in unsatisfactory performance in real-world applications. In this work, we investigate whether catalysis can be used to pre-process the input state to enhance the coherence fraction of an output state from a quantum channel. Specifically, we study whether using a processed state $\rho_s'$ as the input to a quantum channel $\Lambda$, instead of the original state $\rho_s$, can yield an output state $\Lambda(\rho_s')$ whose coherence fraction exceeds that of $\Lambda(\rho_s)$. We analyze the conditions under which such an improvement is possible. We also provide a practical application of our setup for the phase discrimination task. Furthermore, we establish a necessary and sufficient condition for an incoherent state preserving CPTP(Completely Positive Trace Preserving) map $\mathcal{E}$ to be a particular type of Strictly Incoherent Operation (SIO). This characterization provides a new structural understanding of SIO and clarifies its role in coherence manipulation. Our results offer practical insights into coherence preservation and enhancement in noisy quantum processes and may be useful for optimizing quantum information protocols under realistic conditions. We also provide numerical examples to support our claims.

This paper introduces the concept of exhaustively parametrised, feasibility-respecting quantum circuits for constrained combinatorial optimisation problems. Such circuits can reach, given the right parameter values, every feasible solution with certainty -- including the optimum -- with a fixed number of parameters, while avoiding infeasible solutions altogether. This is in sharp contrast to conventional quantum alternating operator ansatz schemes, which are merely guaranteed to reach the optimum asymptotically. We introduce an abstract pipeline for constructing exhaustively parametrised, feasibility-respecting circuits from a transitive group action on a problem's feasible set. Our constructions rely on the simple combination of the group action with group representation and the novel notion of generating sequences: group elements in fixed order, possibly with repetitions, that generate the entire group. That is, we trace expressivity of parametrised quantum circuits back to the most fundamental concepts of group theory. We apply this pipeline to two concrete examples for the travelling salesperson problem, thus showing that exhaustively parametrised, feasibility-respecting circuits are not an empty definition. Furthermore, we provide numerical proof-of-principles on instances with up to nine cities, comparing the suitability of our constructions for parameter optimisation purposes against established mixers.

In this work, we extend the class of previously introduced non-Euclidean neural quantum states (NQS) which consists only of Poincaré hyperbolic GRU, to new variants including Poincaré RNN as well as Lorentz RNN and Lorentz GRU. In addition to constructing and introducing the new non-Euclidean hyperbolic NQS ansatzes, we generalized the results of our earlier work regarding the definitive outperformances delivered by hyperbolic Poincaré GRU NQS ansatzes when benchmarked against their Euclidean counterparts in the Variational Monte Carlo (VMC) experiments involving the quantum many-body settings of the Heisenberg $J_1J_2$ and $J_1J_2J_3$ models, which exhibit hierarchical structures in the forms of the different degrees of nearest-neighbor interactions. Here, in particular, using larger systems consisting of 100 spins, we found that all four hyperbolic RNN/GRU NQS variants always outperformed their respective Euclidean counterparts. Specifically, for all $J_2$ and $(J_2,J_3)$ couplings considered, including $J_2=0.0$, Lorentz RNN NQS and Poincaré RNN NQS always outperformd Euclidean RNN NQS, while Lorentz/Poincaré GRU NQS always outperformed Euclidean GRU NQS, with a single exception when $J_2=0.0$ for Poincaré GRU NQS. Furthermore, among the four hyperbolic NQS ansatzes, depending on the specific $J_2$ or $(J_2, J_3)$ couplings, on four out of eight experiment settings, Lorentz GRU and Poincaré GRU took turns to be the top performing variant among all Euclidean and hyperbolic NQS ansatzes considered, while Lorentz RNN, with up to three times fewer parameters, was capable of not only surpassing the Euclidean GRU eight out of eight times but also outperforming both Lorentz GRU and Poincaré GRU four out of eight times, to emerge as the best overall hyperbolic NQS ansatz.

Quantum interior point methods (QIPMs) promise polynomial speed-ups over classical solvers for linear programming by outsourcing the solution of Newton linear systems to quantum linear solvers (QLSAs). However, asymptotic speed-ups do not necessarily translate to practical advantages on realistic problem instances. In this work, I evaluate whether practical advantage of a standard hybrid QIPM pipeline can already be excluded relative to the classical open-source solver HiGHS on a broad and diverse collection of LP instances spanning eight problem families, including public benchmark libraries, such as MIPlib, and relaxations of combinatorial optimisation problems. Following the hybrid benchmarking paradigm initiated by Cade et al., I derive rigorous lower bounds on the quantum runtime under a series of highly benevolent assumptions and compare them against classical runtimes. I equip the QIPMs with the best-performing functional QLSA, the Chebyshev-based method, as identified by Lefterovici et al., and evaluate two Newton system formulations proposed by Mohammadisiahroudi et al.: the modified normal equation system and the orthogonal subspace system. The exclusion analysis yields a consistent negative picture: across all instances and for any realistic quantum cycle duration, the quantum runtime lower bounds already exceed the classical runtimes, establishing that these hybrid QIPMs will offer no practical advantage over good classical solvers for realistic linear programming instances.

Phase retrievability of a quantum channel asks whether pure states can be reconstructed from suitable measurements. In this paper, we study this problem from three complementary viewpoints: quantum information theory, operator-valued frames, and the physical realization through quantum interferometry. We first show that a quantum channel is phase retrievable if and only if its complementary channel is pure-state informationally complete. This structural characterization leads to several consequences for phase retrievability, including criteria involving the dimension of the complementary operator system, Choi-rank type bounds, and specific results for entanglement breaking channels and twirling channels. We then introduce an interferometric coupling in which two arm channels are coherently recombined through port operators \(M_i(\theta)=A_i+e^{i\theta}B_i\). Unlike classical mixing, this construction produces interference cross terms that can enlarge the complementary operator system and thereby enhance phase retrievability. From the frame theory viewpoint, the interferometer realizes a coherent coupling of operator-valued frames. To quantify this effect, we introduce injectivity indices for completely positive maps. The examples in Section~5 show that coherent interference can significantly improve phase retrieval behavior even when the arm channels are individually not phase retrievable.

In the noisy intermediate-scale quantum (NISQ) regime, quantum devices contain hardware-specific noise sources which restrict device-invariant error mitigation strategies. We explore transfer learning approaches to apply noise models learned on one quantum device to a different device with the help of a small amount of data. We create a real-hardware dataset from two IBM quantum devices, ibm_fez (source) and ibm_marrakesh (target), comprising 170 noisy and ideal circuit output distributions, with device calibration features added. We train a residual neural network on the source device to map noisy to ideal outcomes. The zero-shot transfer test shows a KL divergence of 1.6706 (up from 0.3014), establishing device specificity. With K = 20 fine-tuning samples, KL drops to 1.1924 (28.6% improvement over zero-shot), recovering 34.9% of the gap between zero-shot and in-domain KL. Ablation studies reveal that the major cause of mismatches across devices is CX gate error, followed by readout error. The results show quantum noise can be learned and fine-tuned with minimal samples, and provide a plausible approach to cross-device quantum error mitigation.

Quantum batteries (QBs) have emerged as a promising route for fast energy storage and on-chip power supply in quantum devices. Given the limited analytical understanding of open Floquet QBs, we employ the kicked-Ising model as a tractable platform to systematically study its performance under realistic conditions, including finite temperature effects and environmental dissipation. Starting from Gibbs states of the transverse-field Ising model, we incorporate thermal and decoherence effects along the evolution, using both analytical and numerical approaches. Taking ergotropy as a central figure of merit, we characterize the injected and extractable energy, and identify regimes where charging remains robust despite environmental effects. Our results provide a systematic framework for assessing QB performance under thermal and dissipative effects.

Noise in contemporary quantum hardware is highly non-uniform across qubits and couplers, giving rise to localized low-noise "islands" within otherwise noisy device topologies. As quantum workloads scale, executions are increasingly forced to traverse high-noise regions, degrading algorithmic fidelity. Circuit cutting provides a route to circumvent such regions by decomposing large circuits into smaller subcircuits, but its practicality is limited by exponential sampling overhead and the lack of systematic guidance on how cut strategies should align with heterogeneous hardware noise. In this work, we present a hardware-noise-aware circuit cutting framework that explicitly exploits the spatial non-uniformity of noise in quantum devices. Rather than proposing a new cut-finding algorithm, we formalize the problem of device-constraint selection under realistic hardware noise and show that this choice critically determines both execution overhead and effective noise. Using a unified gate- and wire-cutting formulation, we demonstrate that small, hardware-informed relaxations in the device constraint yield exponential reductions in execution overhead while preserving alignment with low-noise hardware regions. Across representative workloads, our method achieves an average reduction in the number of circuit executions ranging from 5-54x for 20-qubit circuits, and enables tractable circuit cutting for 50-qubit circuits and application-level benchmarks where conventional strategies incur prohibitive overhead. These results establish noise-aware device-constraint selection as a necessary ingredient for making circuit cutting resource-efficient and practically deployable on contemporary quantum hardware.

We analyze device-dependent correlation sets generated by fixed local dichotomic measurements for two-qubit systems in the $(2,m,2)$ Bell scenario. We consider three fundamental state spaces for the composite system: the separable state space, the standard quantum state space, and the maximal tensor-product state space, which contains beyond-quantum states compatible with local quantum measurements. We formulate the corresponding correlation sets for general fixed dichotomic measurements and, in the traceless case, derive particularly simple explicit formulae for their support and gauge functions. These functions furnish dual operational characterizations of the three correlation sets: the support functions give optimal witnesses for entanglement and beyond-quantum states, whereas the gauge functions quantify the robustness of these detections against depolarizing noise. We further derive convex-hull representations that elucidate the extremal structures of the correlation sets and the physical states realizing them, showing in particular that extremal quantum correlations are realized by maximally entangled states. The fundamental limits of these dual operational tasks are governed solely by the smaller of the numbers of linearly independent measurement directions available to Alice and Bob. When both parties have three linearly independent measurement directions, our entanglement criterion detects Werner states up to the optimal PPT threshold $p_{\mathrm{crit}}=2/3$. For beyond-quantum-state detection, a nontrivial separation from the quantum set occurs only under the same measurement condition; in that case, the same optimal noise threshold is attained for an extremal state in the maximal tensor-product state space.

Entanglement distillation is the process of converting noisy entangled states into maximally entangled pure states via local operations and classical communication. A long-standing, unresolved question is which entangled states are amenable to distillation, known as the distillability problem. We solve this for Bell-diagonal qutrits with Weyl structure, and present a noise-robust scheme for entanglement distillation. In particular, we find that violating the positive partial transposition (PPT) criterion is necessary and sufficient for the 1-distillability of these states. For this, we construct a Schmidt rank 2 eigenvector of the partially transposed density matrix associated with its unique, three-fold degenerate negative eigenvalue. This feature makes the derived entanglement distillation protocol resilient to white-noise effects on the quantum states. Our results thus make noisy entangled qutrit pairs more accessible for future quantum technologies.

Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly fall into two categories: gradient-based and gradient-free algorithms. The associated optimization landscape is often high-dimensional, non-convex, and populated by numerous local minima, making efficient gradient-free search strategies essential. To address this, we introduce a gradient-free matrix product state/tensor train (MPS/TT) sampling heuristic for discrete quantum optimal control. In our approach, the MPS defines a score function over the space of discrete control parameters, which in turn induces a sampling distribution over candidate control sequences. This distribution is iteratively refined through selection of better performing sequences and local tensor updates to bias the search toward high-performing sequences. We evaluate the method on a range of benchmark problems, including single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer. Across these tasks, the method exhibits stable convergence behavior and competitive empirical performance relative to established gradient-free baselines. These results suggest that tensor network sampling offers a viable heuristic framework for discrete quantum control.

Zero-noise extrapolation (ZNE) mitigates errors in near-term quantum devices by extrapolating measurements obtained at amplified noise levels to estimate noise-free expectation values. In practice, commonly used extrapolation models are fitted without enforcing physical constraints, which can yield predictions outside the valid range of quantum observables. In this work, we introduce physically bounded variants of polynomial, exponential, and polynomial--exponential extrapolation models by explicitly parameterizing the zero-noise estimate and constraining it during optimization. We evaluate the approach using a large synthetic benchmark comprising 180,000 circuits and approximately 3.6 million ZNE experiments generated under realistic device noise models derived from IBM quantum backends. We also perform preliminary validation on real quantum hardware using GHZ and W-state circuits. Across the synthetic benchmark, bounded extrapolation substantially reduces unphysical predictions and improves the stability of exponential- and polynomial--exponential-family models, whereas polynomial models show little difference between bounded and unbounded variants. Hardware experiments show similar qualitative behaviour: bounded models generally avoid pathological extrapolations and often provide a more reliable balance between accuracy and usable coverage. At the same time, the results highlight practical limitations of current devices, including stronger-than-expected noise effects and variability not fully captured by simulation models. These results suggest that enforcing physical constraints during extrapolation improves the reliability of ZNE and that this approach can be incorporated into existing workflows with minimal modification.

The paper presents a scheme to detect entanglement arising from the quantum nature of gravity between a spin qubit and photons, using Stokes parameters. One of the crucial tests of the general theory of relativity is the bending of light due to the curvature. Recently, a quantum counterpart of this experiment to test the quantum nature of the gravitational interaction has been proposed, in which the spin-2, massless graviton yields entanglement between matter and a photon sector. Hence, it provides one of the most crucial experimental signatures for testing the quantum nature of gravity in a lab, since only spin-2-induced entanglement can yield the correct deflection of light due to matter. Here, we propose a positive partial-transpose (PPT) witness criterion for witnessing such an entanglement. We scan the entangled states in this context by studying the overlap of the final state, which is proportional to the entanglement phase. We exploit the Stokes observables to measure the photon state and the spins in the matter sector, thereby constructing a witness for the quantum nature of gravity in this setup. To quantify this entanglement, we will couple the photon to a local oscillator, whose phase need to be controlled to probe the orthogonal components of the macroscopic interference in the laser beam. We have shown that for a non-maximally entangled state mediated by the quantum nature of gravity, the witness attains a maximal negativity of $-0.052$. Our findings indicate that this witness effectively detects entanglement within the range $0.71 \leq |\gamma| < 1$, where $\gamma$ is the overlap between the two coherent states of the photon, providing a clear signature of quantum correlations.

Quantum error mitigation (QEM) is essential for extracting reliable results from near-term quantum devices, yet practical deployments must balance mitigation strength against runtime overhead under time-varying noise. We introduce \emph{GSC-QEMit}, a telemetry-driven, \textbf{context--forecast--bandit} framework for \emph{adaptive} mitigation that switches between lightweight suppression and heavier intervention as drift evolves. GSC-QEMit composes three coupled modules: (G) a Growing Hierarchical Self-Organizing Map (GHSOM) that clusters streaming telemetry into operating contexts; (S) an uncertainty-aware subsampled Gaussian-process forecaster that predicts short-horizon fidelity degradation; and (C) a cost-aware contextual multi-armed bandit (CMAB) that selects mitigation actions via Thompson sampling with explicit intervention cost. We evaluate GSC-QEMit on benchmark circuit families (GHZ, Quantum Fourier Transform, and Grover search) under nonstationary noise regimes simulated in Qiskit Aer, using an instrumented testbed where action labels correspond to graded mitigation intensity. Across Clifford, non-Clifford, and structured workloads, GSC-QEMit improves average logical fidelity by \textbf{+9.0\%} relative to unmitigated execution while reducing unnecessary heavy interventions by reserving them for inferred noise spikes. The resulting policies exhibit a favorable fidelity--cost trade-off and transfer across the evaluated workloads without circuit-specific tuning.

At the core of the quantum Internet lie quantum repeaters that enable remote end-to-end entanglement generation. Fundamentally, the entanglement generation rate and fidelity of quantum repeaters constitute the bottleneck for end-to-end performance. To achieve high rates, quantum repeaters employ quantum memory multiplexing. In a high-rate standard repeater, each memory sequentially generates an entanglement with its neighboring nodes and then applies entanglement swapping. This, however, results in low fidelity due to decoherence of the first-formed entanglement in the sequential generation process. By allocating different numbers of memories to simultaneously form entanglements with the left and right adjacent nodes, quantum repeaters reduce high waiting times and achieve high fidelity. In such a repeater, a mismatch problem arises due to the difference between the probabilistic number of generated entanglements on both sides. Consequently, some entanglements remain stored until opposite entanglements are available. The mismatch problem reduces the repeater rate and particularly the entanglement fidelity. In this paper, we consider the mismatch problem in an asymmetric repeater with different distances to its adjacent nodes. To mitigate the mismatch problem, we derive a dynamic optimal memory allocation. Under the optimal allocation, we derive statistical lower bounds on the achievable rate and fidelity. We demonstrate that the optimal allocation significantly improves the fidelity while maintaining a comparable rate to the standard repeater. In contrast, our results show that fixed memory allocation may be detrimental to the fidelity.

We investigate the excitation of a three-level ladder-type atom by a unidirectional field with a pair of indistinguishable photons. Starting from an analytical expression for the two-photon absorption probability, we determine the two-photon state that maximizes the population of the upper atomic state at a chosen time and show that, in the limit of an infinitely long pulse, perfect excitation is possible. The optimal state is identified as the time-reversed counterpart of the two-photon state emitted in spontaneous cascade decay. We then compare this ideal excitation strategy with experimentally accessible families of states, including symmetrized Gaussian product states, temporally correlated Gaussian states, and coherent pulses. We analyze how the optimal excitation conditions depend on the ratio of atomic decay rates and on the separation of the atomic transition frequencies. For indistinguishable photons described by Gaussian pulses, quantum interference may shift the maxima of the marginal spectral distribution away from the atomic resonances and qualitatively modify the optimal excitation strategy. Our results clarify the role of indistinguishability and correlations in two-photon absorption and provide guidance for designing realistic excitation schemes in quantum-optical light-matter interfaces .

The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, because of the need to choose a particular gauge for the vector potential. Nonetheless, in many situations all physical observables of the ground state remain entirely translation invariant. In this work, we introduce a projected entangled-pair state (PEPS) wavefunction with a pattern of virtual flux tensors, for which all physical expectation values are translation invariant by construction, possibly within an enlarged unit cell reflecting any symmetry breaking in the target state. Moreover, we show that the usual contraction and optimization methods for translation-invariant PEPS can be used, with the magnetic flux per plaquette only entering as a continuous parameter in the tensor network contractions. Therefore, our approach provides a method for simulating an interacting many-body system in a uniform magnetic field independently of the gauge choice for the vector potential and bypassing the need to consider extended magnetic unit cells.

A challenge with the Quantum Approximate Optimisation Algorithm (QAOA), and variational algorithms in general, is finding good variational parameters, a task which in itself can be NP-hard. Recent work has sought to de-variationalise QAOA by picking well-informed guesses for the variational parameters. The Linear Ramp QAOA (LR-QAOA) achieves this by using parameter schedules inspired by the quantum adiabatic algorithm. We go a step further and use spectral gap information from an adiabatic Hamiltonian, with the QAOA mixer Hamiltonian as our initial Hamiltonian, to make smooth ramps which we call Spectral Gap Informed Ramps (SGIR-QAOA). SGIR-QAOA schedules perform slow evolution where the spectral gap of the adiabatic Hamiltonian is small. We show that SGIR-QAOA has performance improvements over LR-QAOA on Grover's problem at constant depth and that SGIR-QAOA requires shorter depths to achieve the same optimal solution probability. We then show that these performance benefits extend to a problem with potential practical applications -- the Maximum Independent Set (MIS) problem. Finally, we demonstrate the scalability of the SGIR-QAOA method using extrapolated spectral gap information for scales that the spectral gap cannot be exactly evaluated, and show that the advantage appears to persist under mild depolarising noise.

Rare earth ion (REI)-doped oxide thin films are attractive for the application of quantum interconnects due to their stable optical levels and scalability$^{1-3}$. Among them, Er$^{3+}$ doped CaWO$_{4}$ is promising because it possesses narrow optical linewidth transitions and a long spin coherence time$^{4-6}$. The electron spin coherence is limited at high temperatures by paramagnetic impurities and by the presence of the 14.3% $^{183}$W nuclear spin. To further increase the spin coherence time at millikelvin temperatures, where the paramagnetic impurities are frozen out, our approach is to synthesize chemically and isotopically purified thin films as a host material. We first grow non-isotopically enriched Er$^{3+}$ doped CaWO$_{4}$ thin films, which exhibit a 214(13) MHz photoluminescence (PL) inhomogeneous linewidth, indicating the thin film has high crystalline quality. We then grow isotopically enriched CaWO$_{4}$ thin films using an isotopically purified $^{186}$WO$_{3}$ source. Time of flight secondary ion mass spectrometry (ToF-SIMS) was used to measure the relative concentration of W isotopes. $^{183}$W, the only W isotope that has a net nuclear spin and is the major cause of spin decoherence, was at a relative abundance of 1.2%, a factor of 10 lower than natural abundance. We also observed PL emission from single ions after integrating nano-photonic devices with the thin film. These results establish isotopically engineered CaWO$_{4}$ thin films as a promising platform for future studies of nuclear-spin-limited coherence and for scalable rare-earth-ion-based quantum nanophotonic devices.

We provide evidence of quantum kernel advantage under noiseless simulation in binary insurance classification on MIMIC-CXR chest radiographs using quantum support vector machines (QSVM) with frozen embeddings from three medical foundation models (MedSigLIP-448, RAD-DINO, ViT-patch32). We propose a two-tier fair comparison framework in which both classifiers receive identical PCA-q features. At Tier 1 (untuned QSVM vs. untuned linear SVM, C = 1 both sides), QSVM wins minority-class F1 in all 18 tested configurations (17 at p < 0.001, 1 at p < 0.01). The classical linear kernel collapses to majority-class prediction on 90-100% of seeds at every qubit count, while QSVM maintains non-trivial recall. At q = 11 (MedSigLIP-448 plateau center), QSVM achieves mean F1 = 0.343 vs. classical F1 = 0.050 (F1 gain = +0.293, p < 0.001) without hyperparameter tuning. Under Tier 2 (untuned QSVM vs. C-tuned RBF SVM), QSVM wins all seven tested configurations (mean gain +0.068, max +0.112). Eigenspectrum analysis reveals quantum kernel effective rank reaches 69.80 at q = 11, far exceeding linear kernel rank, while classical collapse remains C-invariant. A full qubit sweep reveals architecture-dependent concentration onset across models. Code: this https URL

We investigate the spin dynamics of a dipole-coupled system by comparing a direct solution of the Schrodinger equation for quantum spins with simulations of classical spins. Although classical spins have long been used in microscopic spin dynamics simulations, we demonstrate that their results differ significantly from those of quantum spins. Using Free Induction Decay as a benchmark, we find that while the overall patterns are qualitatively similar, significant discrepancies emerge at both short and long timescales. We trace these differences to fundamental distinctions in the two descriptions.

It was pointed out in [JSW+25] that widely-studied optimization problems such as D-regular max-k-XORSAT can be reduced to decoding of LDPC codes, using quantum algorithms related to Regev's reduction. LDPC codes have very good decoders, such as Belief Propagation (BP), and this therefore makes D-regular max-k-XORSAT an enticing target for this class of quantum algorithms. However, BP was found insufficient to achieve quantum advantage. Here, we develop an intrinsically quantum decoding technique, which decodes classical LDPC codes subject to coherent superpositions of bit flip errors. For average-case instances of D-regular max-k-XORSAT drawn from Gallager's ensemble, this quantum decoder strongly outperforms classical belief propagation at many values of k and D. For some (k,D) the approximate optima achievable using this decoder surpass both Prange's algorithm and simulated annealing. However, we stop short of achieving quantum advantage because we identify an enhancement to Prange's algorithm that recovers a precise tie, much as a precise tie was observed between the standard version of Prange's algorithm and a more limited version of locally-quantum decoding in [CT24].

Quantum computers could solve problems beyond the reach of classical devices, but this potential depends on quantum error correction (QEC) to protect fragile quantum states from noise. A central challenge in QEC is decoding: inferring likely physical errors from syndrome patterns generated by repeated stabilizer measurements. Existing decoders, including graph-based and neural approaches, typically return a single correction hypothesis and therefore discard the richer posterior structure of the error distribution conditioned on the observed syndrome. Here we recast QEC decoding as posterior inference using discrete denoising diffusion, exploiting the analogy between stochastic error accumulation and the forward diffusion process. We introduce DiffQEC, a generative decoder that combines a syndrome processor for multi-round spatial-temporal syndrome histories with syndrome feature modulation to condition denoising on the observed syndrome throughout inference. On experimental data from Google's superconducting quantum processor, DiffQEC reduces logical error rates by up to 10.2% relative to minimum-weight perfect matching and by about 5% relative to tensor-network decoding. These improvements persist for larger code distances up to 17 under depolarizing noise and for logical circuits of increasing depth. Beyond accuracy, the learned posterior provides confidence estimates for post-selection and reveals physically meaningful error structure, establishing posterior generative decoding as a practical framework for QEC.

Cooperative emission is well understood for idealized symmetric systems, but its limits in spatially extended, free-space ensembles remain an open question. Here, we derive a universal law for the scaling of the maximum photon emission rate with system size that unifies both ordered arrays and disordered atomic clouds in arbitrary dimensions at fixed density. We demonstrate that, for a fixed atomic density, the maximum emission rate scales universally as the product of the atom number and the system's optical depth, with the latter encoding the dimensional scaling across all regimes from independent emission to the Dicke limit. Furthermore, we establish a scaling law for directional detection, revealing that the observed rate depends on the detector's numerical aperture: small apertures yield Dicke-like quadratic scaling, whereas large apertures recover our integrated universal bound. Our results establish optical depth as the parameter governing many-body cooperative emission in both ordered and disordered ensembles, and reveal that directional and total-emission scalings must be carefully distinguished in experimental settings.

Quantum computing has emerged as a powerful potential accelerator for computational fluid dynamics (CFD), but whether this promise can be realized in practice depends on how fluid information is encoded on quantum hardware. This review provides an architecture-agnostic assessment of encoding strategies for quantum-enhanced fluid simulation, focusing on the trade-offs they impose on state preparation, measurement, boundary treatment, nonlinear dynamics, and temporal evolution. We examine the principal encoding paradigms used in the literature and relate them to representative quantum algorithms for fluid simulation. Through these examples, we show that encoding choices fundamentally shape both the algorithm itself and also the practical feasibility of quantum CFD. For example, highly compact encodings can offer attractive asymptotic advantages but might introduce severe bottlenecks in readout, state preparation, and nonlinear processing, whereas less compact representations may simplify interactions and improve compatibility with analog and near-term hardware. No single encoding is universally optimal, rather the most suitable choice depends strongly on the structure of the fluid problem, the computational objective and the constraints of the target quantum platform. We therefore argue that encoding should be treated as a primary design variable in quantum CFD and revisited iteratively throughout the design pipeline, as different algorithmic components interact and influence one another.

We propose a contextual cavity/circuit QED analogue and extension of the Stern-Gerlach experiment, where the pseudo-spin of a two-state `atomic' transition plays the role of the ``spin'', while the resonant field driving the transition stands for the ``magnetic field''. A phase-sensitive continuous detection of the cavity field coupled to the induced `atomic' dipole affects the stability of the two distinct outcomes. The dressed states comprising the latter give their place to a self-consistent spontaneous dressed-state polarization as the driving strength is lowered. The associated evolution proves anew highly contextual, underpinned by a persistent production of coherent-state superpositions for a particular setting of the monitoring device. Finally, when bistability is absent, we employ the photoelectron `atomic' emission statistics as a diagnostic tool of the cavity field fluctuations.

The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schrödinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.

Semiconductor spin qubits are a promising platform for large-scale quantum computing, but have yet to take full advantage of the broad class of quantum low-density parity check (QLDPC) codes, which promise high encoding rates and efficient logic but require nonlocal connectivity between physical qubits. In this work, we investigate the implementation of QLDPC codes on a tileable, shuttling-based spin qubit architecture. By tailoring syndrome extraction circuits to the shuttling noise model, we significantly improve on previous surface code proposals and extend the feasible shuttling range of the architecture by 5-10x, enabling the implementation of more complex codes with long-range interactions. Taking inspiration from the field of robotics, we develop a coordinated shuttle scheduling algorithm that supports arbitrary codes and use it to benchmark the logical performance of a variety of promising code families. We find that the optimized schedules are up to 86% faster than hand-optimized schedules for certain code families. Through detailed circuit-level simulations, we identify specific QLDPC codes that improve upon prior surface code implementations by orders of magnitude, increasing encoding efficiency and reducing logical error rates. This work demonstrates the potential of shuttling-based spin qubit hardware platforms for scalable and efficient fault-tolerant quantum computation.

Combining recent advances in superconducting quantum hardware, we explore quantum correlations in a previously inaccessible regime by observing \emph{simultaneously} high-dimensional and many-body Bell non-locality. We report a high-confidence Bell violation in the correlations between two $d=64$-dimensional systems encoded in twelve qubits. For system sizes up to $d=32$, the strength of the observed nonlocal correlations exceeds the quantum upper bound for $d=2$ systems, providing direct evidence of high-dimensional nonlocality. Furthermore, we demonstrate that the observed violation is genuinely collective: all qubits contribute to the nonlocal correlations, while most pairwise correlations across the bipartition remain Bell-local. Our work illustrates how present-day quantum processors enable the exploration of fundamental predictions of quantum mechanics in previously inaccessible regimes and, in turn, how fundamental quantum effects can be used to benchmark their performance.

This paper presents an analysis of the applicability of a quantum amplitude redistribution algorithm to the data filtering problem and the results of modeling the algorithm's operation in comparison with a median filter.

Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction. Here, we detail how to apply generalized belief propagation (GBP) - where messages are passed within a hierarchy of overlapping regions of the tensor network - to approximately contract tensor networks and obtain accurate results. The original belief propagation algorithm is a corner case of this approach, corresponding to a particularly simple choice of regions of the tensor network. We implement the GBP algorithm for a number of different region choices on a range of two- and three-dimensional, infinite and finite tensor networks, solving the corresponding fixed point equations both numerically and, in certain tractable cases, analytically. Our examples include calculating the partition function of the fully frustrated Ising model, computing the ground state degeneracy of three-dimensional ice models, measuring observables on the deformed AKLT quantum state and evaluating the norm of randomly generated tensor network states.

We generated a one-dimensional quantum gas confined in an elongated optical dipole trap instead of 2D optical lattices. The sample, comprising thousands of atoms, spans several hundred micrometers and allows for independent control of temperature and chemical potential using Feshbach resonance. This allows us to directly observe and investigate the spatial distribution and associated excitation of 1D quantum gas without any ensemble averaging. In this system, we observed that the dimension of 1D gas will be popped up into 3D due to strong interaction without changing any trapping confinement. During the dimensional crossover, we found that increasing the scattering length leads to the failure of 1D theories, including 1D mean field, Yang-Yang equation, and 1D hydrodynamics. Specifically, the modified Yang-Yang equation effectively describes this 1D system at temperatures beyond the 1D threshold, but it does not account for the effects of stronger interactions. Meanwhile, we observe two possible quantized plateaus of breathing-mode oscillation frequencies predicted by 1D and 3D hydrodynamics, corresponding to weak and strong interactions respectively. And there is also a universal crossover connecting two different regimes where both hydrodynamics fail.

We extend the CDPR lattice reduction algorithm from ideal to module lattices, leveraging the trace orthogonality of the power basis to decompose the module into rank-1 submodules and applying CDPR independently to each. This base module reduction achieves a Hermite factor $\exp(\tilde{O}(\sqrt{n}))$ matching the ideal case, with a module reduction factor $O(1)$ independent of the rank, under a balance hypothesis automatically satisfied for MLWE-distributed bases. To control precision, we introduce CRT-scaled rounding at totally split primes, reducing the Gram-Schmidt rounding error and yielding a bounded-precision implementation. We further reformulate the CDPR sign-selection subproblem as a mixed-integer linear program, determining the optimal balanced discrepancy to be a universal constant $\delta^*\approx 0.4407$. All results build on the class number one condition $h_k^+=1$ established in Part I of this series.

Driven atomic Josephson junctions allow one to monitor phase-coherent dynamics with unprecedented control and flexibility of the system's physical conditions. While cold-atom manifestations of the Josephson effect have been extensively studied in a wide variety of settings, atomic Josephson junctions in synthetic electromagnetic fields remain largely unexplored. Here, we show that synthetic magnetic fields can induce Fraunhofer-like modulations of the critical current in atomic Josephson junctions. Although this effect presents analogies to the Fraunhofer patterns found in superconducting devices, distinctive features emerge due to the neutral nature of the superfluid. We investigate the underlying spatial interference mechanisms and elucidate the role of Josephson vortices in the formation of spatially modulated current distributions based on numerical simulations. Our results open up new avenues for matter-wave circuits to deepen our understanding of spatial coherence in Josephson junctions, which are fundamental to the development of novel quantum technologies.

Strongly-correlated electrons in transition-metal oxides give rise to intriguing emergent phenomena, including high-temperature superconductivity in cuprates. While simplified one-band Hubbard models capture some aspects, explicitly describing the interplay of copper and oxygen orbitals -- as in the three-band Emery model -- is essential to capture the full phenomenology of cuprates. Quantum simulators based on ultracold atoms offer a promising route to study such systems in a controlled setting, but realizing realistic multi-orbital Hubbard models remains challenging. Here we propose an optical superlattice architecture that implements the three-band Emery model with ultracold fermions. By combining lattice beams with controllable interference, we engineer orbital degrees of freedom that reproduce key features of the cuprate band structure, while enabling independent control of orbital-dependent interactions and charge-transfer energy. We show that single-particle quantum walks can benchmark the resulting tight-binding model. Using determinant quantum Monte Carlo, we further investigate thermodynamic properties in the undoped regime and find a finite-temperature metal-insulator crossover accompanied by the onset of antiferromagnetic correlations accessible in current experiments. Finally, we apply a Hamiltonian learning protocol enabling to infer effective single-band Hubbard models from experimental realizations of Emery models. Our results provide a practical pathway to simulate multi-orbital Hubbard physics with quantum gas microscopes.

Magneto-optical traps are central to atomic and molecular quantum technologies and precision tests of fundamental physics, where both sensitivity and bandwidth scale strongly with atom number and loading rate. We demonstrate that employing multiple, closely spaced optical frequency components in the cooling light of a $^{87}$Rb magneto-optical trap -- without utilizing any additional slowing techniques -- can double the steady state atom number and increase the loading rate by up to a factor of 4, compared to a conventional single-frequency implementation. Subsequently, we capture up to $1.0(1)\times10^{10}$ atoms with a loading rate of up to $1.3(2)\times 10^{11}\,\mathrm{atoms\,s^{-1}}$ from a thermal background. Numerical simulations reproduce the observed trends and predict substantially larger gains for increased trap sizes beyond our experimental bounds. By re-examining earlier studies of multi-frequency atom capture in the context of modern experimental hardware and emerging applications, we show that previously identified limitations can be avoided and establish multi-frequency cooling as a practical and scalable route to high-flux cold-atom sources. These results have immediate applications in portable atom-based quantum sensing, where higher bandwidth and precision can be achieved without forgoing compactness, and in atom-interferometric tests of fundamental physics, which benefit from access to larger-mass quantum systems.

A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field theory (an epsilon expansion around six dimensions) and numerical simulations in two dimensions. The results reveal multiscaling of correlation functions at the critical point, and a striking enlarged symmetry of the replica description. This is an analog of the Nishimori phenomenon in the Ising spin glass, in a distinct replica limit. The enlarged symmetry is present microscopically for certain measurement protocols, but more generally can emerge in the infrared, and it fixes the exact value of the exponent for the Edwards-Anderson correlator both in 2D and near the upper critical dimension. We also examine the epsilon expansion for models with power-law interactions and/or long-range measurement.

Slepian developed the Prolate Spheroidal Wavefunction (PSW) spatial-mode basis, which forms the normal modes of the Fresnel-propagation kernel of a free-space optical communications channel bookended by hard-circular apertures. The zero-th order PSW mode has the highest power-transfer eigenvalue, exciting which on the transmitter side therefore maximizes the transmissivity for single-spatial-mode communications. We show that the transmissivity performance of this fundamental PSW mode can be obtained by an aperture-truncated Gaussian beam of an optimized beam waist, despite the two mode shapes deviating from one another in the near-field regime.

We identify a boundary-robust topological signature of open Floquet lattices: although nonadiabatic boundaries strongly reshape the transmission lineshape, the integrated left--right transmission asymmetry saturates to a plateau set by the bulk Floquet winding number. Its origin is a deep-bulk branch-population principle: in the long-sample limit, each propagating Floquet--Bloch branch is generically populated with unit weight, since true Floquet bound states are nongeneric. The robust observable is therefore the cumulative transmission imbalance rather than the boundary-sensitive transmission profile. We propose direct detection by cold-atom transmission spectroscopy. For electronic transport, the same asymmetry admits contact-model-dependent electrical readouts: a coherent Floquet--Landauer--Büttiker interpretation predicts a near-\(2ef\) response in weak SAW devices, whereas a blocking-factor post-processing yields a qualitatively different signal.

We reconsider the problem of regularizing the divergent series $\sum_{n=1}^{\infty}n^{\alpha}$ for $\operatorname{Re}\alpha>-1$, and offer a regularization prescription that yields the Riemann zeta regularization as a special case. The development of the regularization is framed as a two-step problem. The first step is prescribing a regularization of the divergent sum $\sum_{n=1}^{\infty}n^m$ for every non-negative integer $m$; and the second step is the extension of the sum for non-integer $\alpha$. The extension is obtained under the consistency condition that the regularized sum for integer $m$ emerges continuously from the sum for non-integer $\alpha$. The scheme is specified by a differential generator $L=L(\mathrm{d}/\mathrm{d}t)$ through which a generalized spectral function (GSF), $K_L(t)$, is constructed. Under the condition that the GSF has a holomorphic complex extension $K_L(z)$ with $z=0$ as a pole, the case for integer $m$ takes the regularized value $\sum_{n=1}^{\infty} n^m = (2\pi i)^{-1}\oint_C L^m K_L(z) z^{-1}\mathrm{d}z$, where $C$ is a closed contour enclosing only the pole of $K_L(z)$ at the origin. On the other hand, under the consistency condition, the case for non-integer $\alpha$ takes the value $\sum_{n=1}^{\infty}n^{\alpha}=(2\pi i)^{-1}\int_{\tilde{C}} L^{\alpha} K_L(z) z^{-1}\mathrm{d}z$, where $L^{\alpha}$ is the fractional extension of $L^m$ and $\tilde{C}$ is an appropriate deformation of the contour $C$. Here, we obtain the regularization corresponding to the generator $L=h(t) \mathrm{d}/\mathrm{d}t$, where $h(t)$ has the analytic extension $h(z)$ such that $1/h(z)$ is an entire function. We find that the regularized sum is equal to the Riemann zeta regularized value plus terms determined by the generator $L$.

Controlling and generating ultrafast free-electron wavepackets via laser is pivotal for photon-induced near-field electron microscopes (PINEM) and also for developing compact, coherent free-electron radiation sources. Here, we present a quantum echo-enabled high-harmonic generation (QEEHG) scheme that manipulates the quantum phase of electron wavepackets to produce tunable, coherent high-harmonic radiation at ultrashort wavelengths. This framework, inspired by the EEHG concept for free-electron lasers by Stupikov et al. (2009), leverages multiphoton PINEM scattering followed by dispersive chirp sections to induce quantum interference among photon sidebands. Such interference selectively enhances a targeted harmonic order - for instance, the 60th harmonic at 13.3nm from an 800nm seeding - while suppressing unwanted radiations. The optimization of harmonic orders and its non-classical spectral characteristics are analyzed. This quantum echo technique establishes a promising paradigm for compact coherent sources and provides new perspectives for quantum wavefunction shaping in ultrafast electron microscopy and diffraction.

Recent developments have seen the application of finite Gaussian basis sets to the $\alpha(Z\alpha)^{n\geq3}$ vacuum polarization. The energy shift for $s$ and $p$ electron states have been tabulated and their convergence investigated. In this work, we extend this problem to the multi-electron case. Hartee-Fock potentials obtained self-consistently are used to treat the vacuum polarization for lithium-like systems and are found to be in good agreement with comparable results in the literature. The results presented in this work demonstrate the use of Gaussian basis sets for atomic potentials whose Green's functions expressions cannot be simply obtained via analytic or numerical methods.

The erratic non-Hermitian skin effect (ENHSE), emerging from the interplay between disorders and locally nonreciprocal yet globally reciprocal couplings, has reshaped the conventional bulk-boundary correspondence through its disorder-dependent localization properties. Here, we experimentally observe the dynamical phenomena of ENHSE in phononic crystals with disordered imaginary gauge fields. The erratic localization occurs in the bulk independent of the excitation position, with the main and satellite peaks precisely located at the local maxima of the cumulative gauge field in accordance with random-walk extreme-value statistics. Remarkably, the selective manipulation of satellite peaks can be realized by tuning the staggered disorder strengths in a dimerized chain. These findings can deepen the understanding of non-Hermitian physics and establish a new route for disorder-engineered non-Hermitian wave control.

We develop a theoretical framework for designing quantum couplers based on Dirac materials that can modulate the polarization of transmitted quasiparticles without significantly perturbing their propagation. We analyze in detail the conditions required for perfect transmission (Klein tunneling) together with controlled polarization transformation of the incoming states. We then discuss an explicit model of a quantum coupler composed of AA-stacked bilayer graphene nanoribbons with armchair edges and a localized interlayer interaction. Perfect transmission through the desired polarization channels is examined for both narrow and wide couplers. We show that the transmission of polarized states can be finely tuned by external fields.

We investigate the nonequilibrium dynamics of core-hole excitations in a one-dimensional fermionic few-body system consisting of a spin-polarized Fermi bath coupled to a single heavy mobile impurity. The bath is initially prepared in a particle-hole configuration by emptying a selected bath single-particle orbital, while the impurity is displaced with respect to the center of the bath confinement potential. The quench dynamics are initialized by suddenly switching on the impurity-bath interaction. To resolve the resulting dynamics, we combine two complementary \textit{ab initio} approaches, namely the Multi-Layer Multi-Configuration Time-Dependent Hartree method for mixtures and a multi-channel Born-Oppenheimer framework. We show that the postquench response is governed by the interaction strength, impurity confinement, mass imbalance, and the location of the initially prepared hole within the Fermi sea. The density evolution and impurity center-of-mass motion reveal a competition between mixing and demixing of impurity and bath, while the von Neumann entropy demonstrates the buildup of pronounced many-body correlations. Most importantly, the occupation dynamics of the initially emptied orbital identifies deep core holes as substantially more robust against refilling than bulk or edge vacancies. Our results establish core-hole excitations as robust dynamical many-body features in trapped ultracold fermions and provide a controlled route towards probing orthogonality response, correlation buildup, and hole refilling in real time.

Young interference is usually read as the gradual statistical accumulation of random detection events. Here we show that a time-reversed Young (TRY) geometry has a different statistical character: the fringe is not a marginal distribution of detector positions, but a conditional response indexed by a programmed source coordinate. With a fixed detector and a scanned source basis, the observable is an operational hybrid correlator between detector signal and source label. The resulting interference is deterministic at the response-function level, while noise enters only through estimation precision. We formulate this distinction using Fisher information, estimator variance, and noise scaling, clarifying why TRY naturally supports calibration, lock-in readout, null-fringe sensing, and source-plane superresolution.

The challenge of programming classical computers to play traditional, competitive games against human players has helped to advance classical hardware and software. Quantum computers have the potential to play games in a unique way: programmed only with the rules of a game, they should be able to implicitly represent all future paths of a game leading to wins, losses, or draws, and sample from this path set to identify moves that maximize the likelihood of a win. This permits skilled play without hard-coded or machine-learned strategy. As a proof of principle, we present early results obtained after programming the D-Wave quantum annealer with the rules of tic-tac-toe, enabling it to play against a human opponent. We anticipate that, as it has for classical computers, game-playing will serve as an important real-world benchmark for quantum computers.

To date, frequency-dependent squeezed light has been used to reduce quantum noise in interferometric gravitational wave detectors by 6.1 dB (a factor of two). Future upgrades and detectors aim to both reduce quantum noise by 10 dB (a factor of three) and to increase the circulating power in the interferometer arm cavities. Achieving these goals will be extremely challenging due, in part, to the degradations to the squeezed state caused by mode mismatch between the internal interferometer optical cavities and between the auxiliary external cavities. It is therefore imperative to gain a detailed understanding of all sources of mismatch and to obtain experience in mitigating their effects in the current detectors in order to improve astrophysical sensitivity now and in the future. Two types of internal mismatch are identified which are due to the thermal aberrations generated when the test mass optics absorb a small fraction of the circulating arm power. It is found that the dynamics responsible for the degradations caused by the mismatch between the quadratic part of the wavefront of two modes has a characteristic low-pass frequency dependence while the dynamics of the mismatch due to all higher order thermal aberrations has a high-pass behavior. As a consequence, the two types of mismatch are predominantly responsible for different squeezing degradations -- some of which are significant for the current detectors and some of which will only be important for future detectors with longer arms. The behavior of these two types of internal mismatch are described and the implications for detector design, operation, and characterization are discussed.

Electronic final states generated by sudden changes of the Hamiltonian are studied here, with emphasis on nuclear charge variation in $\beta$ decay. A $\lambda$-parametrized family $\hat H(\lambda)$ that continuously connects the initial and final Hamiltonians, so that the electronic response can be represented as a continuous deformation in Hilbert space, is introduced. Within the sudden approximation, transition amplitudes are written as overlaps between eigenstates of distinct Hamiltonians. To relate non-orthogonal one-electron basis sets in a stable way, the paper uses a practical transport scheme based on overlap metrics and truncated singular value decomposition (SVD). This mapping is interpreted as a discrete counterpart of continuous transport along the $\lambda$ path. The formalism is first developed for the one-electron case, where analytic structure and selection rules are made explicit, and then generalized to many-electron systems via nonorthogonal determinant overlap expressions. The resulting formulation gives transition probabilities in bound and continuum channels in a way that is both numerically stable and easy to interpret.

We investigate the nonequilibrium dynamics of a two-dimensional rotating Bose gas confined in a symmetric anharmonic trap, employing the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study states ranging from vortex-free configurations to multicharged (giant) vortices, prepared by tuning the rotation frequency, and analyze their response to sudden interaction and trap quenches. In vortex-free states, interaction quenches induce regular breathing--like dynamics, whereas in the presence of giant vortices they lead to symmetry-breaking surface excitations. In contrast, trap deformations that excite quadrupole-like modes produce stable oscillations in vortex-free condensates but trigger rapid, irregular, and effectively chaotic splitting dynamics in multicharged vortices. To characterize these processes beyond conventional density and phase observables, we employ information-theoretic measures, including marginal and joint entropies, mutual information, and Kullback-Leibler (KL) divergence, supplemented by an angular-resolved KL measure that captures symmetry breaking and azimuthal localization. We find that chaotic splitting is accompanied by a pronounced growth of information-theoretic indicators, signaling the buildup of many-body correlations and increasing complexity in the system dynamics. Our results demonstrate the extreme sensitivity of giant vortices to excitation protocols and establish information-theoretic measures as a powerful framework to quantify correlations and complexity in rotating quantum gases.

Charge separation from the $(4,0)$ to the $(3,1)$ state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the $(3,1)$ singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of $g$-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.

Gatemon qubits are based on a superconductor-quantum dot-superconductor (S-QD-S) junction which enables in situ electrostatic tuning via a gate electrode. For a single-channel QD this structure gives rise to two subgap Andreev bound states (ABSs), and generally leads to a richer quantum phase dynamics as compared to conventional transmons. In a recent work [Phys. Rev. B 111, 214503 (2025)] we derived the quantum phase dynamics from a many-body treatment which leads to an effective gate voltage-dependent Hamiltonian that self-consistently incorporates the phase quantization. It predicts (i) a renormalization of the junction's effective capacitance and (ii) the presence of gate voltage and occupation-dependent charge offsets in junctions with tunneling asymmetry. Here, we quantify the observable impact of these effects on the qubit's energy spectrum and anharmonicity, by studying the interplay of the two Andreev branches as a function of dot-gate voltages and junction transparencies. We show the relation of these predictions to simplified gatemon models and propose a protocol to experimentally detect the predicted charge offsets.

Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that lack conventional order and are defined by coherent superpositions of an extensive number of many-body configurations. Realising and probing such exotic states experimentally is an outstanding challenge both in solid-state and synthetic quantum systems, not least due to the difficulty of detecting the fragile coherences between many-body states. Here, we report a large-scale (>3,000 sites) realisation of a two-dimensional U(1) lattice gauge theory with ultracold atoms in a square optical superlattice and demonstrate non-equilibrium preparation of extended regions of U(1) quantum spin liquids. We demonstrate Gauss's law validity in a quench experiment, enabled by a new microscopy technique for detecting doubly occupied sites. We observe characteristic real-space correlations and momentum-space pinch points, hallmarks of the emergent U(1) gauge structure. Using round-trip interferometric protocols, we directly observe large-scale coherence between many-body configurations, providing strong evidence for quantum spin liquid regions extending over ~100 lattice sites. Our results establish non-equilibrium quantum simulation protocols as a powerful route for accessing and probing exotic, highly-entangled states beyond those hosted by the engineered Hamiltonian in thermal equilibrium.

A matter wave propagating through curved spacetime accumulates phase that encodes both geometry and gauge structure. We develop a semiclassical framework for charged spin-$1/2$ matter-wave interferometers based on a WKB expansion of the covariant Dirac equation, in which the phase decomposes into dynamical, spin, and electromagnetic Aharonov-Bohm (AB) contributions. In a freely falling detector frame, all three channels are governed by local tidal fields. In a weak gravitational-wave (GW) background, the dynamical and spin phases probe the gravitoelectric and gravitomagnetic sectors of curvature, while the AB phase arises from curvature-induced electromagnetic fields obtained from Maxwell's equations in curved spacetime. For a Mach-Zehnder interferometer (MZI), all three responses are determined by the same tidal scale, $\ddot{h}_A \sim \Omega^2_{gw}h_0$, and filtered by a common geometric kernel, while entering through distinct physical couplings. In particular, the AB contribution depends not only on the enclosed flux but also on spatial variations of the induced fields and exhibits an intrinsic frequency dependence set by the traversal time. These results provide a unified description of matter-wave interferometric phases in time-dependent GW backgrounds and identify complementary dynamical, spin, and electromagnetic pathways through which spacetime curvature imprints itself on quantum interference.

Characterizing large noisy multiparty quantum states using genuine multiparty entanglement is a challenging task. In this paper, we calculate lower bounds of genuine multiparty entanglement localized over a chosen multiparty subsystem of multi-qubit stabilizer states in the noiseless and noisy scenario. In the absence of noise, adopting a graph-based technique, we perform the calculation for arbitrary graph states as representatives of the stabilizer states, and show that the graph operations required for the calculation has a polynomial scaling with the system size. As demonstrations, we compute the localized genuine multiparty entanglement over subsystems of large graphs having linear, ladder, and square structures. We also extend the calculation for graph states subjected to single-qubit Markovian or non-Markovian Pauli noise on all qubits, and demonstrate, for a specific lower bound of the localizable genuine multiparty entanglement corresponding to a specific Pauli measurement setup, the existence of a critical noise strength beyond which all of the post measured states are biseparable. The calculation is also useful for arbitrary large stabilizer states under noise due to the local unitary connection between stabilizer states and graph states. We demonstrate this by considering a toric code defined on a square lattice, and computing a lower bound of localizable genuine multiparty entanglement over a non-trivial loop of the code. Similar to the graph states, we show the existence of the critical noise strength in this case also, and discuss its interesting features.

In this work, we consider two-sender, one-receiver communication over a discrete memoryless multiple-access channel without feedback, where two senders may cooperate on channel coding by using preshared resources, such as shared randomness, quantum states and measurements, or nonlocal correlations. We present the capacity region when senders employ cooperative encoding with quantum and nonlocal resources, extending beyond shared randomness, and derive a sum rate that serves as a lower bound to the sum capacity; the lower bound is computable by exploiting specific strategies. We also compute the sum capacities for two instances. One is when senders apply local resources for cooperative encoding. The other is when senders exploit nonclassical resources for encoding against channels constructed by referring to nonlocal games; in this way, correlated noise other than independent errors occurs on code words. Comparing the exact sum capacities and lower bounds, we show that nonlocal and quantum resources for cooperative encoding enable higher sum capacities over local ones. The Clauser-Horne-Shimony-Holt and magic square games are considered for constructing multiple-access channels, and we demonstrate the usefulness of nonlocal and quantum resources to achieve higher-sum capacities.

Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between them. However, there has not been a graphical language for FHilb which is both universal and complete and thus incorporates a set of rules rich enough to derive any equality of the underlying formalism solely by rewriting. In this paper, we introduce the qufinite ZXW calculus - a graphical language for reasoning about finite-dimensional quantum theory. We set up a unique normal form to represent an arbitrary tensor and prove the completeness of this calculus by demonstrating that any qufinite ZXW diagram can be rewritten into its normal form. This result implies the equivalence of the qufinite ZXW calculus and the category FHilb, leading to a purely diagrammatic framework for finite-dimensional quantum theory with the same reasoning power. In addition, we identify several domains where the application of the qufinite ZXW calculus holds promise. These domains include spin networks, interacting mixed-dimensional systems in quantum chemistry, quantum programming, high-level description of quantum algorithms, and mixed-dimensional quantum computing. Our work paves the way for a comprehensive diagrammatic description of quantum physics, opening the doors of this area to the wider public.

We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of local magnetic field and spin-spin interactions of the Ising-type using fidelity susceptibility (FS) and entanglement as the probes. We assume the code to be embedded on the surface of a wide cylinder of height $M$ and circumference $D$ with $M\ll D$. We demonstrate a power-law divergence of FS across the QPT, and determine the quantum critical points (QCPs) via a finite-size scaling analysis. We verify these results by mapping the perturbed Kitaev code to the 2D Ising model with nearest- and next-nearest-neighbor interactions, and computing the single-site magnetization as order parameter using quantum Monte-Carlo technique. We also demonstrate a finite size odd-even dichotomy in the occurrence of the QPT in the Kitaev ladder with respect to the odd and even values of $D$, when the system is perturbed with only Ising interaction. Our results also indicate a higher robustness of the topological phase of the Kitaev code against local perturbations if the boundary is made open along one direction. We further consider a local entanglement witness operator designed specifically to capture a lower bound to the localizable entanglement on the vertical non-trivial loop of the code. We show that the first derivative of the expectation value of the witness operator exhibits a logarithmic divergence across the QPT, and perform the finite-size scaling analysis. We demonstrate similar behaviour of the expectation value of the appropriately constructed witness operator also in the case of locally perturbed color code with open boundaries.

Quantum Conference Key Agreement (CKA) provides a secure method for multi-party communication. A recently developed interference-based prepare-and-measure quantum CKA possesses the advantages of measurement-device-independence, namely, being immune to side-channels from the detector side. Besides, it achieves good key rate performance, especially for high-loss channels, due to the use of single photon interference. Meanwhile, several fully passive QKD schemes have been proposed, which eliminate all side channels from the source modulation side. We extend the fully passive idea to an interference-based CKA, which has a high level of implementation security for many-user communication.

We apply a Bayesian agent-based framework inspired by QBism to iterations of two quantum games, the CHSH game and the quantum prisoners' dilemma. In each two-player game, players hold beliefs about an amount of shared entanglement and about the actions or beliefs of the other player. Each takes actions which maximize their expected utility and revises their beliefs with the classical Bayes rule between rounds. We simulate iterated play to see if and how players can learn about the presence of shared entanglement and to explore how their performance, their beliefs, and the game's structure interrelate. In the CHSH game, we find that players can learn that entanglement is present and use this to achieve quantum advantage. We find that they can only do so if they also believe the other player will act correctly to exploit the entanglement. In the case of low or zero entanglement in the CHSH game, the players cannot achieve quantum advantage, even in the case where they believe the entanglement is higher than it is. For the prisoners dilemma, we show that assuming 1-fold rational players (rational players who believe the other player is also rational) reduces the quantum extension [Eisert, Wilkens, and Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)] of the prisoners dilemma to a game with only two strategies, one of which (defect) is dominant for low entanglement, and the other (the quantum strategy Q) is dominant for high entanglement. For intermediate entanglement, neither strategy is dominant. We again show that players can learn entanglement in iterated play. We also show that strong belief in entanglement causes optimal play even in the absence of entanglement -- showing that belief in entanglement is acting as a proxy for the players trusting each other. Our work points to possible future applications in resource detection and quantum algorithm design.

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of \textit{multicopy state teleportation}, where Alice has $k$ identical copies of an arbitrary unknown $d$-dimensional qudit state $\vert\psi\rangle$ to teleport a single copy of $\vert\psi\rangle$ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob's correction. Alice may perform a joint measurement on her half of the entangled state and the $k$ copies of $\vert\psi\rangle$. We prove that the maximal probability of success for teleporting the exact state $\vert\psi\rangle$ to Bob is $p(d,k)=\frac{k}{d(k-1+d)}$ and present an explicit protocol to attain this performance. Then, by utilising $k$ copies of an arbitrary target state $\vert\psi\rangle$, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.

We propose a scalable and deterministic protocol for growing large multi-qubit states starting from two-qubit non-maximally entangled pure states, where the bipartite entanglement in the resultant state is higher than the maximum of the available entangled qubit-pairs. This is achieved via a truncation of the Hilbert space corresponding to a subsystem of qubits to a space that hosts a single qubit, brought about by a multi-qubit measurement assisted by the graph basis. We prove its equivalence to a repetitive two-qubit measurement-based protocol, and demonstrate realization of the required two-qubit measurement via a two-qubit parity measurement, thereby establishing the implementability of the protocol. We derive lower and upper bounds of the bipartite entanglement concentrated after a given number of rounds of measurements, where the entanglement of the available qubit-pairs are not-necessarily equal. We further discuss the effect of possible imperfections that may arise in the protocol, and its robustness towards such imperfections. We demonstrate the usefulness of our proposal by applying it to create generalized GHZ states on arbitrary number of qubits, thereby underlining the possibility of creating maximally entangled qubit pairs via qubit-local projection measurements.

Distinguishable and non-distinguishable quantum states are fundamental resources in quantum mechanics and quantum technologies. Interactions with the environment often induce decoherence, impacting both the distinguishability and non-distinguishability between quantum states. In this paper, we investigate mixed unitary quantum channels and the conditions under which fidelity, a measure of quantum state closeness, is preserved. More precisely, for quantum channels in the form $\Phi(\rho) = \sum_{i=1}^N p_i U_i \rho U_i^*$, we analyze their effect on quantum state $|\varphi\rangle$ through the associated purification $|\Psi\rangle$, explore the structure of such quantum channels that preserve either distinguishable or non-distinguishable states and then discuss the challenges of maintaining fidelity, particularly under the influence of phase damping.

Compact scalar field theories on lattices are capable of describing a large class of many-body systems, such as interacting bosons, superconducting circuit networks, spin systems and more. We show that a generic quantum geometric many-body coupling induces quantized Chern couplings, implementing a lattice network version of a Florianini-Jackiw theory. Quantum geometry thus unlocks a direct mapping from scalar fields to anyons with fractional exchange phases, relevant for quantum error correction codes and quantum chemistry computation applications. In contrast to more familiar local Chern-Simons constructions with a uniform level, the compact-phase quantum geometry considered here yields pair-dependent topological couplings that can be nonlocal in node space and are encoded by a nonuniform first-Chern matrix. This feature introduces the notion of non-identical anyons, i.e., excitations that do not mutually satisfy the same exchange statistics. Such non-identical exchange statistics open up a microscopic pathway to a virtually unexplored class of non-local field theories breaking the Wigner superselection rule, allowing to explore non-local communication (all-to-all qubit gates) with local control.

Programmable neutral atom arrays show great promise for fault-tolerant quantum computing. A dominant physical error on this platform is qubit leakage and loss, notably decay errors from the Rydberg state during two-qubit gates. Such leakage events are particularly detrimental as they propagate, generating correlated errors that severely degrade the effective error distance of quantum error correction codes. Here, we present a novel approach to address Rydberg decay errors leveraging measurement-based quantum computation (MBQC). Our scheme strategically exploits the inherent geometric structure of topological cluster states and only uses final leakage detection information to locate propagated errors originating from Rydberg decay. This eliminates the need for complex and atom-species-specific mid-circuit leakage detection, offering broader applicability, e.g., to the well-established Rb atom platform. We demonstrate a high error threshold of 3.65\% per CZ gate for pure Rydberg decay and achieve a favorable error distance $d_e \approx d$. Our method compares favorably with state-of-the-art erasure conversion protocols in the sub-threshold performance, offering comparable or marginally larger logical error rates while significantly reducing experimental overhead.

The two-qubit controlled-not (C-NOT) gate is an essential component for gate-based quantum circuits. In fact, its operation, combined with single qubit rotations allows to realise any quantum circuit. Several strategies have been adopted in order to build quantum gates. Among them, photonics offers the dual advantage of excellent isolation from the environment and ease of manipulation at the single qubit level. Here we adopt a scalable time-multiplexed approach in order to build a fully reconfigurable architecture capable of implementing a post-selected C-NOT gate with a fidelity of $(93.8 \pm 1.4)\%$. We then show how our time-multiplexed platform can be employed to combine a C-NOT and a single qubit gate in order to generate the four Bell states.

This paper introduces a robust and scalable framework for implementing nested affine transformations in quantum circuits. Utilizing Hadamard-supported conditional initialization and block encoding, the proposed method systematically applies sequential affine transformations while preserving state normalization. This approach provides an effective method for generating combinatorial amplitude patterns within quantum states with demonstrated applications in combinatorics and signal processing. The utility of the framework is exemplified through two key applications: financial risk assessment, where it efficiently computes portfolio returns using combinatorial sum of amplitudes, and discrete signal processing, where it enables precise manipulation of Fourier coefficients for enhanced signal reconstruction.

We report on the characteristics of a microwave photon counter device based on a superconducting transmon qubit. Its design is similar to [arXiv:2307.03614], with an additional bandwidth tuning circuit that allows optimizing the device efficiency and noise. Owing to this new feature and to improvements in device fabrication, a power sensitivity of $3 \cdot 10^{-23} \mathrm{W}/\sqrt{\mathrm{Hz}}$ is reached. We confirm the high performance of the device by measuring single spin microwave fluorescence.

Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve universality for continuous variable measurement based quantum computation with only Gaussian measurements. For normalised states, the simplest hypergraph states are formed from $k$-adic interactions among a collection of $k$ harmonic oscillator ground states. However such powerful resources have not yet been observed in experiments and their robustness and scalability have not been tested. Here we develop and analyse necessary criteria for hypergraph nonclassicality based on simultaneous nonlinear squeezing in the nullifiers of hypergraph states. We put forward an essential analysis of their robustness to realistic scenarios involving thermalisation or loss and suggest several basic proof-of-principle options for experiments to observe nonclassicality in hypergraph states.

Qubit leakage and loss, particularly Rydberg-induced decay during two-qubit gates, pose significant challenges to fault-tolerant quantum computing with neutral atom arrays, as they propagate to correlated errors and degrade code distance. Here, we present a hardware-efficient scheme for addressing Rydberg decay using the SWAP-Leakage Reduction Circuit (SWAP-LRC) protocol, which leverages ancilla-data qubit swaps for in-line leakage mitigation. This strategy eliminates the need for atom-species-specific mid-circuit detection or additional ancillary qubits. Based on experimental detection capabilities, we present two specialized decoders. For detectable leakage/loss (e.g., in $^{171}$Yb), our Located Decoder achieves a high threshold of 2.33\% per CNOT gate and an improved error distance, significantly outperforming conventional Pauli error models. More interestingly, for scenarios where only one error type is detectable (e.g., atom loss for $^{87}$Rb), our Critical Decoder specifically targets and mitigates the most detrimental critical faults caused by correlated leakage, achieving an error distance comparable to standard Pauli errors. Our findings offer insights for handling complex non-Pauli errors for neutral atom quantum computation.

We study the two-point correlation functions and the bipartite entanglement in the ground state of the exactly-solvable variable-range extended Ising model of qubits in the presence of a transverse field on a one-dimensional lattice. We introduce the variation in the range of interaction by varying the coordination number, $\mathcal{Z}$, of each qubit, where the interaction strength between a pair of qubits at a distance $r$ varies as $\sim r^{-\alpha}$. We show that the algebraic nature of the correlation functions is present only up to $r=\mathcal{Z}$, above which it exhibits short-range exponential scaling. We also show that at the critical point, the bipartite entanglement exhibits a power-law decrease ($\sim\mathcal{Z}^{-\gamma}$) with increasing coordination number irrespective of the partition size and the value of $\alpha$ for $\alpha>1$. We further consider a sudden quench of the system starting from the ground state of the infinite-field limit of the system Hamiltonian via turning on the critical Hamiltonian, and demonstrate that the long-time averaged bipartite entanglement exhibits a qualitatively similar variation ($\sim\mathcal{Z}^{-\gamma}$) with $\mathcal{Z}$.

Frequency combs have revolutionized communication, metrology, and spectroscopy. Considerable efforts have been devoted to developing integrated combs, primarily leveraging Pockels or Kerr nonlinearities. Here, we demonstrate an alternative frequency comb generated via cavity Floquet engineering. By periodically modulating the cavity resonance frequency through a driven mechanical oscillator, a Floquet cavity with multiple equally spaced frequency components is created. These sidebands exhibit nearest-neighbor coupling and are phase-locked to the external modulation drive. A pump tone interacts with the pre-modulated cavity to generate the output frequency comb, which we implement in an on-chip microwave cavity optomechanical system. This approach operates independently of a pumping threshold and is insensitive to pump detuning. Consequently, it enables comb generation under far-sideband pumping with nanowatt-scale total power consumption, providing an ultra-low-power platform for integrated frequency comb synthesis.

In the present update work we consider properly defined two-parameter quasi-probability densities that, e.g., can be used as witness for quantum behaviour for a class of pure states as expressed in terms of a self-adjoint observable angular position and the corresponding angular momentum operator L. It is shown that negative values of the corresponding quasi-probability densities may reveal the quantum nature of superpositions of angular momentum eigenstates with a fractional mean value of L but in an ambiguous manner. For a suitable choice of parameters these quasi-probability densities are positive and are in accordance with Borns rule in quantum mechanics. It is also shown that experimental data of the uncertainties for the angular position and L observables can be sufficient to reveal some unique quantum-mechanical features of such states without necessarily making use of quasi-probability densities.

The fidelity and quantum nondemolition character of the dispersive readout in circuit QED are limited by unwanted transitions to highly excited states at specific photon numbers in the readout resonator. This observation can be explained by multiphoton resonances between computational states and highly excited states in strongly driven nonlinear systems, analogous to multiphoton ionization in atoms and molecules. In this work, we utilize the multilevel nature of high-$E_J/E_C$ transmons to probe the excited-state dynamics induced by strong drives during readout. With up to 10 resolvable states, we quantify the critical photon number of ionization, the resulting state after ionization, and the fraction of the population transferred to highly excited states. Moreover, using pulse-shaping to control the photon number in the readout resonator in the high-power regime, we tune the adiabaticity of the transition and verify that transmon ionization is a Landau-Zener-type transition. We further extend these methods to a typical transmon with $E_J/E_C \approx 55$ and probe the offset-charge dependence of ionization dynamics in a timed-resolved manner. Our experimental results agree well with the theoretical prediction from a semiclassical driven transmon model and may guide future exploration of strongly driven nonlinear oscillators.

We introduce a device-independent quantum key distribution protocol for N parties, using the multipartite Hardy paradox to certify genuine multipartite nonlocality. Unlike traditional multipartite protocols that extract the key from measurement outcomes, our approach generates the shared secret key directly from the parties' choices of measurement settings. This settings-based method, certified by the maximal violation of the multipartite Hardy paradox, achieves a positive key rate and offers a fresh perspective on secure key distribution. Notably, the Hardy paradox enables any two parties to create a secret key with a rate much higher than the N-party key, due to more robust pairwise correlations. This unique capability, inherent to the multipartite Hardy paradox, allows for tailored key distribution within the group, enhancing flexibility. Our work establishes a new paradigm for device-independent conference key agreement, where keys are generated directly from measurement settings using non-maximally entangled states. This approach ensures robust security in untrusted quantum networks and enables pairwise key rates that surpass the N-party rate, offering unprecedented flexibility in key distribution. By challenging conventional methods, it paves the way for scalable, noise-resilient multiparty quantum communication systems.

We propose using Point-to-Multipoint quantum key distribution (QKD) via time division multiplexing (TDM) and wavelength division multiplexing (WDM) in passive optical networks (PON) to improve the security of online voting systems.

We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a structured classical input. At the core of our algorithm lies the ability to efficiently construct the block-encoding of Laplacians (and persistent Laplacians) based on the classical description of the given complex. From such block-encodings, Betti numbers (and persistent Betti numbers) can be estimated. The complexity of our method is polylogarithmic in the number of simplices in both simplex-sparse and simplex-dense regimes, thus offering an advantage over existing works. Moreover, prior quantum algorithms based on spectral methods incur significant overhead due to their reliance on estimating the kernel of combinatorial Laplacians, particularly when the Betti number is small. We introduce a new approach for estimating Betti numbers based on homology tracking and homology property testing, which enables exponential quantum speedups over both classical and prior quantum approaches under sparsity and structure assumptions. We further initiate the study of homology triviality and equivalence testing as natural property testing problems in topological data analysis, and provide efficient quantum algorithms with time complexity nearly linear in the number of simplices when the rank of the boundary operator is large. In addition, we develop a cohomological approach based on block-encoded projections onto cocycle spaces, enabling rank-independent testing of homology equivalence. This yields the first quantum algorithms for constructing and manipulating r-cocycles in time polylogarithmic in the size of the complex. Together, these results establish a new direction in quantum topological data analysis and demonstrate that computing topological invariants can serve as a fertile ground for provable quantum advantage.

Within the "complexity=anything" proposal of holography, the complexity growth rate (CGR) can exhibit jumps, interpreted as phase transitions. We demonstrate that the location and amplitude of these jumps are governed by the dynamics of bulk fields, which, via the fluid-gravity correspondence, map to the boundary energy-momentum tensor. The behavior of the CGR near these critical points exhibits scaling and universality. We show that the CGR satisfies a Callan-Symanzik-like equation near the transitions. Our results provide a new information-theoretic interpretation of the Callan-Symanzik equation, with the CGR running with the energy scale.

Recent experiments demonstrated that the spin state of individual atoms on surfaces can be quantum-coherently controlled through all-electric electron spin resonance. By constructing interacting arrays of atoms this results in an atomic-scale qubit platform. However, the static exchange coupling between qubits, limited lifetime and polarization of the initial state, impose significant limits on high-fidelity quantum control. We address this issue using open quantum systems simulation and quantum optimal control theory. We demonstrate the conditions under which high-fidelity operations ($\mathcal{F} \gtrsim 0.9$) are feasible in this qubit platform, and show how the Krotov method of quantum optimal control theory adapts to specific noise sources to outperform the conventional Rabi drivings. Finally, we re-examine the experimental setup used in the initial demonstration of this qubit platform and propose optimized experimental designs to maximize gate fidelity in this platform.

With the advent of exquisite quantum emulators, storing highly entangled many-body states becomes essential. While entanglement typically builds over time when evolving a quantum system initialized in a product state, freezing that information at any given instant requires quenching to a Hamiltonian with the time-evolved state as an eigenstate, a concept we realize via an emergent Hamiltonian framework. While the emergent Hamiltonian is generically nonlocal and may lack a closed form, we show examples where it is exact and local, thereby enabling, in principle, indefinite state storage limited only by experimental imperfections. Unlike other phenomena, such as many-body localization, our method preserves both local and global properties of the quantum state. In some of our examples, we demonstrate that this protocol can be used to store maximally entangled multiqubit states, such as tensor products of Bell states, or fragile, globally distributed entangled states, in the form of Greenberger-Horne-Zeilinger states, which are often challenging to initialize in actual devices.

We analyze the tensor network loop cluster expansion, introduced in [G. Park, J. Gray, and G. K.-L. Chan, Phys. Rev. B 112, 174310 (2025)] as a systematic correction to belief propagation, in the context of general quantum many-body problems. We provide numerical examples of the accuracy and practical applicability of the approach for the computation of ground-state observables for high bond dimension tensor networks, in two- and three-dimensions, with open and periodic boundary conditions, and for spin and fermion problems. We find that the contraction error converges approximately exponentially with cluster size, enabling accurate local observable and energy estimates for many systems where standard contraction methods are otherwise impractical.

We study communication over a quantum action-dependent channel, where the transmitter first performs an action that "shocks" the channel environment, and subsequently encodes a message into a transmission sent through the channel. This two-stage interaction arises in various settings, including rewriting over defective memory and quantum effects such as measurement-induced state collapse. Our model can be viewed as a quantum generalization of Weissman's classical action-dependent channel (2010). Here, however, Alice cannot have a copy of the environment state due to the no-cloning theorem. Instead, she may share entanglement with this environment. We derive achievable rates for reliable message transmission via the quantum action-dependent channel, with either causal or non-causal channel side information (CSI). As a case study, we analyze memory storage with depolarization and selective rewriting, demonstrating how action-dependent control influences performance.

In this paper, we derive a new proof of security for the Extended B92 QKD protocol. We derive a general entropic uncertainty relation for QKD protocols with data filtering and rejection. Our bound requires one to determine the size of a particular set derived from a classical sampling strategy. Finally, we show how our methods can be used to readily prove security of the Extended B92 protocol, providing, to our knowledge, the first finite key proof of security for this protocol against general, coherent, attacks.

As atom-cavity systems are becoming more sophisticated, the limitations of the Jaynes-Cummings model are becoming more apparent. In this paper, we therefore take a more dynamical approach to the modelling of atom-cavity systems and do not reduce the electromagnetic field inside the resonator to a single mode. Our approach shows that the decay rate Gamma_cav of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate Gamma_free due to constructive interference effects of the emitted light. In general, however, we find that Gamma_cav = Gamma_free to a very good approximation which might explain why atom-cavity experiments with planar mirrors have not been able to operate in the so-called strong coupling regime.

In their recent work, Nature, {\bf 646}, 813 (2025), Aziz and Howl claim that classical (unquantized) gravity can generate entanglement of quantized matter if matter is treated within quantum field theory which is, no doubt, our ultimate theory to use. We show that the perturbative result of Aziz and Howl in interaction picture is inconsistent with our exact and simple non-perturbative derivation in Heisenberg picture, that fundamentally precludes the claimed entanglement.

Periodic driving enables the engineering of complex quantum matter, yet in interacting systems it generically leads to energy absorption, which limits the lifetime of the engineered states. To address this challenge, dynamical freezing has been proposed as a mechanism for stabilizing non-equilibrium states over parametrically long timescales. While theory predicts robust freezing under simplifying assumptions, realistic platforms inevitably include additional interaction processes that alter its stability. Here, we report the experimental observation of dynamical freezing in programmable Rydberg atom arrays of up to 100 atoms in one and two dimensions. We find that while single-frequency driving produces pronounced suppression of excitation dynamics, the freezing behavior is restricted to a narrow parameter regime due to interaction-induced heating channels present in realistic simulators. Using a perturbative Floquet analysis of the fully interacting atomic system, we identify the dominant microscopic heating processes responsible for this destabilization. Leveraging this understanding, we design a dual-parameter modulation of detuning and Rabi frequency that coherently cancels these absorption pathways and substantially broadens the freezing regime, making it also robust across different geometries. Our results reveal how heating processes shape the stability of dynamical freezing in interacting Floquet systems and demonstrates a route to control driven many-body dynamics in realistic experimental platforms.

Quantum asymmetry and coherence are genuinely quantum resources that are essential to realize quantum advantage in information technologies. However, all quantum processes are fundamentally constrained by quantum speed limits, which raises the question on the corresponding bounds on the rate of consumption of asymmetry and coherence. In the present work, we derive a formulation of the quantum speed limit for observables in terms of the trace-norm asymmetry of the time-dependent quantum state relative to the observable. This quantum speed limit can be directly observed in experiment through weak value measurement and provides a lower bound to the quantum Fisher information about the parameter conjugate to the observable. It can be further related to quantum coherence relative to the eigenbasis of the observable. We obtain a complementary relation for the speed of three mutually unbiased observables for a single qubit. As an application, we derive a notion of a quantum thermodynamic speed limit.

Quantum thermometry aims at determining temperature with ultimate precision in the quantum regime. Standard equilibrium approaches, limited by the Quantum Fisher Information given by static energy fluctuations, lose sensitivity outside a fixed temperature window. Non-equilibrium strategies have therefore been recently proposed to overcome these limits, but their advantages are typically model-dependent or tailored for a specific purpose. This Letter establishes a general, model-independent result showing that any temperature-dependent unitary driving applied to a thermalized probe enhances its quantum Fisher information with respect to its equilibrium value. Such information gain is expressed analytically through a positive semi-definite kernel of information currents that quantify the flow of statistical distinguishability. Our results, together with an analysis of the relation between information gain and control cost, are benchmarked on a driven spin-$1/2$ thermometer, furthermore showing that resonant modulations remarkably restore the quadratic-in-time scaling of the Fisher information and allow to shift the sensitivity peak across arbitrary temperature ranges.

Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary features in time evolution are growing and yet limited in scalability and controllability. We develop here a general theory to control an arbitrary number of bosonic modes under time-dependent non-Hermitian Hamiltonian. Far beyond the subspace of few excitations, our control theory operates in the Heisenberg picture and exploits the gauge potential underlying the instantaneous frames rather than the eigenspectrum. In particular, instantaneous frames are defined by time-dependent ancillary operators as linear combinations of the laboratory-frame operators, while the gauge potential arises from the unitary transformation between the time-dependent and stationary ancillary frames. We find that upper triangularization condition of the non-Hermitian Hamiltonian's coefficient matrix in the stationary ancillary frame yields two nonadiabatic passages in both bra and ket spaces and also the exact solutions of the time-dependent Schrödinger equation. At the end of these passages, probability conservation of wave function is automatically restored without brute-force normalization. Our theory is exemplified by perfect and nonreciprocal state transfers in a cavity magnonic system under non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation with all quantum-jump terms retained. Under certain conditions, perfect state transfer holds for arbitrary initial states and is irrelevant to both parity-time symmetry of coefficient matrix and exceptional points of eigenspectrum. The nonreciprocal transfer is consistent with coherent perfect absorption, providing a first-principles route to coherent control of non-Hermitian continuous-variable systems.

We show that the standard approach to characterize collective entanglement via genuine multiparty entanglement (GME) leads to an area law in ground and thermal Gibbs states of local Hamiltonians. To capture the truly collective part one needs to go beyond this short-range contribution tied to interfaces between subregions. Genuine network multiparty entanglement (GNME) achieves a systematic resolution of this goal by analyzing whether a $k$-party state can be prepared by a quantum network consisting of $(k-1)$-partite resources. We develop tools to certify and quantify GNME, and benchmark them for GHZ, W and Dicke states. We then study the 1d transverse field Ising model, where we find a sharp peak of GNME near the critical phase transition, and rapid suppression elsewhere. Finite temperature leads to a faster death of GNME compared to GME. Furthermore, certain 2d quantum spin liquids do not have GNME in microscopic subregions while possessing strong GME. This approach will allow to chart truly collective entanglement in quantum matter both in and out of equilibrium.

Illegal, unreported, and unregulated (IUU) fishing causes global economic losses of 10-25 billion USD annually and undermines marine sustainability and governance. Synthetic Aperture Radar (SAR) provides reliable maritime surveillance under all weather and lighting conditions, but classifying small maritime objects in SAR imagery remains challenging. We investigate quantum machine learning for this task, focusing on quantum kernel methods (QKMs) applied to real and complex SAR chips extracted from the SARFish dataset. We tackle two binary classification problems, the first for distinguishing vessels from non-vessels, and the second for distinguishing fishing vessels from other types of vessels. We compare QKMs applied to real and complex SAR chips against classical Laplacian, RBF, and linear kernels applied to real SAR chips. We restrict the comparison to be between just kernel based models so that the comparison is as fair and meaningful as possible. Using noiseless numerical simulations of the quantum kernels, we find that with the real SAR chips, QKMs are capable of obtaining equal or better performance than the classical kernels in the best case. However, the specific quantum kernel used to encode the complex SAR data overfits and performs poorly. This work presents the first application of QKMs to maritime classification in SAR imagery and offers insight into the potential and current limitations of quantum-enhanced learning for maritime surveillance.

Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme that enables multiple parties to share quantum uncertainty, in terms of the max relative entropy, generated by a single party. Our scheme is based upon maximum-confidence measurements and takes advantages of weak measurements to allow a number of parties to perform state discrimination on a single quantum system. We review known sequential state discrimination and show how our scheme would work through a number of examples where ensembles may or may not contain symmetries. Our results will have a role to play in understanding the ultimate limits of sequential information extraction and guide the development of quantum resource sharing in sequential settings.

Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine learning kernels, and other advanced quantum algorithms. Existing state-of-the-art techniques, including Qubitization, Quantum Singular Value Transformation (QSVT), and Quantum Signal Processing (QSP), rely heavily on block-encoding the Hermitian matrix. These methods are often constrained by the complexity of preparing the block-encoded state, the overhead associated with the required ancillary qubits, or the challenging problem of angle synthesis for the polynomial's phase factors, which limits the achievable circuit depth and overall efficiency. In this work, we propose a novel and resource-efficient approach to implement arbitrary polynomials of a Hermitian matrix by leveraging the Generalized Quantum Signal Processing (GQSP) framework. Our method circumvents the need for block-encoding and avoids the compounding post-selection overheads characteristic of LCU-based constructions, achieving a stable, degree-independent success probability. We derive closed-form expressions for symmetric polynomial expansions and demonstrate how linear combinations of GQSP circuits can realize the desired transformation. This approach reduces resource overhead and opens new pathways for quantum algorithm design for functions of Hermitian matrices, particularly in settings where the Hermitian operator arises naturally from symmetric combinations of unitaries.

This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. We introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels, following a similar approach as of Zou et al. (2015) on classical secret sharing. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.

Halls exact variance decomposition [Phys. Rev. A 64, 052103 (2001)] splits the quantum variance of an observable into the ensemble variance of an optimal position based estimate and a residual nonclassical inaccuracy. We evaluate this decomposition in Bohmian mechanics. For momentum, the optimal estimate coincides with the Bohmian guidance field, and the inaccuracy is proportional to the ensemble average of the quantum potential. This gives a variance level identity separating momentum fluctuations into classical statistical dispersion and a quantum contribution from amplitude variations. The real and imaginary parts of the weak value map directly onto the two decomposition terms. By contrast, the inaccuracy vanishes for spin. This distinction is traced to the kinematic status of velocity in the primitive ontology, showing how the decomposition distinguishes observables dynamically coupled to local beables from merely contextual ones.

Thermodynamic trade-off relations dictate fundamental limits on the performance of thermodynamic tasks through costs such as heat dissipation. Here, we propose a framework called thermodynamic recycling to circumvent these limits in quantum processors by exploiting failure branches of quantum algorithms, which are usually discarded. The key component is an athermal bath naturally generated during the resetting of a failure branch. By coupling this bath to a target system prior to relaxation, thermodynamic tasks can be performed beyond conventional thermodynamic limits. We apply this framework to information erasure and derive the reduction in heat dissipation analytically. As a demonstration, we implement our framework on IBM's superconducting quantum processor by combining the Harrow--Hassidim--Lloyd algorithm with three-qubit quantum error correction, thereby reducing the heat dissipated in erasing syndrome information. Despite substantial noise and errors in current hardware, our method achieves erasure with heat dissipation below the Landauer limit. This work establishes an operational connection between quantum computing and quantum thermodynamics for resource-efficient quantum computation.

It is commonly thought that observers in distinct branches of an Everettian multiverse cannot communicate without violating the linearity of quantum theory. Here we show a counterexample, demonstrating that inter-branch communication is in fact possible, entirely within standard quantum theory. We do this by considering a Wigner's-friend scenario, where an observer (Wigner) can have quantum control over another observer (the friend). We present a thought experiment where the friend in superposition can receive a message written by a distinct copy of themselves in the multiverse, with the aid of Wigner. To maintain the unitarity of quantum theory, the observers must have no memory of the message that they sent. Our thought experiment challenges conventional wisdom regarding the ultimate limits of what is possible in an Everettian multiverse. It has a surprising potential application which involves using knowledge-creation paradoxes for testing Everettian quantum theory against single-world theories.

Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to their geometric locality and practical relevance. In these codes, stabilizer measurements yield a syndrome that must be decoded into a recovery operation, making decoding a central bottleneck for scalable real time operation. Existing decoders are commonly classified into two categories. Classical algorithmic decoders provide strong and well established baselines, but may incur substantial computational overhead at large code distances or under stringent latency constraints. Machine learning based decoders offer fast GPU inference and flexible function approximation, yet many approaches do not explicitly exploit the lattice geometry and local structure of topological codes, which can limit performance. In this work, we propose QuantumSMoE, a quantum vision transformer based decoder that incorporates code structure through plus shaped embeddings and adaptive masking to capture local interactions and lattice connectivity, and improves scalability via a mixture of experts layer with a novel auxiliary loss. Experiments on the toric code demonstrate that QuantumSMoE outperforms state-of-the-art machine learning decoders as well as widely used classical baselines.

Two applications of gates from the B gate equivalence class can generate all two-qubit gates. This local equivalence class is invariant under the mirror (multiplication with the SWAP gate) operation, inverse (Hermitian conjugate) operation, and the combined inverse and mirror operations. The last two symmetries are associated with the ability of a two-qubit gate to generate the two-qubit local gates and the SWAP gate in two applications. No single local equivalence class of two-qubit gates, except the B gate equivalence class, has these two symmetries. Only the planar regions of the Weyl chamber, describing the mirror operation, contain the local equivalence classes with either one of the two symmetries. We show that there exist one-parameter families of local equivalence classes on these planes, with and without the B gate equivalence class, such that each of them can be used to construct a parameterized universal two-qubit quantum circuit that involves only two nonlocal two-qubit gates. We also discuss the implementation of the gates from a few families of local equivalence classes on superconducting quantum computers for optimal generation of all two-qubit gates. We provide upper bounds on the number of two-qubit gates required to generate an arbitrary $n$-qubit gate for two families, each of which is conjectured to generate all two-qubit gates in two applications. We show that there exists a positive correlation between the area of the convex hull of the squared eigenvalues of the nonlocal part of a parameterized two-qubit gate and the fractional volume of the Weyl chamber covered in two applications of the parameterized two-qubit gate for two families of local equivalence classes.

We unveil a fundamental temperature bias in transient quantum thermometry under Markovian dynamics. For qubit probes evolving in a thermal Markovian environment, we prove that transient precision beyond the steady-state benchmark can be achieved if and only if the probe is initially colder than the bath temperature to be estimated. Cold probes are therefore both necessary and sufficient for enhanced transient precision in the Markovian regime. We then investigate the fate of this bias in the presence of environmental memory. In particular, in a non-Markovian scenario generated by an auxiliary-mediated system-bath coupling, we find that the cold-probe requirement for enhanced transient precision persists, indicating that the temperature bias survives certain forms of memory effects. In contrast, for a non-Markovian collisional model with perfect swap interactions between bath ancillas, transient enhancement is entirely absent regardless of the probe's initial temperature. This indicates that strong non-Markovianity can lead to the complete disappearance of the enhancement effect, placing hot and cold probes on equal footing, with neither capable of achieving enhanced precision in this regime.

Engineering quantum tunnelling in phase space has emerged as a viable method for creating a protected logical qubit manifold with biased-noise properties. A promising approach is to combine a Kerr nonlinearity with a multi-photon drive, resulting in a system known as a Kerr parametric oscillator (KPO). In this work, we implement a three-photon KPO and explore its potential as a protected bosonic qutrit. We confirm quantum coherence by demonstrating three-photon Rabi oscillations and performing direct Wigner function measurements that reveal the formation of three-component cat-like states. Crucially, we observe a breathing-like dynamic in phase space, a characteristic feature of driven quantum systems. This dynamic arises from macroscopic temporal interference between the cat-qutrit manifold and the excited states. The frequency of resulting oscillations in the mean photon number provides a direct, time-domain measurement of the energy gap separating the qutrit from the excited states, thereby establishing an experimental hallmark of qutrit manifold protection. Furthermore, we identify a parasitic higher-order pump term as the primary mechanism constraining the mean photon number, highlighting its mitigation as a requisite for maximising protection. Our findings elucidate the basic quantum properties of the three-photon KPO and establish the first step towards its use as an alternative qutrit platform.

Prompted by the longstanding interpretational controversy in quantum mechanics, quantum tunneling is heuristically addressed within the Everettian quantum multiverse. In this framework, the universal wavefunction splits into decohered reflected and transmitted branches under the environmetal effect after encountring a potential barrier. The observed tunneling is then experienced by the observer located in a tunneled world. The tunneling probability and the tunneling time are investigated in terms of the tunneled world relative weights and the branching duration, respectively. The macroscopic quantum tunneling, recently honored, is also discussed and the corresponding macroscopic tunneling time is approached based on the obtained results and known data.

Non-Hermitian degeneracies of Lindblad generators (Liouvillian exceptional points) can induce non-exponential relaxation and higher-order poles in dynamical response functions. A collective spin coupled to a polarized Markovian bath exhibits an \emph{exceptional spectral phase} in which defective Liouvillian modes imprint super-Lorentzian features in frequency-resolved spectra. We compute the emission spectrum via the Liouvillian resolvent, identify symmetry-sector selection rules, and demonstrate that exceptional-point signatures are strongly state-dependent: they are suppressed in steady-state fluorescence yet become unambiguous for generic (infinite-temperature or random) initial states. Our results provide an experimentally accessible spectroscopic diagnostic of many-body Liouvillian exceptional phases and clarify when steady-state emission can (and cannot) reveal them.

We investigate the quantum dynamics of ligand--receptor electron transfer and conformational response in a prototypical viral binding complex, using the SARS-CoV-2 Spike protein bound to the human ACE2 receptor as a model system. Treating the ACE2--Spike interface as an open quantum system embedded in a biological environment, we simulate how vibrational interactions and environmental memory reshape the coupled receptor--ligand dynamics and modulate vibrationally assisted electron transfer (VA-ET). Using a Non-Markovian Stochastic Schr"odinger Equation (NMSSE) approach, we simulate electron transfer between donor and acceptor states in ACE2 modulated by a specific vibrational mode of the Spike protein. The influence of environmental memory (non-Markovian dynamics) and non-Condon effects (vibrational modulation of electronic coupling) are analyzed in detail. In the Markovian limit with an Ohmic bath, population dynamics reduce to exponential kinetics, and extracted transfer rates agree with semiclassical Marcus--Jortner predictions in the appropriate regime. Beyond the Markovian, high-temperature limit, we observe clear deviations: non-exponential decay, coherent oscillatory features, and enhanced sensitivity to the vibrational frequency. Incorporating off-diagonal system--bath coupling alongside diagonal coupling shows that nuclear motion can dynamically gate electron tunneling, sharpening the frequency selectivity of the VA-ET mechanism. Finally, a structured (sub-Ohmic) environmental spectral density with long-lived correlations (``memory'') preserves electronic--vibrational coherence over longer times, amplifying vibrational selectivity under non-Condon coupling. Our results support the proposition that ACE2--Spike binding may exploit vibrational assistance and quantum coherence as a molecular recognition mechanism.

On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive potentials that are steeper than the quadratic ones, give rise to normalizable eigenstates, which may be considered as a manifestation of effective self-trapping in the linear system. These states constitute full continuous spectra in both the 1D and 2D cases. In 1D, they are spatially even and odd eigenstates. The 2D states may carry any value of the vorticity (alias magnetic quantum number). Asymptotic expressions for wave functions of the 1D and 2D eigenstates, valid far from the center, are derived analytically, demonstrating excellent agreement with full numerical solutions. Special exact solutions for vortex states are obtained in the 2D case. These findings suggest an extension of the concept of bound states in the continuum, in quantum mechanics and paraxial photonics. Gross-Pitaevskii equations are briefly considered as the nonlinear extension of the 1D and 2D settings. In 1D, the cubic nonlinearity slightly deforms the eigenstates, maintaining their stability

The transition probability of a spin driven by a rotating magnetic field is reformulated. This work shows that, once projection onto the measurement basis is properly accounted for, the laboratory measured probability is governed by both intrinsic spin dynamics and the time dependence of the measurement basis. For the rotating-field eigenbasis, this yields an additional kinematic modulation, leading to measurable deviations under strong driving. A unified probability expression is derived that subsumes the classic 1937 and 1954 formulations as limiting cases, while correcting the conventional treatment of magnetic resonance transitions.

Randomized compiling (RC) is an established tool to tailor arbitrary quantum noise channels into Pauli errors. The effect of both spatial and temporal noise correlations in randomly compiled circuits, however, is not fully understood. Here, we show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the circuit fidelity of randomly compiled circuits. Surprisingly, we show that this fidelity is always increased by the presence of correlations, suggesting that correlations are a resource in randomly compiled circuits. To leading order in system-bath coupling, we also show that RC suppresses the quantum component of bath correlations, implying that one can safely treat weak noise as being classical. Finally, through extensive numerical simulations, we show that our results remain valid for many relevant non-Clifford circuits. These results clarify how RC mitigates memory effects and enhances circuit robustness.

We demonstrate that absolutely maximally entangled (AME) states consisting of $N=4n$ qudits with $n\in\{1,2,3,...\}$, each of even local dimension, cannot be realized as graph states. This result imposes strong constraints on AME states in composite local dimensions and characterizes the limitations of graph-state constructions for highly entangled multipartite quantum systems. In particular, this study provides an independent solution of the recently discussed case of the AME state of four quhexes and clarifies its characterization within the stabilizer formalism, complementing the results found recently in [H. Cha, arXiv:2603.13442]. At the same time, we provide a general construction for mixed $k$-uniform states whose purity is determined by the optimal stabilizer representations. For the specific case of $(N=4,d=6)$, this yields a mixed AME state of optimal purity $1/2$, not subject to canonical graph-state constraints.

The use of Bohmian mechanics as a practical tool for modeling non-relativistic quantum phenomena of matter provides clear evidence of its success, not only as a way to interpret the foundations of quantum mechanics, but also as a computational framework. In the literature, it is frequently argued that such a realistic view-based on deterministic trajectories cannot account for phenomena involving the "creation" and "annihilation" of photons. In this paper, by revisiting and rehabilitating earlier proposals, we show how quantum optics can be modeled using Bohmian trajectories for electrons in physical space, together with well-defined electromagnetic fields evolving in time. By paying special attention to an experiment demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it vindicates the pedagogical use of this simple Bohmian framework to compute, understand, and visualize quantum electrodynamics phenomena. Second, given that measurements are ultimately indicated on matter pointers, it clarifies what it means to measure photon or electromagnetic-field properties, even when they are considered non-ontic elements.

Fair threshold estimation for bivariate bicycle (BB) codes on the quantum erasure channel runs into two recurring problems: decoder-baseline unfairness and the conflation of finite-size pseudo-thresholds with true asymptotic thresholds. We run both uninformed and \emph{erasure-aware} minimum-weight perfect matching (MWPM) toric code baselines alongside BP-OSD decoding of BB codes. With standard depolarizing-weight MWPM and no erasure information, performance matches random guessing on the erasure channel in our tested regime -- so prior work that compares against this baseline is really comparing decoders, not codes. Using 200{,}000 shots per point and bootstrap confidence intervals, we sweep five BB code sizes from $N=144$ to $N=1296$. Pseudo-thresholds (WER = 0.10) run from $p^* = 0.370$ to $0.471$; finite-size scaling (FSS) gives an asymptotic threshold $p^*_\infty \approx 0.488$, within 2.4\% of the zero-rate limit and without maximum-likelihood decoding. On the fair baseline, BB at $N=1296$ has a modest edge in threshold over the toric code at twice the qubit count, and a 12$\times$ lower normalized overhead -- the latter is where the practical advantage sits. All runs are reproducible from recorded seeds and package versions.

In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all $N$. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by $N$. We also touch upon the question of the complexity of SSP, and multiparty entanglement.

We extend Quantum Computing Quantum Monte Carlo (QCQMC) beyond ground-state energy estimation by systematically constructing the quantum circuits used for state preparation. Replacing the original Variational Quantum Eigensolver (VQE) prescription with task-adapted unitaries, we show that QCQMC can address excited-state spectra via Variational Fast Forwarding and the Variational Unitary Matrix Product Operator (VUMPO), combinatorial optimization via a symmetry-preserving VQE ansatz, and finite-temperature observables via Haar-random unitaries. Benchmarks on molecular, condensed-matter, nuclear-structure, and graph-optimization problems demostrate that the QMC diffusion step consistently improves the energy accuracy of the underlying state-preparation method across all tested domains. For weakly correlated systems, VUMPO achieves near-exact energies with significantly shallower circuits by offloading optimization to a classical tensor-network pre-training step, while for strongly correlated systems, the QMC correction becomes essential. We further provide a proof-of-concept demonstration that Haar-random basis state preparation within QCQMC yields finite-temperature estimates from pure-state dynamics.

We experimentally demonstrate local robust shadows on a trapped-ion quantum computing system, a protocol developed to counteract measurement errors. We alternate between a calibration stage and the shadow estimation stage and also introduce Pauli-X-twirling before measurements in both stages to symmetrize error rates. We then demonstrate the protocol on a trapped-ion quantum computer with artificially shortened measurement pulse duration. This yields faster experiments at the cost of increased error rates which are subsequently mitigated by the robust shadow protocol. We benchmark this approach on three exemplary quantum states: a local Haar random state, as well as standard and Pauli-correlation-encoded QAOA states. In all three cases, the local robust shadow protocol succeeds at mitigating the increased error rates hailing from shorter measurement pulse durations.

Beyond ground state energy estimation, quantum phase estimation (QPE) applied to many-electron systems has the potential to output an approximation of the ground state, enabling in a second step an evaluation of observables other than the energy. We here focus on the impact of approximate controlled-unitaries implementations on QPE precision. After recalling the role of the QPE free parameters, we derive first-order and unified conditions on the unitaries that are necessary to control the QPE energy estimation precision together with the QPE output state precision, important in case we want to leverage the full potential of QPE. We apply these conditions to a Trotterization case, leading to tighter or more general bounds than in previous works. The main results in this article are formal. First numerical illustrations on the H2 molecule provide useful insights.

We find that rank deficiency of the local Hamiltonian in a classically fragmented model is the key mechanism leading to quantum Hilbert space fragmentation. The rank deficiency produces local null directions that can generate entangled frozen states (EFS): entangled states embedded in mobile classical Krylov sectors that do not evolve under Hamiltonian dynamics. When the entangled frozen subspace is non-empty, the mobile classical sector splits into a mobile quantum Krylov subspace and an entangled frozen subspace, and the model exhibits quantum fragmentation. We establish this mechanism in four models of increasing symmetry structure: an asymmetric qubit projector with no symmetry, the $\mathbb{Z}_2$-symmetric GHZ projector, a $\mathbb{Z}_3$-symmetric cyclic qutrit projector, and the Temperley-Lieb model. For the asymmetric and GHZ projector models, we obtain closed-form expressions for irreducible Krylov dimensions, degeneracies, and sector multiplicities. The all-mobile-sector EFS in these two models exhibits a sub-volume-law bipartite entanglement entropy scaling as $S \sim \sqrt{L}$. Further, we introduce the notion of weak and strong quantum fragmentation, the quantum counterpart of the weak-strong distinction in classical fragmentation. After removing the EFS, the mobile quantum Krylov subspace decomposes into irreducible blocks. In the weak case, the number of irreducible blocks remains $O(1)$, each is individually ergodic with Gaussian Orthogonal Ensemble (GOE) level statistics, and the unresolved spectrum follows an $m$GOE distribution. In the strong case, the number of irreducible blocks grows with system size, and the gap-ratio distribution approaches Poisson as $L\to\infty$.

Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends on the data encoding. For address/amplitude encodings such as FRQI, a pixel shift acts as modular addition on an index register, whereas many MERA-inspired QCNNs are equivariant only under cyclic permutations of physical qubits. We formalize this mismatch and construct QCNN layers that commute exactly with the pixel cyclic shift (PCS) symmetry induced by the encoding. Our main technical result is a constructive characterization of all PCS-equivariant unitaries: conjugation by the quantum Fourier transform (QFT) diagonalizes translations, so any PCS-equivariant layer is a Fourier-mode multiplexer followed by an inverse QFT (IQFT). Building on this characterization, we introduce a deep PCS-QCNN with measurement-induced pooling, deferred conditioning, and inter-layer QFT cancellation. We also analyze trainability at random initialization and prove a lower bound on the expected squared gradient norm that remains constant in a depth-scaling regime, ruling out a depth-induced barren plateau in that sense.

Periodically driven quantum systems can exhibit subharmonic response, usually characterized through physical observables and often discussed in interacting settings. Here we show that a sharp subharmonic signature already appears in the entanglement spectrum of a number-conserving free-fermion system. We study a two-step driven Su-Schrieffer-Heeger chain whose Floquet operator supports symmetry-protected edge modes at quasienergies $0$ and $\pi$. When the initial state is a coherent superposition of these two edge sectors, we show that the subsystem correlation matrix alternates between two stroboscopic structures, and the entanglement spectrum is period-doubled as a set, while an overlap-tracked entanglement level shows a robust period-doubling response with Fourier weight concentrated at half the drive frequency. By contrast, diagonal edge densities remain flat by sublattice symmetry, while an off-diagonal edge-bond observable provides the corresponding linear one-body comparator. The effect disappears both when the initial state is replaced by a stroboscopically stationary Floquet eigenstate built from the same topological mode content, and when the system is placed in the topologically trivial phase where no edge modes exist. Altogether, these establish zero-$\pi$ Floquet topology as a necessary condition and coherent nonequilibrium preparation as the additional sufficient ingredient. Our results identify entanglement spectroscopy as a sharp subsystem-resolved probe of Floquet topological coherence.

This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a two-fold way. The first part is devoted in establishing an exact correspondence between quantum evolution and classical Hamiltonian flow on a Kahler manifold. This correspondence enables a geometric quantization scheme that identifies a family of classical Hamiltonian systems admitting exponentially compressed quantum representations-appropriate for quantum simulation. In the second part we demonstrate that Liouville-integrable Hamiltonian dynamics induce finite-dimensional unitary evolution through action-angle variables and Koopman-von Neumann encoding. This allows efficient quantum representation and parallel evolution of large phase-space ensembles, where entangled encodings provide exponential compression in ensemble size and enable quantum speed-ups in observable estimation via amplitude estimation techniques. For non-integrable systems, Lie canonical perturbation theory is incorporated to construct near-symplectic transformations that map dynamics to approximately integrable forms, preserving unitary evolution up to a controlled error. We derive the resulting quantum computational complexity of the proposed quantum-symplectic scheme, revealing both an exponential compression in memory requirements and a potential polynomial speed-up with respect to the system size. Finally, the transport evolution equation governing the quantum phase-space observables is obtained.

The efficient execution of fault-tolerant quantum algorithms is fundamentally limited by the production rate of magic states required for non-Clifford operations. While circuit optimization typically targets T-depth, static T-depth does not reliably predict executable performance under bounded T-state delivery. We introduce a model that captures demand-supply imbalance using two key quantities: slack ratio, a structural indicator of scheduling flexibility, and Delta_max, a measure of cumulative demand surplus. We show that Delta_max is a strong schedule-level indicator of execution slowdown and yields a provable lower bound on executable makespan for a fixed schedule. Empirical evaluation on constructed directed acyclic graph (DAG) families, with arithmetic circuits and exact quantum Fourier transform (QFT) traces providing additional grounding, shows that slack ratio is a stronger structural predictor than T-depth for stall and inversion risk, while Delta_max is the strongest predictor of slowdown. Across 4,904 instances, the lower bound shows zero violations, with 88.9% of cases within one cycle. These results highlight the importance of explicitly modeling delivery constraints in fault-tolerant quantum compilation.

Closed chaotic quantum systems relax after a quench into a Gibbs ensemble. At late times, the relaxation speed is determined by their conservation laws and hydrodynamics. As a result, there exist pairs of initial states which thermalize to the same ensemble, yet exhibit drastically different hydrodynamic relaxation. We show in two chaotic spin chains how this enables a simple and robust realization of the quantum Mpemba effect: a system initially closer to equilibrium relaxes slower than one that starts farther away, despite both approaching the same final state.

We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the physical eigenvalue spectrum can be compared. We explain the ideas of the symmetry classification of symmetric matrix spaces and how that yields Dyson's threefold and Altland-Zirnbauer's tenfold way. We also outline how the joint probability density function of the eigenvalues can be calculated from a given probability density function on the matrix space. Furthermore, we dive into the subtleties of the unfolding procedure. For this purpose, we explain the ideas of the local mean level spacing, the local level spacing distribution and the $k$-point correlation functions. We outline the techniques of orthogonal polynomials, determinantal and Pfaffian point processes and their related Fredholm determinants and Pfaffians as well as the supersymmetry method. Moreover, we relate the local spectral statistics to effective Lagrangians that give the relation to non-linear $\sigma$-models. In all these discussions, we also make brief excursions to non-Hermitian random matrix theory which are useful when studying open quantum systems, for instance.

We establish a rigorous bundle isomorphism between the complex velocity field \(\eta_{\mu} = \pi_{\mu} - i u_{\mu}\), obtained by averaging matter dynamics over stochastic gravitational fluctuations, and the symmetric logarithmic derivative (SLD) operator \(L_{\mu}\) of quantum estimation theory. The isomorphism \(\widetilde{\mathcal{T}}: \Gamma(E/{\sim}) \to \Gamma(\mathcal{L})\) maps gauge-equivalence classes of sections of the pullback bundle \(E = \pi_2^*(T^*M)\) over \(\mathcal{C} \times M\) to SLD operators on the Hilbert space \(\mathcal{H}_0 = L^2(\mathcal{C}, \nu_0)\), where \(\mathcal{C}\) is the infinite-dimensional Fréchet manifold of matter fields and \(\nu_0\) is a fixed Gaussian measure. We prove that \(\widetilde{\mathcal{T}}\) and the associated quantum Fisher metric are independent of the choice of \(\nu_0\), rendering the construction intrinsic to the physical probability density. The Fisher metric acquires a simple form in terms of \(\eta_{\mu}\): \(g_{\mu\nu}^{\mathrm{FS}} = -\frac{4m^2}{\hbar^2} \operatorname{Re}\langle(\eta_{\mu} - \langle\eta_{\mu}\rangle) (\eta_{\nu} - \langle\eta_{\nu}\rangle)\rangle_{\mathcal{P}}\). As a consequence, the flat \(U(1)\) connection defined by \(\eta_{\mu}\) yields a quantized holonomy for non-contractible spacetime loops, predicting topological phases observable in atom interferometry.

One intriguing property of non-Hermitian systems is the breakdown of adiabatic theorem and chiral state conversion as the system dynamically encircles exceptional points. However, the subtle dependence of the chiral dynamics on the loop geometry, the starting point, the encircling speed and especially the noise has not been studied systematically. Here we propose a non-chirality degree $\chi_c$ to measure the chirality quantitatively and analyze it in dynamics without noise by exact solution and dynamics with noise by numerical integration. The exact dynamics starting from the broken phase show chirality oscillations, which are extremely sensitive to noise when the speed is small. The encircling speed and the noise strength are found to compete with each other in determining $\chi_c$, resulting in two distinguished limits, namely the noisy limit and the clean limit. The critical boundary between the two limits satisfies a simple scaling law, which could be explained in terms of first-order perturbation theory and the condition number of the transfer matrix. Our findings reveal the essential role played by noise in non-Hermitian dynamics and are relevant for both theoretical and experimental investigations.

We provide a complete structural characterization of perfect quantum strategies for arbitrary quantum magic rectangle games. We derive necessary and sufficient conditions that jointly constrain the shared state and measurement operators, establishing a unified analytical framework for perfect nonlocal strategies in this setting. Our results show that all perfect quantum solution states (PQSS) must exhibit a specific algebraic--combinatorial structure, ruling out a priori assumptions about particular entangled resources and clarifying the full class of states compatible with perfect correlations. We further show that perfect quantum strategies do not exist for $2 \times n$ quantum magic rectangle games with odd $n$, and introduce a corresponding quantum magic rectangle inequality to characterize optimal non-perfect strategies. While our results are structural, they may provide a foundation for future developments in quantum information and quantum cryptography based on perfect nonlocal correlations.

The quantum instrument (QI) formalism is required to model mid-circuit measurements (MCMs) and the dependence of the post-measurement state on the measurement outcome. Correctly modeling QIs is essential for applications using MCMs, such as adaptive circuits and quantum error correction. Although QIs yield a joint quantum-classical state after measurement, errors in QIs can still be represented by a $d^2 \times d^2$ superoperator (e.g., process or transfer matrix) for each outcome, just as superoperators describe Markovian errors on unitary gates. However, because the joint quantum-classical system has a distinct error model for each outcome, this complicates the usual interpretation of process- or transfer-matrix error models. This Note offers practical guidance on understanding and interpreting QI error models.

Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected surface code coupled to a continuous, un-reset quantum environment at zero and finite temperature. Using the generalized Caldeira-Leggett framework, we map the long-time evolution of the logical qubit to a boundary conformal field theory, establishing an exact equivalence to the anisotropic Kondo model. We evaluate computational times for a finite code distance $L$ for all spatial and temporal correlations. Our analysis reveals that a true thermodynamic threshold exists strictly for short-range environments ($z>1/(s+1)$). In critical or long-range regimes, the macroscopic footprint of the code weaponizes the continuous bath, hindering the topological protection.

This work investigates the emergent thermalization regimes in a chaotic Tavis-Cummings (TC) model and their implications in quantum spectroscopy. While the TC model is a cornerstone of cavity quantum electrodynamics, traditional treatments often overlook many-body effects that arise in the thermodynamic limit. We utilize the Eigenstate Thermalization Hypothesis to demonstrate that a non-integrable excitonic Hamiltonian within the material manifold drives local thermalization. By tuning the polariton splitting $g$, we observe two dynamical regimes: a thermalizing regime at low interactions driven by quantum chaos and ergodicity, and a non-thermalizing regime at high interactions where strong coupling suppresses ergodicity. We further show that these regimes have direct implications on output photon statistics, specifically influencing the correlation times $\tau_c$ of the cavity population and the second-order correlation function $g^{(2)}(t+\tau)$. We propose that entangled-biphoton spectroscopy serves as an ideal experimental platform to probe these effects and to allow the characterization of the underlying many-body exciton-coupling disorder $\sigma$ through coincidence measurements of the output. Taken together, these results exploit a naturally occurring many-body phenomenon to bridge theoretical predictions with experimental observables.

Optimal quantum linear equation solvers provide complexity $O(\kappa\log(1/\epsilon))$, where $\kappa$ is the condition number and $\epsilon$ is the allowable error. The optimal solver using a discrete adiabatic approach [PRX Quantum 3, 040303 (2022)] has large analytically proven constant factors for the upper bound on the complexity. The constant factors were later found to be about 1,200 times smaller in numerical testing [Quantum 9, 1887 (2025)]. This meant it is about an order of magnitude more efficient than using a randomised approach from [PRX Quantum 6, 040373 (2025)], which has far smaller analytically proven constant factors. Recently, a ``Shortcut'' method has been found to provide an optimal solver which also has small proven constant factors. In the present work, we conduct a comprehensive numerical analysis comparing this method with the adiabatic solver for two families of random linear systems. We find that, in the case where the solution norm is unknown, the adiabatic solver provides slightly better performance. If the solution norm is known, then the shortcut method provides significantly better performance for non-Hermitian matrices.

The conservation law for the orbital plus spin angular momentum of a free Dirac particle in curved spacetime requires that the affine connection has the antisymmetric part: the torsion tensor, which extends general relativity to the Einstein$-$Cartan theory of gravity. In the presence of torsion, the Dirac equation becomes a nonlinear, cubic equation in the spinor wave function. We show that the energy eigenvalues of the corresponding Hamiltonian as functions of the momentum are different for the fermion and antifermion components of the spinor, violating charge conjugation symmetry, and also depend on the helicity. Consequently, particles of matter and antimatter have different dispersion relations and therefore different masses. This mass difference increases with density and becomes significant near the Cartan density, which existed in the early Universe. Because antimatter particles were more massive than matter particles, they were also slower during pair production in the early Universe and therefore had higher cross sections for gravitational capture by primordial black holes. This difference might have led to the matter$-$antimatter imbalance in the observable Universe: the missing antimatter fell into black holes.

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin-foam models for quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin-foam model and discuss the role of the causal structure in the reconstruction of a semiclassical spacetime geometry.

We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $\eta$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.

We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincaré, {\bf 22} (2021), 3199-3234] where quantum channels realize the transport. Relying on this general machinery, we introduce $p$-Wasserstein distances and divergences and study their fundamental geometric properties. Finally, we prove triangle inequality for quadratic Wasserstein divergences under the sole assumption that an arbitrary one of the states involved is pure, which is a generalization of our previous result in this direction.

Recently proposed by the author theory of the Q-balls mechanism of high-Tc superconductivity in cuprates is applied to explanation of known experimental data. The Q-balls (nontopological solitons) of coherently condensed spin/charge density wave fluctuations (SDW/CDW) with zero static mean and with the wave-vector that connects the 'nested' regions of the Fermi surface in doped cuprates cause pairing of the 'nested' fermions into local superconducting condensates. Hence, the Q-balls possess lower total energy in comparison with not condensed thermal SDW/CDW fluctuations in the same volume. Here it is demonstrated analytically that scattering of itinerant fermions on the Q-balls causes linear temperature dependence of electrical resistivity in the interval of temperatures above T$_c$, reminiscent of the famous 'Plankian' behavior in the 'strange metal' phase. Calculated diamagnetic response of Q-balls gas and contour plot of the Q-balls phase diagram, with lower temperatures dome touching the upper 'strange metal' one, are in qualitative accord with experimental data in high-T$_c$ cuprates. The Q-ball semiclassical field breaks chiral symmetry along the Matsubara time axis in Euclidean space-time and possesses conserved Noether "charge" Q that makes the Q-ball volume finite. Thus, the Q-balls 'gas' is formed via first order phase transition below a temperature T$^*$ greater than bulk T$_c$. The superconducting condensates inside the Q-balls induce a spectral gap on the nested parts of the Fermi surface that might be responsible for a pseudogap phase in cuprates, where the Q-ball scenario was supported recently by micro X-ray diffraction data in HgBa$_2$CuO$_{4+y}$. Finally, it is found that scattering of spin excitations on the condensates of Cooper pairs inside the Q-balls leads to the famous hourglass dispersion close to antiferromagnetic wave vectors in the Brillouin zone.

We construct a semiclassical theory for electrons in a non-Hermitian periodic system subject to perturbations varying slowly in space and time. We derive the energy of the wavepacket to first order in the gradients of the perturbations. Applying the theory to the specific case of a uniform external magnetic field, we obtain an expression for the orbital magnetization energy. Using the principles of non-Hermitian dynamics, we define a physically meaningful non-Hermitian generalization of the angular momentum operator and show that it is compatible with the real part of the orbital magnetic moment. The imaginary part of the orbital magnetic moment is also discussed and shown to originate from an imaginary counterpart to the angular momentum that gives rise to a non-Hermitian generalization of the Aharonov-Bohm effect.

Quantum simulations of electronic structure and strongly correlated quantum phases are widely regarded as among the most promising applications of quantum computing. These computations naturally benefit from native fermionic encodings, which intrinsically restrict the Hilbert space to physical states consistent with fermionic statistics and conservation laws like particle number and magnetization independent of gate errors. While ultracold atoms in optical lattices are established as powerful analog simulators of strongly correlated fermionic matter, neutral-atom platforms have concurrently emerged as versatile, scalable architectures for spin-based digital quantum computation. Unifying these capabilities requires high-fidelity gates that preserve motional degrees of freedom of fermionic atoms, paving the way for a new generation of programmable fermionic quantum processors. Here we demonstrate collisional entangling gates with fidelities up to 99.75(6)% and Bell state lifetimes exceeding $10\,s$, realized via controlled interactions of fermionic atoms in an optical superlattice. Using quantum gas microscopy, we microscopically characterize spin-exchange and pair-tunneling gates, and realize a robust, composite pair-exchange gate, a fundamental primitive for quantum chemistry simulations. Our results establish controlled collisions in optical lattices as a competitive and complementary approach to high entangling gate fidelities in neutral-atom quantum computers. When embedded within a fermionic architecture, this capability enables the preparation of complex quantum states and advanced readout protocols for a new class of scalable analog-digital hybrid quantum simulators. Combined with local addressing, these gates mark a crucial step towards a fully digital fermionic quantum computer based on the controlled motion and entanglement of fermionic neutral atoms.

The kicked Ising model has been studied extensively as a model of quantum chaos. Bertini, Kos, and Prosen studied the system in the thermodynamic limit, finding an analytic expression for the spectral form factor, $K(t)$, at the self-dual point with periodic boundary conditions. The spectral form factor is the 2nd moment of the trace of the time evolution operator, and we study the higher moments of this random variable in the kicked Ising model. A previous study of these higher moments by Flack, Bertini, and Prosen showed that, surprisingly, the trace behaves like a real Gaussian random variable when the system has periodic boundary conditions at the self dual point. By contrast, we investigate the model with open boundary conditions at the self dual point and find that the trace of the time evolution operator behaves as a complex Gaussian random variable as expected from random matrix universality based on the circular orthogonal ensemble. This result highlights a surprisingly strong effect of boundary conditions on the statistics of the trace. We also study a generalization of the spectral form factor known as the Loschmidt spectral form factor and present results for different boundary conditions.

Previous work on Jackiw-Teitelboim (JT) gravity has shown that, at low temperatures, the annealed entropy becomes negative and departs from the quenched entropy. From the perspective of the random-matrix theory (RMT) dual of JT gravity, this effect is encoded in the continuous spectrum at the spectral edge that is universally described by the Airy model. At low temperature, the quenched entropy exhibits a power law dependence determined by the symmetry class of the RMT ensemble. Here we study the same question in the Sachdev-Ye-Kitaev (SYK) model which possesses much more structure than RMT. Through numerical simulations, we find that the level spacing statistics of the SYK model match the relevant RMT ensembles even near the spectral edge, thus leading to an agreement with the RMT prediction for the power-law behaviour of the quenched entropy at low temperatures. We also show similar effects in supersymmetric wormholes filled with matter, which is modeled by the $\mathcal N = 2$ supersymmetric SYK model. Numerically extracting the spectral edge properties of the BPS operators allows us to compute the quenched entanglement entropy of the wormhole in the large particle number limit.

In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this setting, each finite group $G$ determines a family of numerical invariants associated with closed orientable surfaces, expressed in terms of the degrees of the complex irreducible characters of $G$. These invariants can be viewed as natural extensions of the commuting probability $d(G)$, which measures the probability that two randomly chosen elements of $G$ commute and has been extensively studied in the literature. By analyzing these higher-genus analogues, we establish new quantitative criteria relating the values of these invariants to key structural features of finite groups, such as commutativity, nilpotency, supersolvability and solvability. Our results generalize several classical theorems concerning the commuting probability, thereby linking ideas from finite group theory and topological quantum field theory.

This work presents an exact microcanonical combinatorial analysis of the one-dimensional antiferromagnetic Ising model. At the primary ground-state level crossing $B/J=2$, degeneracies follow the Fibonacci and Lucas sequences for open chains and periodic rings, respectively. We extend this framework to the complete excitation spectrum, demonstrating that the density of states is constructed from topological defects governed by linear Diophantine equations and $p$-fold Fibonacci convolutions. Open boundaries act as fractional defects, densifying the chain spectrum into energy steps of $2J$, whereas the closed ring remains quantized in units of $4J$. Notably, this exact topological counting exposes non-trivial spectral gaps near the fully polarized limit, strictly forbidding the penultimate macroscopic energy levels in both topologies. Through the transfer matrix formalism, we derive exact closed-form expressions for the critical degeneracies at all energy levels. These results provide a rigorous analytical foundation for extracting exact residual entropies and exposing the intrinsic number-theoretic architecture of quantum critical manifolds.

We demonstrate that an anisotropic and rotated Fermi surface can generate a finite transverse response in electron transport, even in the absence of a magnetic field or Berry curvature. Using a two-dimensional continuum model, we show that broken $k_y \to -k_y$ symmetry inherent to anistropic bandstructures leads to a nonzero transverse conductivity. We construct a lattice model with direction-dependent nearest- and next-nearest-neighbor hoppings that faithfully reproduces the continuum dispersion and allows controlled rotation of the Fermi contour. Employing a multiterminal geometry and the Büttiker-probe method, we compute the resulting transverse voltage and establish its direct correspondence with the continuum transverse response. The effect increases with the degree of anisotropy and vanishes at rotation angles where mirror symmetry is restored. Unlike the quantum Hall effect, the transverse response predicted here is not quantized but varies continuously with the band-structure parameters. Our results provide a symmetry-based route to engineer transverse signals in low-symmetry materials without magnetic fields or topological effects.

Bound states, known as particles tied together and moving as a whole, are profound correlated effects induced by particle-particle interactions. While dimer-monomer bound states are manifested as a single particle attached to a dimer bound pair, it is still unclear about quantum walks and Bloch oscillations of dimer-monomer bound states. Here, we revisit three-particle bound states in the Bose-Hubbard model and find that interaction-induced impurities adjacent to bound pair and boundaries cause two kinds of bound states: one is dimer-monomer bound state and the other is bound edge state. In quantum walks, the spread velocity of dimer-monomer bound state is determined by the maximal group velocity of their energy band, which is much smaller than that in the single-particle case. In Bloch oscillations, the period of dimer-monomer bound states is one third of that in the single-particle case. Emergence of bound edge states also requires that interaction-induced defects are greater than the effective tunneling strength of three-particle bound state. Our work provides new insights to basic mechanics and collective dynamics of three-particle bound states.

Quantum computing is increasingly practiced through programming, yet most educational offerings emphasize algorithmic or framework-level use rather than software engineering concerns such as testing, abstraction, tooling, and lifecycle management. This paper reports on the design and first offering of a cross-listed undergraduate--graduate course that frames quantum computing through a software engineering lens, focusing on early-stage competence relevant to software engineering practice. The course integrates foundational quantum concepts with software engineering perspectives, emphasizing executable artifacts, empirical reasoning, and trade-offs arising from probabilistic behaviour, noise, and evolving toolchains. Evidence is drawn from instructor observations, supplemented by anonymous student feedback, a background survey, and inspection of student work. Despite minimal prior exposure to quantum computing, students were able to engage productively with quantum software engineering topics once a foundational understanding of quantum information and quantum algorithms, expressed through executable artifacts, was established. This experience report contributes a modular course design, a scalable assessment model for mixed academic levels, and transferable lessons for software engineering educators developing quantum computing curricula.

A generalization for the quantum information retrieval protocol recently illustrated by Verlinde and van der Heijden for evaporating black holes is provided to inclusions of type III von Neumann factors. The physical interest of such scenario arises in Quantum Field Theory, where local algebras are type III von Neumann algebras. The formula obtained can be easily interpreted in terms of the statistical dimension of superselection sectors in the case of black holes undergoing charge evaporation, thanks to the index-statistics theorem, leading to a thermodynamic interpretation. A constraint on the values of the index leads to a final remark about the quantization of the charge emitted by the black hole during the evaporation process.

We present a theoretical framework for biexciton dynamics in molecular aggregates that explicitly treats populations and coherences across excitation manifolds within a reduced density-matrix formalism. By extending kinetic descriptions beyond the weak-coupling limit, the approach captures the influence of exciton delocalization and exciton-exciton annihilation while remaining computationally tractable within a Markovian description of environmental relaxation. Using this framework, we investigate how the spatial profile and momentum composition of the initial biexciton state govern fluorescence decay and transport. Incoherent initial conditions lead to strongly non-exponential relaxation and time-dependent diffusion driven by nonlinear population kinetics. In contrast, coherently prepared biexciton states exhibit pronounced early-time coherent transport, whose character depends sensitively on whether the initial state is prepared as a standing-wave or traveling-wave superposition of single-exciton modes. Despite nearly identical emission dynamics for J and H aggregate, biexciton transport properties differ markedly due to band structure-dependent interference effect. Our results demonstrate that biexciton dynamics remains strongly influenced by initial-state coherence and momentum composition. Besides initial-state preparation, the coherent-to-incoherent crossover and the diffusive spreading of the exciton density are sensitive to internal conversion processes such as exciton fusion and the decay to the first excited state. The present work establishes initial-state preparation as a key control parameter for many-exciton transport in excitonic systems and provides a general framework for interpreting nonlinear optical experiments beyond population-based descriptions.

In this paper, we study a system of bosons trapped in a confining potential, interacting with a quantized field of coherent photons in the mean field description of non-relativistic Quantum Electrodynamics (QED) obtained by [N. Leopold and P. Pickl , 2017]. We derive the effective nonlinear cascade equations governing the emission and absorption of coherent photons by the boson subsystem in a combined weak-coupling and macroscopic time limit. We demonstrate that solutions to this nonlinear cascade describe a monotone decreasing energy flow in the boson subsystem. Thereby, we prove that a Bose-Einstein condensate (BEC) forms dynamically, under conservation of the total boson $L^2$ mass. We note that this process is crucially different from thermal relaxation to the ground state, and fundamentally depends on the nonlinear nature of the cascade dynamics.

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing quantum approaches to solve nonlinear PDEs suffer from the issues of curse of dimensionality and convergence during the linearization process. In this paper, a Lindbladian homotopy analysis method (LHAM) is proposed as a quantum differential equation solver to simulate non-unitary and nonlinear dynamics. The original nonlinear problem is first converted to a recursive sequence of linear PDEs with the homotopy analysis method and reformulated as a higher-dimensional lower block triangular linear homogeneous autonomous system. The solution is then embedded in the density matrix and obtained through the Lindbladian dynamics simulation. Compared to other methods such as Carleman linearization and the Koopman-von Neumann approach where the dimension of Hilbert space increases polynomially with the inverse of truncation error, the Hilbert space dimension in LHAM increases only logarithmically. LHAM is demonstrated with nonlinear PDEs including Burgers' equation and reduced magnetohydrodynamics equations.