The growing demand for robust quantum programming frameworks has unveiled a critical limitation: current large language model (LLM) based quantum code assistants heavily rely on remote APIs, introducing challenges related to privacy, latency, and excessive usage costs. Addressing this gap, we propose PennyCoder, a novel lightweight framework for quantum code generation, explicitly designed for local and embedded deployment to enable on-device quantum programming assistance without external API dependence. PennyCoder leverages a fine-tuned version of the LLaMA 3.1-8B model, adapted through parameter-efficient Low-Rank Adaptation (LoRA) techniques combined with domain-specific instruction tuning optimized for the specialized syntax and computational logic of quantum programming in PennyLane, including tasks in quantum machine learning and quantum reinforcement learning. Unlike prior work focused on cloud-based quantum code generation, our approach emphasizes device-native operability while maintaining high model efficacy. We rigorously evaluated PennyCoder over a comprehensive quantum programming dataset, achieving 44.3% accuracy with our fine-tuned model (compared to 33.7% for the base LLaMA 3.1-8B and 40.1% for the RAG-augmented baseline), demonstrating a significant improvement in functional correctness.

In his Comment on our recent paper ``The laws of physics do not prohibit counterfactual communication'', \textit{npj Quantum Information} (2022) 8:60, Popescu argues that the claims of the paper are invalid. Here, we refute his argument, showing that it is based on ignoring the specifics of what we set out to prove (that counterfactual communication is possible \emph{for post-selected particles}, and more specifically in these cases is not prohibited by the weak trace or consistent histories criteria for particle path), followed by an unwarranted simplification of the protocol. Moreover, the Comment's excursion into interpretation is misplaced. Our communication protocol is a precisely defined one that allows two remote parties, albeit rarely, to communicate an arbitrarily long binary message, with arbitrarily high accuracy. This is not a matter of interpretation -- as the concrete example given in our paper in question illustrates. As for our overarching claim that no particles are exchanged in the course of this communication, we have already demonstrated this both theoretically and experimentally, in the postselected case we consider, as per the weak trace and consistent histories criteria for path of a quantum particle.

All experimental evidence {indicates} that the vacuum is not void, but filled with something truly quantum. This is reflected by terms such as {zero-point} fluctuations, and Dirac's sea of virtual particle-antiparticle pairs, and last but not least the vacuum is the medium responsible for Maxwell's displacement current. While quantum electrodynamics (QED) is an exceptionally successful theory, it remains a perturbative framework rather than a fully self-contained one. Inherently, it includes singularities and divergences, which prevent the precise calculation of fundamental quantities such as the fine-structure constant $\alpha$. Any direct attempt to compute $\alpha$ results in divergent values. However, and most remarkable, what can be determined is how $\alpha$ ``runs", meaning how it varies with energy or exchanged momentum. In this article, we review the historical development of these ideas, the current state of knowledge, and ongoing efforts to find ways to move further. This includes a simple model to describe vacuum polarization in the low-energy regime, when considering only small (linear) deviations from the equilibrium {state}, relating {Maxwell's displacement} in the vacuum, to the quantum properties of the vacuum.

Quantum simulations of lattice gauge theories (LGTs) with both dynamical matter and gauge fields provide a promising approach to studying strongly coupled problems beyond classical computational reach. Yet, implementing gauge-invariant encodings and real-time evolution remains experimentally challenging. Here, we demonstrate a resource-efficient encoding of a $\mathbb{Z}_2$ LGT using a hybrid qubit-oscillator trapped-ion quantum device, where qubits represent gauge fields and vibrational modes naturally encode bosonic matter fields. This architecture utilises synthetic dimensions to construct higher-dimensional lattice geometries and combines digital and analogue techniques to prepare initial states, realise gauge-invariant real-time evolution, and measure the relevant observables. We experimentally probe dynamics obeying Gauss's law in a $\mathbb{Z}_2$ link and extend this to a loop geometry, marking the first steps towards higher-dimensional LGTs. In this quasi-2D setup, we observe Aharonov-Bohm interference for the first time with dynamical gauge fields encoding magnetic flux, demonstrating the interplay between charge and flux. Our results chart a promising path for scalable quantum simulations of bosonic gauge theories and outline a roadmap for realising exotic LGTs in higher dimensions.

Hybrid quantum-classical frameworks leverage quantum computing for machine learning; however, variational quantum circuits (VQCs) are limited by the need for local measurements. We introduce an adaptive non-local observable (ANO) paradigm within VQCs for quantum reinforcement learning (QRL), jointly optimizing circuit parameters and multi-qubit measurements. The ANO-VQC architecture serves as the function approximator in Deep Q-Network (DQN) and Asynchronous Advantage Actor-Critic (A3C) algorithms. On multiple benchmark tasks, ANO-VQC agents outperform baseline VQCs. Ablation studies reveal that adaptive measurements enhance the function space without increasing circuit depth. Our results demonstrate that adaptive multi-qubit observables can enable practical quantum advantages in reinforcement learning.

The Quantum Internet introduces a fundamental shift in the network design, since its key objective is the distribution and manipulation of quantum entanglement, rather than the transmission of classical information. This shift breaks key classical Internet design principles, such as the end-to-end argument, due to the inherently stateful and non-local nature of entangled states that require coordinated in-network operations. Consequently, in this paper we propose a novel hierarchical Quantum Internet architecture centered around the concept of entanglement-defined controller, enabling scalable and efficient management of the aforementioned in-network operations. However, architecture alone is insufficient for network scalability, which requires a quantum-native control plane that fundamentally rethinks addressing and routing. Consequently, we propose a quantum addressing scheme that embraces the principles and quantum phenomena within the node identifiers. Built upon this addressing scheme, we also design a quantum-native routing protocol that exhibits scalable and compact routing tables, by efficiently operating over entanglement-aware topologies. Finally, we design a quantum address splitting functionality based on Schrödinger's oracles that generalizes classical match-and-forward logic to the quantum domain. Together, these contributions demonstrate, for the first time, the key advantages of quantum-by-design network functioning.

Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding and prohibitive circuit complexity. In this work, we present a resource-efficient quantum algorithm that reformulates the convolution product as a structured matrix multiplication via a novel sparse reshaping formalism. Leveraging the observation that localized convolutions can be encoded as doubly block-Toeplitz matrix multiplications, we construct a quantum framework wherein sparse input patches are prepared using optimized key-value QRAM state encoding, while convolutional filters are represented as quantum states in superposition. The convolution outputs are computed through inner product estimation using a low-depth SWAP test circuit, which yields probabilistic amplitude information with reduced sampling overhead. Our architecture supports batched convolution across multiple filters using a generalized SWAP circuit. Compared to prior quantum convolutional approaches, our method eliminates redundant preparation costs, scales logarithmically with input size under sparsity, and enables direct integration into hybrid quantum-classical machine learning pipelines. This work provides a scalable and physically realizable pathway toward quantum-enhanced feature extraction, opening up new possibilities for quantum convolutional neural networks and data-driven quantum inference.

Motivated by the recent advances in optical imaging and tracking of wave-packet propagation in optical cavities, we systematically explore the non-Hermitian polariton dynamics within a decay-tunable multimode cavity model. The complex eigen-spectrum of the model Hamiltonian allows us to predict the incoherent-coherent transition induced by photon losses, which defines an exceptional point at resonance and evolves analytically as the wavevector shifts off-resonantly. The resulting dispersion relation, group velocity, and relaxation rate exhibit striking signatures, such as curve crossing, level repulsion, turnover, bifurcation, and coalescence, as the decay rate crosses the critical transition or the wavevector crosses the resonance. The spectral characterization leads to surprising features in the non-Hermitian wave packet dynamics: (i) maximal population relaxation rate at the critical transition; (ii) reversed propagation in the center-of-mass motion; (iii) ballistic-to-diffusion transition; (iv) contraction in the displacement and width of the polariton wave-packet. These dynamical features have complementary symmetry between the upper-polariton (UP) branch and lower-polariton (LP) branch in the two-dimensional phase diagram spanned by the photon decay rate and wavevector. Thus, the combination of complex spectral characterization and non-Hermitian wave packet propagation establishes the photon decay rate as a powerful control parameter for polariton transport, reveals the underlying symmetry in lossy cavities, and presents a starting point to incorporate other dissipative mechanisms.

Recent work (Nathan et al, arXiv:2405.05671) proposed an architecture for a dissipatively stabilized GKP qubit, and protocols for protected Clifford gates. Here we propose a protocol for a protected non-Clifford $\sqrt{T}$ gate at the physical qubit level, based on the inclusion of a quartic flux potential generated by ancillary Josephson junctions. We show that such a gate is topologically robust with exponentially suppressed infidelity from control or device imperfections, and operates on microsecond timescales for GHz resonators. We analyze the resilience of the protocol to noise, imperfect control, and imperfect targeting of circuit parameters.

Entanglement entropy is a fundamental measure of quantum correlations and a key resource underpinning advances in quantum information and many-body physics. We uncover a universal relationship between bipartite entanglement entropy and particle number after the barrier in a one-dimensional Fermi-Hubbard system with an external asymmetric potential. Using Kolmogorov-Arnold Networks - a novel machine learning architecture - we learn this relationship across a broad range of interaction strengths with near-perfect predictive accuracy. Furthermore, we propose a simple analytical binary-entropy-like expression that quantitatively captures the observed correlation for fixed parameters. Our findings open new avenues for characterizing quantum correlations in transport phenomena and provide a powerful framework for predicting entanglement evolution in quantum systems.

In this work, we study the electromagnetic energy and energy rate spectra produced by a point particle in the presence of plane wave fields. Our approach is based on a semiclassical formulation, in which the current distribution that generates electromagnetic radiation is treated classically while the radiation field is quantum. Unlike the classical energy spectrum--which exhibits divergences linked to the duration of interaction between the particle and the external field--the semiclassical spectrum is finite because radiation is produced during the quantum transition from an initial state without photons to the final state with photons at time $t$. In our formulation, we find that the maximum energy spectrum emitted by the particle is linearly proportional to time or phase, depending on the external field. This allowed us not only to extract the maximum energy rate spectra emitted by the particle but also to correlate them with energy rates derived in the framework of Classical Electrodynamics and Quantum Electrodynamics.

Young's double slit experiment has often been used to illustrate the concept of complementarity in quantum mechanics. If information can in principle be obtained about the path of the photon, then the visibility of the interference fringes is reduced or even destroyed. This Gedanken experiment discussed by Bohr and Einstein can be realized when the slit is replaced by individual atoms sensitive to the transferred recoil momentum of a photon which "passes through the slit". Early pioneering experiments were done with trapped ions and atom pairs created via photo-dissociation. Recently, it became possible to perform interference experiments with single neutral atoms cooled to the absolute ground state of a harmonic oscillator potential. The slits are now single atoms representing a two-level system, and the excitation in the harmonic oscillator potential is the which-way marker. In this note, we analyze and generalize two recent experiments performed with single atoms and emphasize the different ways they record which-way information.

Learning the behaviour of chaotic systems remains challenging due to instability in long-term predictions and difficulties in accurately capturing invariant statistical properties. While quantum machine learning offers a promising route to efficiently capture physical properties from high-dimensional data, its practical deployment is hindered by current hardware noise and limited scalability. We introduce a quantum-informed machine learning framework for learning partial differential equations, with an application focus on chaotic systems. A quantum circuit Born machine is employed to learn the invariant properties of chaotic dynamical systems, achieving substantial memory efficiency by representing these complex physical statistics with a compact set of trainable circuit parameters. This approach reduces the data storage requirement by over two orders of magnitude compared to the raw simulation data. The resulting statistical quantum-informed prior is then incorporated into a Koopman-based auto-regressive model to address issues such as gradient vanishing or explosion, while maintaining long-term statistical fidelity. The framework is evaluated on three representative systems: the Kuramoto-Sivashinsky equation, two-dimensional Kolmogorov flow and turbulent channel flow. In all cases, the quantum-informed model achieves superior performance compared to its classical counterparts without quantum priors. This hybrid architecture offers a practical route for learning dynamical systems using near-term quantum hardware.

A diagrammatic multi-reference generalization of many-body perturbation theory was recently introduced [J. Phys. Chem. Lett., 2025, 16, 3047]. This framework allows us to extend single-reference (SR) Green's function methods defined at the diagrammatic level naturally into multi-reference case, as previously exemplified by the formulation of multi-reference direct random phase approximation (MR-dRPA) and the multi-reference second-order screened exchange approximation (MR-SOSEX). In this work, we further elaborate this framework and use it to develop MR generalizations of two other RPA variants, namely, particle-hole (ph) RPA with exchange (MR-RPAx) and particle-particle RPA (MR-ppRPA). We define these two MR generalizations by infinite order resummations of the generalized `ring' and `ladder' diagrams with antisymmetrized interaction vertices, respectively, which incorporate the contributions from the active-space connected two-body Green's functions. As for MR-dRPA, we derive unified sets of equations that hold at both SR and MR levels for RPAx and ppRPA, respectively. We perform numerical studies of prototypical systems using the three MR-RPA methods and carry out a perturbative analysis to gain a deeper understanding of their behaviors. We find that error cancellation between the second and third orders is a key factor for both SR-RPA and MR-RPA. In addition, we observe that MR-phRPA (MR-dRPA and MR-RPAx) and MR-ppRPA tend to overestimate and underestimate correlation energies, respectively, suggesting that a better accuracy can be achieved by further combining these two channels in the future.

We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible discretization of the parameter space, we incorporate both group cochains and parameter-space differentials, enabling the systematic construction of equivariant topological invariants. We derive a fixed-point formula for the higher Berry invariant in the case where the symmetry action has isolated fixed points. This reveals that the phase transition point between Haldane and trivial phases acts as a monopole-like defect where higher Berry curvature emanates. We further discuss hierarchical structures of topological defects in the parameter space, governed by symmetry reductions and compatibility with subgroup structures.

We propose a variational framework for solving ground-state problems of open quantum systems governed by quantum stochastic differential equations (QSDEs). This formulation naturally accommodates bosonic operators, as commonly encountered in quantum chemistry and quantum optics. By parameterizing a dissipative quantum optical system, we minimize its steady-state energy to approximate the ground state of a target Hamiltonian. The system converges to a unique steady state regardless of its initial condition, and the design inherently guarantees physical realizability. To enhance robustness against persistent disturbances, we incorporate H-infinity control into the system architecture. Numerical comparisons with the quantum approximate optimization algorithm (QAOA) highlight the method's structural advantages, stability, and physical implementability. This framework is compatible with experimental platforms such as cavity quantum electrodynamics (QED) and photonic crystal circuits.

We study the ultimate precision limits of a spin chain, strongly coupled to a heat bath, for measuring a general parameter and report the results for specific cases of magnetometry and thermometry. Employing a full polaron transform, we derive the effective Hamiltonian and obtain analytical expressions for the quantum Fisher information (QFI) of equilibrium states in both weak coupling (WC) and strong coupling (SC) regimes for a general parameter, explicitly accounting for finite-size (FS) effects. Furthermore, we utilize Hill's nanothermodynamics to calculate an effective QFI expression at SC. Our results reveal a potential advantage of SC for thermometry at low temperatures and demonstrate enhanced magnetometric precision through control of the anisotropy parameter. Crucially, we show that neglecting FS effects leads to considerable errors in ultimate precision bounds for equilibrium thermometry. This work also highlights the inadequacy of phenomenological approaches in describing the metrological capability and thermodynamic behavior of systems at SC. Additionally, we demonstrate the effect of bath on system's phase transition at SC.

Cluster states are a useful resource in quantum computation, and can be generated by applying entangling gates between next-neighbor qubits. Heralded entangling gates offer the advantage of high post-selected fidelity, and can be used to create cluster states at the expense of large space-time overheads. We propose a low-overhead protocol to generate and merge high-fidelity many-atom entangled states into a 3D cluster state that supports fault-tolerant universal logical operations. Our simulations indicate that a state-of-the-art high-finesse optical cavity is sufficient for constructing a scalable fault-tolerant cluster state with loss and Pauli errors remaining an order of magnitude below their respective thresholds. This protocol reduces the space-time resource requirements for cluster state construction, highlighting the measurement-based method as an alternative approach to achieving large-scale error-corrected quantum processing with neutral atoms.

Bosons with density-dependent hopping on a one dimensional lattice have been shown to emulate anyonic particles with fractional exchange statistics. Leveraging this, we construct a Josephson junction setup, where an insulating barrier in the form of a Mott-insulator is sandwiched between two superfluid phases. This is obtained by spatially varying either the statistical phase or the strength of the on-site interaction potential on which the ground state of the system depends. Utilizing numerical methods such as exact diagonalization and density renormalization group theory, the ground state properties of this setup are investigated to understand the Josephson effect in a strongly correlated regime. The dynamical properties of this model for different configurations of this model are analyzed to find the configurations that can produce the Josephson effect. Furthermore, it is observed that continuous particle flow over time is achievable in this proposed model solely by creating an initial phase difference without any external biasing.

We investigate the quantum behavior of a charm-anticharm bound system under the influence of a magnetic field within the symplectic formulation of Quantum Mechanics. Employing a perturbative approach, we obtain the ground and first excited states of the system described by the Cornell potential, which incorporates both confining and nonconfining interactions. After perfoming a Bohlin mapping in phase space, we solve the time-independent symplectic Pauli-Schrödinger-type equation and determine the corresponding Wigner function. Special attention is given to the observation of the confinement of the quark-antiquark (meson $c\overline{c}$) that is revealed in the phase space structure. And the introduction of spin effect (external magnetic field) in modifying the quantum characteristics of the system. Our results reveal that the magnetic enhances the negativity of the Wigner function, signaling stronger quantum interference and a departure from classical behavior. The negativity thus serve as a quantitative measure of the system's non-classicality. In addition we have computed the mass spectra of the $c\overline{c}$ meson and present result are in agreement with experimental data, improving previous theoretical studies.

We introduce a novel stochastic model for charge noise in superconducting charge qubits based on memory multi-fractional Brownian motion (mmfBm), capable of capturing non-stationary and long-memory effects. This framework reproduces key experimental features of decoherence and offers new insights into environmental interactions with superconducting quantum devices.

The rapid scaling of superconducting quantum computers has highlighted the impact of device-level variability on overall circuit fidelity. In particular, fabrication-induced fluctuations in device parameters such as capacitance and Josephson critical current pose significant challenges to large-scale integration. We propose a simulation methodology for estimating qubit fidelity based on classical circuit simulation, using a conventional Simulation Program with Integrated Circuit Emphasis (SPICE) simulator. This approach enables the evaluation of the performance of superconducting quantum circuits with 10000 qubits on standard laptop computers. The proposed method provides an accessible tool for the early stage assessment of large-scale superconducting quantum circuit performance.

Very recently, Sharoglazova et al. performed an experiment measuring the energy-velocity relationship and Bohmian velocity in coupled waveguides. Their data show a discrepancy between the semi-classical `speed' $v=\sqrt{2|\Delta|/m}$ and Bohmian velocity $v_s$ for $\Delta<-\hbar J_0$, leading them to claim a challenge to Bohmian mechanics. Here, we definitively demonstrate this experiment poses no challenge to Bohmian mechanics. First, $v$ and $v_S$ represent fundamentally distinct physical quantities -- comparing them is physically unjustified and cannot adjudicate between Copenhagen and Bohmian interpretations. Second, we rigorously show that both interpretations predict identical photon tunneling dynamics in coupled waveguides.

Quantum Latin squares are a generalization of classical Latin squares in quantum field and have wide applications in unitary error bases, mutually unbiased bases, $k$-uniform states and quantum error correcting codes. In this paper, we put forward some new quantum Latin squares with special properties, such as idempotent quantum Latin square, self-orthogonal quantum Latin square, holey quantum Latin square, and the notions of orthogonality on them. We present some forceful construction methods including PBD constructions and filling in holes constructions for non-classical quantum Latin squares. As consequences, we establish the existence of non-classical 2-idempotent MOQLS$(v)$, non-classical 2, 3-MOQLS$(v)$ and non-classical SOQLS$(v)$ except possibly for several definite values.

We introduce a new theoretical framework -- the polarized Houston basis -- to model nonequilibrium dynamics in driven open quantum systems, formulated for use within the quantum master equation. This basis extends conventional Houston states by incorporating field-induced polarization effects, enabling a more accurate description of excitation dynamics under external driving. Using a one-dimensional dimer-chain model, we examine band population dynamics through projections onto polarized Houston states, original Houston states, and naive Bloch states. We find that the polarized Houston basis significantly suppresses spurious Bloch-state excitations and virtual transitions present in standard Houston approaches, allowing for a cleaner extraction of real excitations. When implemented in the relaxation time approximation of the quantum master equation, this formalism also yields a substantial reduction of unphysical DC currents in insulating systems. Our results highlight the polarized Houston basis as a powerful tool for simulating nonequilibrium phenomena in light-driven open quantum materials.

This third paper in this series continues the investigation of atom-field interactions in the presence of a conductor or a dielectric medium, focusing on quantum information related basic issues such as decoherence and entanglement. Here we consider the entanglement between two atoms with internal degrees of freedom modeled by a harmonic oscillator, with varying separations between them and varying distances between them and a conducting surface. These are configurations familiar in the Casimir-Polder effect, but the behavior of atom-surface entanglement is quite different from the well-studied behavior of field-induced forces. For one, while the attractive force between an atom and a conducting surface increases as they come closer, the entanglement between the atom and the quantum field actually decreases as the atom gets closer to the conductor, as shown in \cite{Rong,AFD2}. We show how different factors play out, ranging from the coupling between the atoms and the field to the coupling between the atoms, going beyond the weak coupling restrictions often found necessary in the literature. Gathering our results for the entanglement dependence on each variable concerned, we can provide a spatial topography of quantum entanglement, thus enabling a visualized understanding of the behavior of quantum field-mediated entanglement. In particular we can quantify the definition of a three-dimensional \textit{entanglement domain} between the two atoms, how it varies with their coupling, their separation and their distances from the conducting surface, and for practical applications, how to exercise effective control of the entanglement between two atoms by changing these parameters. Our findings are expected to be useful for studies of atom-field-medium interactions in vacuum and surface physics.

Gaussian states hold a fundamental place in quantum mechanics, quantum information, and quantum computing. Many subfields, including quantum simulation of continuous-variable systems, quantum chemistry, and quantum machine learning, rely on the ability to accurately and efficiently prepare states that reflect a Gaussian profile in their probability amplitudes. Although Gaussian states are natural in continuous-variable systems, the practical interest in digital, gate-based quantum computers demands discrete approximations of Gaussian distributions over a computational basis of size \(2^n\). Because of the exponential scaling of naive amplitude-encoding approaches and the cost of certain block-encoding or Hamiltonian simulation techniques, a resource-efficient preparation of approximate Gaussian states is required. In this work, we propose and analyze a circuit-based approach that starts with single-qubit rotations to form an exponential amplitude profile and then applies the quantum Fourier transform to map those amplitudes into an approximate Gaussian distribution. We demonstrate that this procedure achieves high fidelity with the target Gaussian state while allowing optional pruning of small controlled-phase angles in the quantum Fourier transform, thus reducing gate complexity to near-linear in \(\mathcal{O}(n)\). We conclude that the proposed technique is a promising route to make Gaussian states accessible on noisy quantum hardware and to pave the way for scalable implementations on future devices. The implementation of this algorithm is available at the Classiq library: this https URL.

Quantum annealing is a promising metaheuristic for solving constrained combinatorial optimization problems. However, parameter tuning difficulties and hardware noise often prevent optimal solutions from being properly encoded as the ground states of the problem Hamiltonian. This study investigates mid-anneal measurement as a mitigation approach for such situations, analyzing its effectiveness and underlying physical mechanisms. We introduce a quantitative metric to evaluate the effectiveness of mid-anneal measurement and apply it to the graph bipartitioning problem and the quadratic knapsack problem. Our findings reveal that mid-anneal measurement is most effective when the energy difference between desired solutions and ground states is small, with effectiveness strongly governed by the energy structure. Furthermore, the effectiveness increases as the Hamming distance between the ground and excited states gets small, highlighting the role of state similarity. Analysis of fully-connected Ising models demonstrates that the effectiveness of mid-anneal measurement persists with increasing system size, indicating its scalability and practical applicability to large-scale quantum annealing.

We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in the X and Z bases, single-qubit Hadamard (H) gates, and three-qubit controlled-controlled-Z (CCZ) gates. State teleportations between [[4, 2, 2]] (2D) and [[8, 3, 2]] (3D) error-detecting color codes allow one to make use of the respective transversal H and CCZ gates that these codes possess. As such, minimizing the number of logical quantum teleportation operations, not the number of logical quantum non-Clifford gates, is the relevant optimization goal. To help hardware developers characterize this architecture, we also provide an experimental protocol tailored to testing logical quantum circuits expressed in it.

Corresponding to a finite dimensional Hilbert space $H$ with $\dim H=n$, we define a geometric algebra $\gscript (H)$ with $\dim\sqbrac{\gscript (H)}=2^n$. The algebra $\gscript (H)$ is a Hilbert space that contains $H$ as a subspace. We interpret the unit vectors of $H$ as states of individual fermions of the same type and $\gscript (H)$ as a fermion quantum field whose unit vectors represent states of collections of interacting fermions. We discuss creation operators on $\gscript (H)$ and provide their matrix representations. Evolution operators provided by self-adjoint Hamiltonians on $H$ and $\gscript (H)$ are considered. Boson-Fermion quantum fields are constructed. Extensions of operators from $H$ to $\gscript (H)$ are studied. Finally, we present a generalization of our work to infinite dimensional separable Hilbert spaces.

Single photons source (SPS) is a key component required by quantum communication devices. We report the finding of bright diamond-based SPS created by nature millions of years ago. It is shown that narrow ($\leq$ 2 nm) lines observed within the 500-800 nm range in photoluminescence (PL) spectra of the surface layer of untreated Yakut diamonds rich in nitrogen and hydrogen belong to SPS. Moreover, unknown narrow-line PL observed earlier in nitrogen- and hydrogen-rich diamonds from various deposits around the world are thought to be associated with SPS. Thus, the diamond rim, which until now was sent to the dumps or, at best, used as an abrasive powder, turned out to be a valuable material suitable for use in quantum technologies.

Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of chemical moieties in such datasets. In this contribution, we introduce the quantum molecular structure encoding (QMSE) scheme, which encodes the molecular bond orders and interatomic couplings expressed as a hybrid Coulomb-adjacency matrix, directly as one- and two-qubit rotations within parameterised circuits. We show that this strategy provides an efficient and interpretable method in improving state separability between encoded molecules compared to other fingerprint encoding methods, which is especially crucial for the success in preparing feature maps in QML workflows. To benchmark our method, we train a parameterised ansatz on molecular datasets to perform classification of state phases and regression on boiling points, demonstrating the competitive trainability and generalisation capabilities of QMSE. We further prove a fidelity-preserving chain-contraction theorem that reuses common substructures to cut qubit counts, with an application to long-chain fatty acids. We expect this scalable and interpretable encoding framework to greatly pave the way for practical QML applications of molecular datasets.

Recent experiments show ~0.1 ms coherence time for a single electron charge qubit on a solid neon surface. This remarkably long coherence time is believed to result from the intrinsic purity of solid neon as a qubit host. In this paper, we present theoretical studies on the decoherence mechanisms of an electron's charge (lateral motional) states on solid neon. At the typical experimental temperature of ~10 mK, the two main decoherence mechanisms are the phonon-induced displacement of the neon surface and the phonon-induced modulation of the neon permittivity (dielectric constant). With a qubit frequency increasing from 1 GHz to 10 GHz, the charge coherence time decreases from about 366 s to 7 ms, and from about 27 s to 0.3 ms, respectively, limited by the two mechanisms above. The calculated coherence times are at least one order longer than the observed ones at ~6.4 GHz qubit frequency, suggesting plenty of room for experimental improvement.

We investigate two non-Hermitian two-photon quantum Rabi models (tpQRM) that exhibit $\mathcal{PT}$ symmetry: the biased tpQRM (btpQRM), in which the qubit bias is purely imaginary, and the dissipative tpQRM (dtpQRM), where the two-photon coupling is made imaginary to introduce dissipation. For both models, we derive exact solutions by employing Bogoliubov transformations. In the btpQRM, we identify spectral collapse at a critical coupling strength, with accompanying $\mathcal{PT}$ symmetry breaking that correlates with exceptional points (EPs) arising from coalescing eigenstates. We establish a direct correspondence between $\mathcal{PT}$-broken regions and the doubly degenerate points of the Hermitian tpQRM, and analyze the effects of qubit bias via an adiabatic approximation. In the dtpQRM, although no spectral collapse occurs, both EPs and Juddian-type degeneracies are present, with well-separated behaviors distinguished by parity conservation. Through biorthogonal fidelity susceptibility and c-product, we successfully identify and classify the nature of these two types of level crossings. Finally, we compare the dynamical evolution of both models, revealing fundamentally different pathways to steady states governed by their respective non-Hermitian spectral structures. Our results provide exact characterizations of $\mathcal{PT}$-symmetric non-Hermitian tpQRMs and may offer theoretical insights for future experimental realizations.

Neural quantum states (NQS) have emerged as powerful tools for simulating many-body quantum systems, but their practical use is often hindered by limitations of current sampling techniques. Markov chain Monte Carlo (MCMC) methods suffer from slow mixing and require manual tuning, while autoregressive NQS impose restrictive architectural constraints that complicate the enforcement of symmetries and the construction of determinant-based multi-state wave functions. In this work, we introduce Neural Importance Resampling (NIR), a new sampling algorithm that combines importance resampling with a separately trained autoregressive proposal network. This approach enables efficient and unbiased sampling without constraining the NQS architecture. We demonstrate that NIR supports stable and scalable training, including for multi-state NQS, and mitigates issues faced by MCMC and autoregressive approaches. Numerical experiments on the 2D transverse-field Ising model show that NIR outperforms MCMC in challenging regimes and yields results competitive with density matrix renormalization group (DMRG) methods. Our results establish NIR as a robust alternative for sampling in variational NQS algorithms.

Quantum algorithms have gained increasing attention for addressing complex combinatorial problems in finance, notably portfolio optimization. This study systematically benchmarks two prominent variational quantum approaches, Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), under diverse experimental settings, including different asset universes, ansatz architectures, and circuit depths. Although both methods demonstrate effective cost function minimization, the resulting portfolios often violate essential financial criteria, such as adequate diversification and realistic risk exposure. To bridge the gap between computational optimization and practical viability, we introduce an Expert Analysis Evaluation framework in which financial professionals assess the economic soundness and the market feasibility of quantum-optimized portfolios. Our results highlight a critical disparity between algorithmic performance and financial applicability, emphasizing the necessity of incorporating expert judgment into quantum-assisted decision-making pipelines.

This paper provides an integrated perspective on addressing key challenges in developing reliable and secure Quantum Neural Networks (QNNs) in the Noisy Intermediate-Scale Quantum (NISQ) era. In this paper, we present an integrated framework that leverages and combines existing approaches to enhance QNN efficiency, security, and privacy. Specifically, established optimization strategies, including efficient parameter initialization, residual quantum circuit connections, and systematic quantum architecture exploration, are integrated to mitigate issues such as barren plateaus and error propagation. Moreover, the methodology incorporates current defensive mechanisms against adversarial attacks. Finally, Quantum Federated Learning (QFL) is adopted within this framework to facilitate privacy-preserving collaborative training across distributed quantum systems. Collectively, this synthesized approach seeks to enhance the robustness and real-world applicability of QNNs, laying the foundation for reliable quantum-enhanced machine learning applications in finance, healthcare, and cybersecurity.

In this paper, we propose an expansion of the Expected Maximum Improvement over Confident Regions (EMICoRe) Variational Quantum Eigensolver (VQE) -- a technique advanced by Nicoli et al., which utilizes both quantum and classical components to approximate the ground state of a quantum system -- by introducing an alternative threshold for EMICoRe's Confident Region that depends on both the Gaussian process (GP) prior variance and the model's change in predicted energy over a set number of iterations. This modification is a more lenient threshold for the Confident Region and accounts for natural fluctuations in the predicted energy that EMICoRe punishes by eliminating the exploratory benefits presented by the Confident Region. We test both algorithms with the original EMICoRe model as a baseline and our results suggest improvement over EMICoRe's state-of-the-art results for a common benchmark for VQEs, the Ising Hamiltonian, and similar performance for more complex optimization regimes. We analyze the accuracy in approximated ground state energy and how the threshold evolves during optimization to compare the EMICoRe model with the proposed alternative. After comparison, we discuss the potential optimization of the degrees of freedom present in the new threshold for better performance and a more varied choice of system to be approximated.

First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling of two-electron interactions. However, existing schemes employ uniform discretizations, so the resolution required to capture electron-nuclear cusps in high-density regions oversamples low-density regions, wasting computational resources. We address this by deploying non-uniform, molecule-adaptive grids that concentrate points where electronic density is high. Using Voronoi partitions of these grids, the molecular Hamiltonian is expressed in a Hermitian form and in a transcorrelated, isospectral form that eliminates Coulomb singularities and yields cusp-free eigenfunctions. Both formulations slot naturally into quantum eigenvalue solvers: Hermitian Quantum Phase Estimation (QPE) and the recent generalised Quantum Eigenvalue Estimation (QEVE) protocol for its non-Hermitian, transcorrelated counterpart. Numerical validation on benchmark systems confirms that this non-heuristic ab initio framework offers a promising path for accurate ground-state chemistry on quantum hardware.

We investigate how accidental counts, the detection events not originating from genuine entangled photon pairs, impact the observed violation of Bell inequalities in photonic experiments. These false coincidences become increasingly significant at higher laser pump powers, limiting the strength of Bell violations and thus the performance of quantum protocols such as device-independent quantum random number generation and quantum key distribution. We propose a simple noise model that quantitatively links the Bell value to the pump strength. Using experimental data from recent SPDC-based Bell tests, we fit the model to a Bell expression, and demonstrate accurate prediction of Bell values across a range of pump settings. Our results provide practical guidance for optimizing source brightness while preserving quantum nonlocality, with direct implications for high-rate, secure quantum technologies.

Applying quantum computing in the computer-aided engineering (CAE) problems are highly expected since quantum computers yield potential exponential speedups for the operations between extremely large matrices and vectors. Although efficient quantum algorithms for the above problems have been intensively investigated, it remains a crucial task to extract all the grid-point values encoded in the prepared quantum states, which was believed to eliminate the achieved quantum advantage. In this paper, we propose a quantum-classical hybrid Fourier space readout (FSR) method to efficiently recover the underlying function from its corresponding quantum state. We provide explicit quantum circuits, followed by theoretical and numerical discussions on its complexity. In particular, the complexity on quantum computers has only a logarithmic dependence on the grid number, while the complexity on classical computers has a linear dependence on the number of target points instead of the grid number. Our result implies that the achieved quantum speedups are not necessarily ruined when we read out the solutions to the CAE problems.

In this work, we investigate the incompatibility of random quantum measurements. Most previous work has focused on characterizing the maximal amount of white noise that any fixed number of incompatible measurements with a fixed number of outcomes in a fixed dimension can tolerate before becoming compatible. This can be used to quantify the maximal amount of incompatibility available in such systems. The present article investigates the incompatibility of several classes of random measurements, i.e., the generic amount of incompatibility available. In particular, we show that for an appropriate choice of parameters, both random dichotomic projective measurements and random basis measurements are close to being maximally incompatible. We use the technique of incompatibility witnesses to certify incompatibility and combine it with tools from random matrices and free probability.

We present a theoretical polarization tomography scheme within the QIUP framework that directly extracts key sample parameters from measured interference visibilities and phase shifts. This approach establishes constant bindings for transmission amplitudes and coherence terms, thereby reducing the number of unknowns required to reconstruct the sample's Jones matrix. Our method is resource-efficient and well-suited for quantum imaging where probing and detection occur at different wavelengths, enabling robust, non-invasive characterization of complex samples.

We present the simulation of the quench dynamics of the Z3 Schwinger model, that describes an approximation of one-dimensional Quantum Electrodynamics, on a digital noisy Rydberg atom platform, aiming at the observation of multiple dynamical quantum phase transitions. In order to reach long-time dynamics, we exploit an enconding dictated by the symmetries, combined with a circuit compression procedure. We focus on a quench that evolves the Dirac vacuum by means of a Hamiltonian depending on a negative mass parameter. This leads to resonant Rabi oscillations between the Dirac vacuum and mesonic states. The population concentration exhibits oscillations with negligible fluctuations of detuned states also with the inclusion of combined noise sources, from which we can clearly detect multiple dynamical phase transitions.

Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally demanding. In this work, we study distributed memory architectures intended for high-performance computing implementations to solve this task. Efficiently distributing the contraction task across multiple nodes is critical, as both computational and memory costs are highly sensitive to the chosen partitioning strategy. While prior work has employed general-purpose hypergraph partitioning algorithms, these approaches often overlook the specific structure and cost characteristics of tensor network contractions. We introduce a simulated annealing-based method that iteratively refines the partitioning to minimize the total operation count, thereby reducing time-to-solution. The algorithm is evaluated on MQT Bench circuits and achieves an 8$\times$ average reduction in computational cost and an 8$\times$ average reduction in memory cost compared to a naive partitioning.

Utility-scale quantum programs contain operations on the order of $>10^{15}$ which must be prepared and piped from a classical co-processor to the control unit of the quantum device. The latency of this process significantly increases with the size of the program: existing high-level classical representations of quantum programs are typically memory intensive and do not naïvely efficiently scale to the degree required to execute utility-scale programs in real-time. To combat this limitation, we propose the utilization of high-level quantum circuit caches and compressors. The first save on the time associated with repetitive tasks and sub-circuits, and the latter are useful for representing the programs/circuits in memory-efficient formats. We present numerical evidence that caches and compressors can offer five orders of magnitude lower latencies during the automatic transpilation of extremely large quantum circuits.

We present a comprehensive analytical study that extends the conventional formulation of Berry curvature, highlighting its derivation in the context of problematic domains of definition of the operators. Our analysis reveals that handling these domains carefully can have a substantial impact on Berry curvature, demonstrating that even Hamiltonians without explicit parameter dependence may exhibit nonzero Berry curvature. This finding emphasizes that Berry curvature is intrinsically related to the eigenvectors rather than the Hamiltonian itself. Our approach utilizes the standard Bloch (k-space) framework for spatially periodic systems, illustrating these effects from first principles and discussing potential implications for solid-state systems.

Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum hardware, and has the potential to significantly improve their performance when optimization techniques are added to the process. One such optimization technique is reducing the number of quantum gates that are needed to execute a circuit. For instance, methods for reducing the number of non-Clifford gates or CNOT gates from a circuit is an extensive research area that has gathered significant interest over the years. For certain hardware platforms such as ion trap quantum computers, we can leverage some of their special properties to further reduce the cost of executing a quantum circuit in them. In this work we use global interactions, such as the Global Mølmer-Sørensen gate present in ion trap hardware, to optimize and synthesize quantum circuits. We design and implement an algorithm that is able to compile an arbitrary quantum circuit into another circuit that uses global gates as the entangling operation, while optimizing the number of global interactions needed. The algorithm is based on the ZX-calculus and uses an specialized circuit extraction routine that groups entangling gates into Global Mølmer-Sørensen gates. We benchmark the algorithm in a variety of circuits, and show how it improves their performance under state-of-the-art hardware considerations in comparison to a naive algorithm and the Qiskit optimizer.

Spin-phonon interaction is known to drive magnetic relaxation in solid-state systems, but little evidence is available on how it affects coherence time. Here we extend fourth-order quantum master equations to account for coherence terms and describe the full effect of up to two-phonon processes on spin dynamics. We numerically implement this method fully ab initio for a single-molecule magnet with large magnetization blocking temperature and show that while strong axial magnetic anisotropy ensures slow magnetic relaxation approaching seconds at 77 K, the superposition of Kramers doublets is coherent for less than 10 ns due to a novel two-phonon pure dephasing mechanism.

In contrast to the usual bulk-boundary correspondence, topological states localized within the bulk of the system have been numerically identified in quasicrystalline structures, termed bulk localized transport (BLT) states. These states exhibit properties different from edge states, one example being that the number of BLT states scales with system size, while the number of edge states scales with system perimeter. Here, we define an algorithm to identify BLT states, which is based on the physically motivated crosshair marker and robustness analyses. Applying the algorithm to the Hofstadter model on the Ammann-Beenker tiling, we find that the BLT states appear mainly for magnetic fluxes within a specific interval. While edge states appear at low densities of states, we find that BLT states can appear at many different densities of states. Many of the BLT states are found to have real-space localization that follows geometric patterns characteristic of the given quasicrystal. Furthermore, BLT states can appear both isolated and in groups within the energy spectrum which could imply greater robustness for the states within such groups. The spatial localization of the states within a certain group can change depending on the Fermi energy.

Ideal quantum measurement requires divergent thermodynamic resources. This is a consequence of the third law of thermodynamics, which prohibits the preparation of the measurement pointer in a fully erased, pure state required for the acquisition of perfect, noiseless measurement information. In this work, we investigate the consequences of finite resources in the emergence of intersubjectivity as a model for measurement processes with multiple observers. Here, intersubjectivity refers to a condition in which observers agree on the observed outcome (agreement), and their local random variables exactly reproduce the original random variable for the system observable (probability reproducibility). While agreement and reproducibility are mutually implied in the case of ideal measurement, finite thermodynamic resources constrain each of them. Starting from the third law of thermodynamics, we derive how the achievability of ideal intersubjectivity is affected by restricted thermodynamic resources. Specifically, we establish a no-go theorem concerning perfect intersubjectivity and present a deviation metric to account for the influence of limited resources. We further present attainable bounds for the agreement and bias that are exclusively dependent on the initial state of the environment. In addition, we show that either by cooling or coarse-graining, we can approximate ideal intersubjectivity even with finite resources. This work bridges quantum thermodynamics and the emergence of classicality in the form of intersubjectivity.

Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular classification. However, such binary classifications become inadequate in describing matrices whose elements vary continuously over time, thereby transitioning through intermediate states near singular configurations. To address this fundamental limitation, we develop a rigorous and original mathematical theory termed Continuity Norm Framework for the Evolution of Nonsingular Matrices. Within this framework, we introduce a novel mathematical structure enabling continuous and differentiable transitions between singular and nonsingular matrix states, explicitly governed by a specialized continuity norm and evolution operators derived through a well-defined differential formulation. Our theoretical formalism rigorously quantifies the proximity of a matrix to singularity, alongside its temporal evolution, through precisely constructed functional relationships involving determinants and their time derivatives. Furthermore, we elucidate the direct applicability and relevance of our approach to physical systems by demonstrating how our formalism can seamlessly describe continuous quantum state transitions-scenarios frequently encountered but insufficiently captured by existing matrix theory. The theory presented herein is meticulously constructed to maintain mathematical exactitude, comprehensive rigor, and broad accessibility, bridging advanced mathematical innovation and clear interpretability for the wider scientific community.

Quantum algorithms are of great interest for their possible use in optimization problems. In particular, variational algorithms that use classical counterparts to optimize parameters hold promise for use in currently existing devices. However, convergence stagnation phenomena pose a challenge for such algorithms. Seeking to avoid such difficulties, we present a framework based on circuits with variable topology with two approaches, one based on ansatz-free evolutionary method known from literature and the other using an introduction of an ansatz with circuital structure inspired by the physics of the Hamiltonian related to the problem, considering a, named here, pseudo-counterdiabatic evolutionary term. The efficiency of the proposed framework was tested on several instances of the set partitioning problem. The two approaches were compared with the Variational Quantum Eigensolver in noisy and non-noisy scenarios. The results demonstrated that optimization using circuits with variable topology presented very encouraging results. Notably, the strategy employing a pseudo-counterdiabatic evolutionary term exhibited remarkable performance, avoiding convergence stagnation in most instances considered. This framework circumvents the need for classical optimizers, and, as a consequence, this procedure based on circuits with variable topology indicates an interesting path in the search for algorithms to solve integer optimization problems targeting efficient applications in larger-scale scenarios.

Magnetic levitation of superconductors is a promising platform to study quantum mechanics in the large-mass limit. One major limitation is the weak trapping potential, which results in low vibrational eigenfrequencies and increased susceptibility to low-frequency noise. While generating strong magnetic fields is relatively straightforward, creating a tightly confined harmonic potential - essentially achieving a large magnetic field gradient - remains a significant challenge. In this work, we demonstrate a potential solution using superconducting cores that concentrate magnetic flux into arbitrarily small volumes. We show the ability to trap superconducting particles using an anti-Helmholtz coil configuration incorporating these cores. However, we observe rapid damping of the levitated particle motion due to flux trapping within the cores, occurring once the lower critical field is exceeded locally. To investigate this mechanism, we employ diamond NV center magnetometry and detect substantial remanent fields persisting after high-current operation of the coils. Finally, we discuss possible strategies to mitigate this effect and improve the levitation properties.

Quantum entanglement is a foundational resource in quantum information science, underpinning applications across physics. However, detecting and quantifying entanglement remains a significant challenge. Here, we introduce a variational quantum algorithm inspired by Uhlmann's theorem to quantify the Bures entanglement of general quantum states, a method that naturally extends to other quantum resources, including genuine multipartite entanglement, quantum discord, quantum coherence, and total correlations, while also enabling reconstruction of the closest free states. The algorithm requires a polynomial number of ancillary qubits and circuit depth relative to the system size, dimensionality, and free state cardinality, making it scalable for practical implementations. Thus, it provides a versatile and efficient framework for quantifying quantum resources, demonstrated through several applications.

We utilize few-level model systems to analyze the polarization and phase properties of below-threshold harmonics (BTH) in aligned molecules. In a two-level system (TLS), we find that the phase of emitted harmonics undergoes a distinct change. For harmonics with photon energies below the transition between the dominant field-dressed states, the phase alternates by $\pi$ between successive odd harmonic orders but remains constant above. Exploiting this behavior, we construct a four-level model composed of two uncoupled TLS subsystems aligned along orthogonal directions. We demonstrate that with selected transition frequencies lower-order harmonics follow the polarization of the linearly polarized driving field while higher-order harmonics exhibit a mirrored polarization. The model predicts that aligned systems with orthogonal transition dipoles may show analogous phase and polarization features in the BTH regime.

As algorithmic tools exemplified by the Quantum Singular Value Transformation (QSVT) continue to emerge as a unifying framework for diverse quantum speedups, the efficient construction of block encodings--their fundamental input model--becomes increasingly crucial. However, devising explicit block encoding circuits remains a well-recognized and challenging problem. One of the most widely studied and versatile approaches to block encoding is the Linear Combination of Unitaries (LCU). Despite its generality, the practical use of LCU is often limited by significant gate overhead, primarily stemming from the multi-controlled gates required in the SELECT oracle. We introduce a compact LCU formulation, dubbed FOQCS-LCU, which leverages the check matrix formalism to implement a constant-depth SELECT oracle using a linear number of singly controlled Pauli gates and ancillae. We demonstrate that, by exploiting the structure of the problem, the cost of the state preparation oracle can also be substantially reduced. We accomplish so by designing a parametrized family of efficient Dicke state preparation routines. We construct explicit block encoding circuits for representative spin models such as the Heisenberg and spin glass Hamiltonians and provide detailed, non-asymptotic gate counts. Our numerical benchmarks validate the efficiency of the FOQCS-LCU approach, illustrating an order-of-magnitude improvement in CNOT count over conventional LCU. This framework opens the door to efficient block encodings of a broad class of structured matrices beyond those explored here.

Levitated optomechanics, the interaction between light and small levitated objects, is a new macroscopic quantum system that is being used as a testing ground for fundamental physics and for the development of sensors with exquisite sensitivity. The utility of this system, when compared to other quantum optomechanical systems, is its extreme isolation from the environment and, by the relatively few degrees of freedom that a levitated object has. While work in the field has strongly focused on the three translational degrees of freedom of this system, it has become increasingly important to understand the induced rotational motion of levitated objects, particularly in optical trapping fields, but also in magnetic and electric traps. These additional three degrees of freedom, which are intrinsic to levitated systems, offer a new set of optomechanical nonlinear interactions that lead to a rich and yet largely unexplored roto-translational motion. The control and utilization of these interactions promise to extend the utility of levitated optomechanics in both fundamental studies and applications. In this review, we provide an overview of levitated optomechanics, before focusing on the roto-translational motion of optically levitated anisotropic objects. We first present a classical treatment of this induced motion, bridging the gap between classical and quantum formalisms. We describe the different types of roto-translational motion for different particle shapes via their interaction with polarized optical trapping fields. Subsequently, we provide an overview of the theoretical and experimental approaches as well as applications that have established this new field. The review concludes with an outlook of promising experiments and applications, including the creation of non-classical states of roto-translational motion, quantum-limited torque sensing and particle characterization methods.

We introduce a simple definition of dynamical entropy for quantum systems under continuous monitoring, inspired by Connes, Narnhofer and Thirring. It quantifies the amount of information gained about the initial condition. A nonzero entropy rate can be obtained by monitoring the thermal fluctuation of an extensive observable in a generic many-body system (away from classical or large N limit). We explicitly compute the entropy rate in the thermodynamic and long-time limit, in terms of the two-point correlation functions. We conjecture a universal Planckian bound for the entropy rate. Related results on the purification rate are also obtained.

In this work, we present a new framework for a relativistic quantum analouge of the classical Otto engine. Considering a single qubit as the working substance, we analyse its interaction with a massless quantum scalar field while undergoing two half-circular rotations at ultra-relativistic velocities. The quantum vacuum serves as a thermal bath through the Unruh effect induced due to the acceleration from the circular motions. We observe that the response function of the qubit gets significantly modified by the presence of the qubit's trajectory. Analysing the transition probability behaviour, we find that in the high-acceleration regime, it asymptotically approaches a constant value, determined solely by the properties of the correlation function. Furthermore, our results emphasize the crucial role of the circular trajectory in determining the engine's work output. In particular, the extracted work increases with detector acceleration and approaches an asymptotic limit in the high-acceleration regime. Notably, the efficiency of this model remains unaffected by the circular motion and is consistent with previously studied models.

We present a general and simple formula for computing the entanglement negativity in free fermions. Our formula allows for deriving several universal bounds on negativity and its rate of change in dynamics. The bound on negativity directly relates the clustering property of correlations in free-fermion states to the entanglement area law, and provides the optimal condition for the area law in mixed free fermion states with long-range correlations. In addition, we establish an area-law bound on entanglement generation in open systems, analogous to previously known results for entanglement entropy in unitary dynamics. Our work provides new analytical insights into fermionic mixed-state entanglement.

Quantum steering enables one party to influence another remote quantum state by local measurement. While steering is fundamental to many quantum information tasks, the existing detection methods in the literature are mainly constrained to either specific measurement scenario or low-dimensional systems. In this work, we propose a majorization lattice framework for steering detection, which is capable of exploring the steering in arbitrary dimension and measurement setting. Steering inequalities for two-qubit states, high-dimensional Werner states and isotropic states are obtained, which set even stringent bars than what have reached yet. Notably, the known high-dimensional results turn out to be some kind of approximate limits of the new approach.

Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms include scalability, reconfigurable connectivity, and native multi-qubit gates, making them particularly well-suited for addressing complex network problems. These problems can often be framed as graph-based tasks, which can be efficiently addressed using quantum walks. In this work, we propose a general implementation of staggered quantum walks with Rydberg atoms, with a particular focus on spatial networks. We also present an efficient algorithm for constructing the tessellations required for the staggered quantum walk. Finally, we demonstrate that our proposal achieves quadratic speedup in spatial search algorithms.

We explore how the fundamental problems in quantum molecular dynamics can be modelled using classical simulators (emulators) of quantum computers and the actual quantum hardware available to us today. The list of problems we tackle includes propagation of a free wave packet, vibration of a harmonic oscillator, and tunneling through a barrier. Each of these problems starts with the initial wave packet setup. Although Qiskit provides a general method for initializing wavefunctions, in most cases it generates deep quantum circuits. While these circuits perform well on noiseless simulators, they suffer from excessive noise on quantum hardware. To overcome this issue, we designed a shallower quantum circuit for preparing a Gaussian-like initial wave packet, which improves the performance on real hardware. Next, quantum circuits are implemented to apply the kinetic and potential energy operators for the evolution of a wavefunction over time. The results of our modelling on classical emulators of quantum hardware agree perfectly with the results obtained using the traditional (classical) methods. This serves as a benchmark and demonstrates that the quantum algorithms and Qiskit codes we developed are accurate. However, the results obtained on the actual quantum hardware available today, such as IBM's superconducting qubits and IonQ's trapped ions, indicate large discrepancies due to hardware limitations. This work highlights both the potential and challenges of using quantum computers to solve fundamental quantum molecular dynamics problems.

Classical shallow networks are universal approximators. Given a sufficient number of neurons, they can reproduce any continuous function to arbitrary precision, with a resource cost that scales linearly in both the input size and the number of trainable parameters. In this work, we present a quantum optical protocol that implements a shallow network with an arbitrary number of neurons. Both the input data and the parameters are encoded into single-photon states. Leveraging the Hong-Ou-Mandel effect, the network output is determined by the coincidence rates measured when the photons interfere at a beam splitter, with multiple neurons prepared as a mixture of single-photon states. Remarkably, once trained, our model requires constant optical resources regardless of the number of input features and neurons.

It is demonstrated that identifying information-theoretic limitations of quantum Bell nonlocality alone cannot completely distinguish quantum theory from generalized nonsignaling theories. To this end, an information-theoretic concept of certifying nonobjective information by the Popescu-Rohrlich box fraction is employed. Furthermore, in the aforementioned demonstration, a partial answer to the question of what distinguishes quantum theory from generalized nonsignaling theories emerges beyond the one provided by the principle of information causality alone. This is accomplished by demonstrating that postquantum models identified by the information causality are isolated by the emergence of the Popescu-Rohrlich box fraction of nonobjective information in Bell-local boxes of a generalized nonsignaling theory, over the two other generalized nonsignaling theories that have simplicial local state spaces.

Machine Learning (ML) serves as a general-purpose, highly adaptable, and versatile framework for investigating complex systems across domains. However, the resulting computational resource demands, in terms of the number of parameters and the volume of data required to train ML models, can be high, often prohibitive. This is the case in astrophysics, where multimedia space data streams usually have to be analyzed. In this context, quantum computing emerges as a compelling and promising alternative, offering the potential to address these challenges in a feasible way. Specifically, a four-step quantum machine learning (QML) workflow is proposed encompassing data encoding, quantum circuit design, model training and evaluation. Then, focusing on the data encoding step, different techniques and models are investigated within a case study centered on the Gamma-Ray Bursts (GRB) signal detection in the astrophysics domain. The results thus obtained demonstrate the effectiveness of QML in astrophysics, highlighting the critical role of data encoding, which significantly affects the QML model performance.

We propose cyclotron resonance as an optical probe for emergent fractionalized excitations in $\mathrm{U}(1)$ quantum spin liquids, focusing on kagome antiferromagnets. In contrast to conventional systems, where cyclotron resonance directly couples to charged carriers, spinons in spin liquids are charge-neutral and interact only through an emergent gauge field. We identify two key mechanisms by which an external physical electromagnetic field induces emergent electric and magnetic fields, enabling indirect coupling to spinons. Using these mechanisms, we compute the absorption rate of the cyclotron resonance response for Dirac spinons forming Landau levels. Our analysis shows that, although the absorption per layer is small, the absence of a skin-depth limitation in insulating spin liquids allows for cumulative absorption comparable to graphene in realistic sample sizes for the recently discovered spin-liquid candidate material YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_{1-y}$(OH)${}_y$]. Our findings shows that cyclotron resonance is a viable experimental probe of spinon Landau quantization and emergent gauge fields, providing powerful positive experimental signatures of quantum spin liquids.

Single-crystal diamond nanocavities have tremendous potential for use in quantum and nonlinear optical technologies. The ability to precisely control their resonant frequencies is essential for many applications, and $\textit{in situ}$ tuning is particularly desirable. In this work, we demonstrate deterministic and non-volatile resonance tuning of a diamond nanocavity. We observed a photorefractive effect in concert with the generation of third-harmonic light within the device. This effect blue-shifted the cavity resonance frequency by $20.9\,\text{GHz}$, exceeding the cavity linewidth. The shift corresponded to a fractional change in refractive index of $-10^{-4}$, and its relaxation occurred over several tens of hours. Although photorefraction is a second-order nonlinear effect and has previously not been observed in diamond owing to its vanishing $\chi^{(2)}$, the observed behaviour is consistent with the generation of non-zero $\chi^{(2)}$ by electric fields from charged crystal defects. This observation could enable the realisation of diamond frequency converters and electro-optical modulators that rely on second-order nonlinearity.

In this work we review, complete, and synthesize results linking generalized coherent stages (nondegradable Gaussian wavefunctions) to the notions of Fermi ellipsoids, quantum blobs, and microlocal pairs introduced in previous work. These geometric objects are Fermi ellipsoids, quantum blobs, and microlocal pairs. In addition we study various symplectic capacities associated with these objects.

We present a novel approach for constructing quasi-isospectral higher-order Hamiltonians from time-independent Lax pairs by reversing the conventional interpretation of the Lax pair operators. Instead of treating the typically second-order $L$-operator as the Hamiltonian, we take the higher-order $M$-operator as the starting point and construct a sequence of quasi-isospectral operators via intertwining techniques. This procedure yields a variety of new higher-order Hamiltonians that are isospectral to each other, except for at least one state. We illustrate the approach with explicit examples derived from the KdV equation and its extensions, discussing the properties of the resulting operators based on rational, hyperbolic, and elliptic function solutions. In some cases, we present infinite sequences of quasi-isospectral Hamiltonians, which we generalise to shape-invariant differential operators capable of generating such sequences. Our framework provides a systematic mechanism for generating new integrable systems from known Lax pairs.

We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian analysis. Instead of fixing the multiplier corresponding to the distortion constraint, we update the multiplier in each iteration. Hence the algorithm solves the original problem itself, rather than the Lagrangian relaxation of it. Moreover, all the other variables are iterated in closed form without solving multi-dimensional nonlinear equations or multivariate optimization problems. Numerical experiments show the accuracy of our proposed algorithm and its improved efficiency over existing methods.

This work presents a quantum-limited optomechanical sensing platform for real-time detection and discrimination of chiral molecules, based on a multilayer hybrid plasmonic-mechanical resonator. Leveraging quantum zero-point motion and engineered photon-phonon interactions, the system achieves ultrahigh displacement sensitivity that approaches the fundamental quantum limit. The multilayer architecture, composed of alternating dielectric and metallic films, supports mechanical resonances with quality factors reaching approximately ten thousand in the megahertz frequency range. These resonances coherently modulate the optical field through radiation pressure and dynamical backaction. Power spectral density measurements reveal distinct mechanical peaks at 0.68, 2.9, 4.3, 5.5, and 6.8 MHz, with optomechanical coupling strengths exceeding twice the intrinsic baseline, enabling highly efficient signal transduction. Lorentzian fitting confirms the presence of sharp mechanical linewidths, while the total force noise, including thermal, shot, and technical contributions, remains below the threshold required for detecting sub-piconewton forces. Time-resolved Raman spectroscopy, which is typically insensitive to chirality, here reveals enantioselective dynamics arising from asymmetric optomechanical interactions, enabling clear spectral distinction between d- and l-enantiomers. Finite-element simulations validate the strong spatial overlap between optical confinement and mechanical displacement modes. This platform offers a scalable and tunable approach to quantum-limited, high-sensitivity chiral molecule detection, with applications in coherent control, precision spectroscopy, and chemical sensing.

Ultrafast multistage electron transfer (ET) in molecular systems with multiple redox centers is fundamental to photochemical energy conversion, including processes in natural photosynthesis, molecular optoelectronics, and organic photovoltaics. These systems often operate under nonequilibrium conditions, where solvent relaxation, intramolecular vibrations, and competing ET pathways jointly determine reaction kinetics and product yields. In this chapter, we present a unified semiclassical framework for modeling ultrafast, competitive ET in multiredox compounds embedded in polar environments with complex relaxation dynamics. The approach constructs diabatic free energy surfaces (FESs) in a multidimensional coordinate space that integrates both polarization and relaxation components of the environment within a unified representation. Electron dynamics are described using a stochastic point-transition method that captures the coupling between nonadiabatic quantum transitions and classical nuclear motion. The formalism generalizes and unifies several established semiclassical models - including the Najbar-Tachiya, Zusman-Beratan, and Sumi-Marcus approaches - and supports efficient simulation of multistage ET cascades. As an application, we investigate ultrafast charge separation in donor-acceptor-acceptor (D-A1-A2) triads, showing how hot charge shift to a secondary acceptor can suppress nonequilibrium charge recombination. Numerical simulations reveal how reorganization energies, vibrational coupling, molecular geometry, and bending angle collectively influence ET efficiency. The proposed framework offers a general and scalable tool for the rational design of photofunctional molecular systems.

By extending the strategy developed by Shiraishi in 2019, we prove that the standard Hubbard model on the $d$-dimensional hypercubic lattice with $d\ge2$ does not admit any nontrivial local conserved quantities. The theorem strongly suggests that the model is non-integrable. To our knowledge, this is the first extension of Shiraishi's proof of the absence of conserved quantities to a fermionic model. Although our proof follows the original strategy of Shiraishi, it is essentially more subtle compared with the proof by Shiraishi and Tasaki of the corresponding theorem for $S=\tfrac12$ quantum spin systems in two or higher dimensions; our proof requires three steps, while that of Shiraishi and Tasaki requires only two steps. It is also necessary to partially determine the conserved quantities of the one-dimensional Hubbard model to accomplish our proof.

We explore the quench dynamics of PT-symmetric non-Hermitian systems by utilizing the biorthogonal formalism. We analyze quench dynamics of observable quantities, the quantum geometric tensor, and various entanglement quantities, including the entanglement entropy, the SVD entropy, and the Tu-Tzeng-Chang entropy. Our results show that a sudden quench into a PT-broken phase generally leads to exponential growth in these quantities, driven by the biorthogonal density matrix's non-positivity. In contrast to generic interacting systems, we observe a surprising linear decay in the TTC entropy for non-interacting fermionic systems. This finding originates from the approximate spectral symmetry of the biorthogonal reduced density matrix, and we confirm our findings using the Yang-Lee and non-Hermitian XXZ models.

We present the basic elements for a modular architecture for time-bin encoded qubits based on quantum Hall edge channels, forming the foundation of a scalable electronic quantum information platform named TEMPO (Time-binned Electronic Modular Platform for Qubits). Quantum states are encoded in temporally separated edge magnetoplasmon (EMP) wave packets propagating along a single chiral edge, eliminating the need for spatial path separation and enhancing coherence. The platform supports full qubit operations$\unicode{x2013}$including initialization, phase modulation, readout, and two-qubit entangling gates$\unicode{x2013}$by leveraging dynamically tunable quantum point contacts and electrostatic control of interferometric loops. We consider the linear dispersion and gate-induced velocity control on EMP propagation and describe strategies for maintaining waveform integrity. Various single-electron sources, including ohmic injection and capacitive excitation, are discussed in the context of coherence. Multi-qubit operations are enabled through synchronized injection and engineered Coulomb interactions between adjacent channels, while single-qubit readout is addressed via spin-based or capacitive charge sensors. Our approach integrates gate-tunable coherent control of chiral edge states, offering a comprehensive pathway toward scalable electron quantum optics in solid-state platforms.

Recently discovered 2D van der Waals magnetic materials, and specifically Iron-Germanium-Telluride ($\rm Fe_{5}GeTe_{2}$), have attracted significant attention both from a fundamental perspective and for potential applications. Key open questions concern their domain structure and magnetic phase transition temperature as a function of sample thickness and external field, as well as implications for integration into devices such as magnetic memories and logic. Here we address key questions using a nitrogen-vacancy center based quantum magnetic microscope, enabling direct imaging of the magnetization of $\rm Fe_{5}GeTe_{2}$ at sub-micron spatial resolution as a function of temperature, magnetic field, and thickness. We employ spatially resolved measures, including magnetization variance and cross-correlation, and find a significant spread in transition temperature yet with no clear dependence on thickness down to 15 nm. We also identify previously unknown stripe features in the optical as well as magnetic images, which we attribute to modulations of the constituting elements during crystal synthesis and subsequent oxidation. Our results suggest that the magnetic anisotropy in this material does not play a crucial role in their magnetic properties, leading to a magnetic phase transition of $\rm Fe_{5}GeTe_{2}$ which is largely thickness-independent down to 15 nm. Our findings could be significant in designing future spintronic devices, magnetic memories and logic with 2D van der Waals magnetic materials.

We introduce the concept of entanglement halos, a set of strongly entangled distant sites within the ground state of a quantum many-body system. Such halos emerge in star-like systems with exponentially decaying couplings, as we show using both free-fermions and the spin-1/2 antiferromagnetic Heisenberg model. Depending on the central connectivity, entanglement halos may exhibit trivial and non trivial symmetry-protected topological features. Our findings highlight how geometry and connectivity can generate complex entanglement structures with rich physical content, which can be experimentally accessible via state-of-the-art technologies.

Quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era presents significant challenges in differentiating quantum software bugs from hardware noise. Traditional debugging techniques from classical software engineering cannot directly resolve this issue due to the inherently stochastic nature of quantum computation mixed with noises from NISQ computers. To address this gap, we propose a statistical approach leveraging probabilistic metrics to differentiate between quantum software bugs and hardware noise. We evaluate our methodology empirically using well-known quantum algorithms, including Grover's algorithm, Deutsch-Jozsa algorithm, and Simon's algorithm. Experimental results demonstrate the efficacy and practical applicability of our approach, providing quantum software developers with a reliable analytical tool to identify and classify unexpected behavior in quantum programs.

We present a transparent and analytically tractable approach to the problem of time-dependent electron transport through tunneling barriers. Using the Single-Electron Approach, we study a model system composed of a time-dependent tunneling barrier coupled to two reservoirs of finite bandwidth. Avoiding Floquet expansions, we derive simple expressions for the time-dependent tunneling current in both adiabatic and non-adiabatic regimes. Our formulation, based on the tunneling Hamiltonian framework, relates barrier modulation to measurable phase shifts in the steady-state current, offering a physically intuitive definition of the tunneling (or traversal) time. Remarkably, in the Markovian limit (wide-band reservoirs), we recover the well-known result of vanishing tunneling time. In contrast, for finite-bandwidth leads, we predict a finite time delay given by the inverse bandwidth. Our findings provide a robust foundation for understanding tunneling dynamics in non-Markovian environments and may serve as a benchmark for experimental investigations involving tunable band structures.

In this note, it is shown that a nonvanishing spatial curvature can generate primordial matter in the post-inflation era. This matter does not depend on the curvature parameter and is described by a stiff equation of state. It can have the properties of spin matter, consisting of particles with a spin quantum number (spin) s = 1/2. Such a matter can be plausibly identified with quark matter at the early stage of the evolution of the universe.

We analyze the zero energy collision of three identical bosons in the same internal state with total orbital angular momentum $L=2$, assuming short range interactions. By solving the Schrödinger equation asymptotically, we derive two expansions of the wave function when three bosons are far apart or a pair of bosons and the third boson are far apart. The scattering hypervolume $D$ is defined for this collision. Unlike the scattering hypervolume defined by one of us in 2008, whose dimension is length to the fourth power, the dimension of $D$ studied in the present paper is length to the eighth power. We then derive the expression of $D$ when the interaction potentials are weak, using the Born's expansion. We also calculate the energy shift of such three bosons with three different momenta $\hbar \mathbf{k_{1}}$, $\hbar\mathbf{k_{2}}$ and $\hbar\mathbf{k_{3}}$ in a large periodic box. The obtained energy shift depends on $D^{(0)}/\Omega^{2}$ and $D/\Omega^{2}$, where $D^{(0)}$ is the three-body scattering hypervolume defined for the three-body $L=0$ collision and $\Omega$ is the volume of the periodic box. We also calculate the contribution of $D$ to the three-body T-matrix element for low-energy collisions. We then calculate the shift of the energy and the three-body recombination rate due to $D^{(0)}$ and $D$ in the dilute homogeneous Bose gas. The contribution to the three-body recombination rate constant from $D$ is proportional to $T^2$ if the temperature $T$ is much larger than the quantum degeneracy temperature but still much lower than the temperature scale at which the thermal de Broglie wave length becomes comparable to the physical range of interaction.

Fluctuations are fundamental in physics and important for understanding and characterizing phase transitions. In this spirit, the phase transition to the Bose-Einstein condensate (BEC) is of specific importance. Whereas fluctuations of the condensate particle number in atomic BECs have been studied in continuous systems, experimental and theoretical studies for lattice systems were so far missing. Here, we explore the condensate particle number fluctuations in an optical lattice BEC across the phase transition in a combined experimental and theoretical study. We present both experimental data using ultracold $^{87}$Rb atoms and numerical simulations based on a hybrid approach combining the Bogoliubov quasiparticle framework with a master equation analysis for modeling the system. We find strongly anomalous fluctuations, where the variance of the condensate number $\delta N_{\rm BEC}^2$ scales with the total atom number as $N^{1+\gamma}$ with an exponent around $\gamma_{\rm theo}=0.74$ and $\gamma_{\rm exp}=0.62$, which we attribute to the 2D/3D crossover geometry and the interactions. Our study highlights the importance of the trap geometry on the character of fluctuations and on fundamental quantum mechanical properties.

Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a sparse structure or a banded structure. We pursue the complexity parameter approach to analyze the spectral statistics of the multiparametric Gaussian ensembles of real asymmetric matrices and derive the ensemble averaged spectral densities for real as well as complex eigenvalues. Considerations of the matrix elements with arbitrary choice of mean and variances render us the freedom to model the desired sparsity in the ensemble. Our formulation provides a common mathematical formulation of the spectral statistics for a wide range of sparse real-asymmetric ensembles and also reveals, thereby, a deep rooted universality among them.

We extend the $(1+1)$-dimensional Dirac-Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate $su(1,1)$ algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the $su(1,1)$ irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

We solve exactly the Schrödinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

We introduce a generalization of the Dunkl-derivative with two parameters to study the Schrödinger equation in Cartesian and polar coordinates in two dimensions. The eigenfunctions and the energy spectrum for the harmonic oscillator and the Coulomb problem are derived in an analytical way and it is shown that our results are properly reduced to those previously reported for the Dunkl derivative with a single parameter.

Exotic entanglement entropy scaling properties usually come with interesting entanglement structures in real space and novel metrics of the spacetime lattice. One prominent example is the rainbow chain where lattice sites symmetric about the center form entangled Bell pairs due to an effective long-range coupling from the strong inhomogeneity of the coupling strength. This manuscript generalizes the rainbow chain to higher dimensional space on lattices with Hausdorff dimension one and enlarged local Hilbert space keeping the Hamiltonian frustration free. The effective Hamiltonian from the Schrieffer-Wolf transformation is given by a stacking of layers of $k$-simplices with $0$-dimensional (fully-connected) antiferromagnetic Hamiltonians, which can be diagonalized analytically with Young operators. The original lattice can be obtained from proliferating disinclination defects in a regular $k$-dimensional cubical lattice, which introduces curvature at the center of the lattice. The model interpolates between the SYK model and the free-fermionic XX spin chain, and hence might be potentially useful in understanding black hole physics and holography.

We propose and analyze a method for improving quantum chemical energy calculations on a quantum computer impaired by decoherence and shot noise. The error mitigation approach relies on the fact that the one- and two-particle reduced density matrices (1- and 2-RDM) of a chemical system need to obey so-called N-representability constraints. We post-process the result of an RDM measurement by projecting it into the subspace where certain N-representability conditions are fulfilled. Furthermore, we utilize that such constraints also hold in the hole and particle-hole sector and perform projections in these sectors as well. We expand earlier work by conducting a careful analysis of the method's performance in the context of quantum computing. Specifically, we consider typical decoherence channels (dephasing, damping, and depolarizing noise) as well as shot noise due to a finite number of projective measurements. We provide analytical considerations and examine numerically three example systems, \ch{H2}, \ch{LiH}, and \ch{BeH2}. From these investigations, we derive our own practical yet effective method to best employ the various projection options. Our results show the approach to significantly lower energy errors and measurement variances of (simulated) quantum computations.

We propose several algorithms for learning unitary operators from quantum statistical queries with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with limited quantum resources, which receives as input only noisy estimates of expected values of measurements. Our approach leverages quantum statistical queries to estimate the Fourier mass of a unitary on a subset of Pauli strings, generalizing previous techniques developed for uniform quantum examples. Specifically, we show that the celebrated quantum Goldreich-Levin algorithm can be implemented with quantum statistical queries, whereas the prior version of the algorithm involves oracle access to the unitary and its inverse. As an application, we prove that quantum Boolean functions with constant total influence or with constant degree are efficiently learnable in our model. Moreover, we prove that $\mathcal{O}(\log n)$-juntas are efficiently learnable and constant-depth circuits are learnable query-efficiently with quantum statistical queries. On the other hand, all previous algorithms for these tasks demand significantly greater resources, such as oracle access to the unitary or direct access to the Choi-Jamiolkowski state. We also demonstrate that, despite these positive results, quantum statistical queries lead to an exponentially larger query complexity for certain tasks, compared to separable measurements to the Choi-Jamiolkowski state. In particular, we show an exponential lower bound for learning a class of phase-oracle unitaries and a double exponential lower bound for testing the unitarity of channels. Taken together, our results indicate that quantum statistical queries offer a unified framework for various unitary learning tasks, with potential applications in quantum machine learning, many-body physics and benchmarking of near-term devices.

Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept of virtual quantum Markov chains (VQMCs), focusing on scenarios where subsystems retain classical information about global systems from measurement statistics. As a generalization of quantum Markov chains, VQMCs characterize states where arbitrary global shadow information can be recovered from subsystems through local quantum operations and measurements. We present an algebraic characterization for virtual quantum Markov chains and show that the virtual quantum recovery is fully determined by the block matrices of a quantum state on its subsystems. Notably, we find a distinction between two classes of tripartite entanglement by showing that the W state is a VQMC while the GHZ state is not. Furthermore, we introduce the virtual non-Markovianity to quantify the non-Markovianity of a given quantum state, which also assesses the optimal sampling overhead for virtually recovering this state. Our findings elucidate distinctions between quantum Markov chains and virtual quantum Markov chains, extending our understanding of quantum recovery to scenarios prioritizing classical information from measurement statistics.

Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these algorithms to be as efficient as possible it is important that we use the fewest number of parameters. We show that, while the general problem of minimising the number of parameters is NP-hard, when we restrict to circuits that are Clifford apart from parametrised phase gates and where each parameter is used just once, we *can* efficiently find the optimal parameter count. We show that when parameter transformations are required to be sufficiently well-behaved, the only rewrites that reduce parameters correspond to simple 'fusions'. Using this we find that a previous circuit optimisation strategy by some of the authors [Kissinger, van de Wetering. PRA (2019)] finds the optimal number of parameters. Our proof uses the ZX-calculus. We also prove that the standard rewrite rules of the ZX-calculus suffice to prove any equality between parametrised Clifford circuits.

We introduce ``dual-unitary shadow tomography'' (DUST), a classical shadow tomography protocol based on dual-unitary brick-wall circuits. To quantify the performance of DUST, we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $\rho(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $\rho(x,t)$ and simulate it numerically using Monte Carlo simulations. For the task of predicting operators with (nearly) full support, we show that DUST outperforms brick-wall Clifford shadows of equal depth. This advantage is further pronounced for small system sizes and our results are generally robust to finite-size effects.

Entanglement distillation is a fundamental information processing task whose implementation is key to quantum communication and modular quantum computing. Noise experienced by such communication and computing platforms occurs not only in the form of Pauli noise such as dephasing (sometimes called $T_2$) but also non-Pauli noise such as amplitude damping (sometimes called $T_1$). We initiate a study of practical and asymptotic distillation over what we call the joint damping-dephasing noise channel. In the practical setting, we propose a distillation scheme that completely isolates away the damping noise. In the asymptotic setting we derive lower bounds on the entanglement sharing capacities including the coherent and reverse coherent information. Like the protocol achieving the reverse coherent information, our scheme uses only backward classical communication. However, for realistic damping noise ($T_1 \neq 2T_2$) our strategy can exceed the reverse coherent strategy, which is the best known for pure damping. In the forward communication setting we numerically exceed the single-letter coherent information strategy by observing the channel displays non-additivity at the two-letter level. The work shows non-additivity can also be found in realistic noise models with magnitudes of non-additivity similar to those found in more idealized noise channels.

Non-stabilizer states are a fundamental resource for universal quantum computation. However,despite broad significance in quantum computing, the emergence of "many-body" non-stabilizerness in interacting quantum systems remains poorly understood due to its analytical intractability. Here we show that Rydberg atom arrays provide a natural reservoir of non-stabilizerness that extends beyond single qubits and arises from quantum correlations engendered by the Rydberg blockade. We demonstrate that this non-stabilizerness can be experimentally accessed in two complementary ways, either by performing quench dynamics or via adiabatic ground state preparation. Using the analytical framework based on matrix product states, we explain the origin of Rydberg nonstabilizerness via a quantum circuit decomposition of the wave function.

Solving combinatorial optimization problems using variational quantum algorithms (VQAs) might be a promise application in the NISQ era. However, the limited trainability of VQAs could hinder their scalability to large problem sizes. In this paper, we improve the trainability of variational quantum eigensolver (VQE) by utilizing convex interpolation to solve portfolio optimization. Based on convex interpolation, the location of the ground state can be evaluated by learning the property of a small subset of basis states in the Hilbert space. This enlightens naturally the proposals of the strategies of close-to-solution initialization, regular cost function landscape, and recursive ansatz equilibrium partition. The successfully implementation of a $40$-qubit experiment using only $10$ superconducting qubits demonstrates the effectiveness of our proposals. Furthermore, the quantum inspiration has also spurred the development of a prototype greedy algorithm. Extensive numerical simulations indicate that the hybridization of VQE and greedy algorithms achieves a mutual complementarity, combining the advantages of both global and local optimization methods. Our proposals can be extended to improve the trainability for solving other large-scale combinatorial optimization problems that are widely used in real applications, paving the way to unleash quantum advantages of NISQ computers in the near future.

The next generation of distributed quantum processors combines single-location quantum computing and quantum networking techniques to permit large entangled qubit groups to be established through remote processors, and quantum algorithms can be executed distributively. We present DisQ, as the first formal model of distributed quantum processors, and permit the analysis of distributed quantum programs in the new computation environment. The core of DisQ is a distributed quantum programming language that combines the concepts of Chemical Abstract Machine (CHAM) and Markov Decision Processes (MDP) with the objective of providing clearly distinguishing quantum concurrent and distributed behaviors. Based on the DisQ language, we develop a simulation relation, based on classical simulation infrastructure, to check the equivalence of a quantum algorithm and its distributed versions so that users can develop the distributed version of a sequential quantum program via a simulation check.

We consider a generic one dimensional spin system of length $ L $, arbitrarily large, with strictly local interactions, for example nearest neighbor, and prove that the dynamical $ \alpha $-Rényi entropies, $ 0 < \alpha \le 1 $, of an initial product state grow at most linearly in time. This result arises from a general relation among dynamical $ \alpha $-Rényi entropies and Lieb-Robinson bounds. We extend our bound on the dynamical generation of entropy to systems with exponential decay of interactions, for values of $\alpha$ close enough to $ 1 $, and moreover to initial pure states with low entanglement, of order $ \log L $, that are typically represented by critical states. We establish that low entanglement states have an efficient MPS representation that persists at least up to times of order $ \log L $. The main technical tools are the Lieb-Robinson bounds, to locally approximate the dynamics of the spin chain, a strict upper bound of Audenaert on $ \alpha $-Rényi entropies and a bound on their concavity. Such a bound, that we provide in an appendix, can be of independent interest.

Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians with an energy gap to the first coupled excited state, the process becomes exceedingly slow as the gap narrows. Rather than strictly following the adiabatic theorem, a more robust approach allows controlled diabatic excitations during the evolution and numerically optimizes the path to eliminate these excitations by the end. In this work, this is achieved via modulated time evolution, using a time dependent oscillating field lambda(t) to modulate the Hamiltonian, in conjunction with a transverse field B(t) whose optimized shape closely resembles a local adiabatic ramp. Beyond modulated time evolution, the quantum approximate optimization algorithm (QAOA), which also employs a transverse field defined as beta(t) over gamma(t), exhibits a shape similar to the local adiabatic ramp. This resemblance offers a more intuitive and physically motivated way to understand the QAOA algorithm through the lens of time evolution.

We present a general framework to implement massive Nambu-Goldstone quasi-particles in driven many-body systems. The underlying mechanism leverages an explicit Lie group structure imprinted into an effective Hamiltonian that governs the dynamics of slow degrees of freedom; the resulting emergent continuous symmetry is weakly explicitly broken, giving rise to a massive Nambu-Goldstone mode, with a spectral mass gap scaling linearly with the drive period. We discuss explicit and experimentally implementable realizations, such as Heisenberg-like spin models that support gapped spin-wave excitations. We provide a protocol to certify the existence of the massive Nambu-Goldstone mode from the dynamics of specific observables, and analyse the dispersion spectrum and their lifetime in the presence of weak explicit symmetry breaking.

We explore the important task of applying a phase $\exp(i\,f(x))$ to a computational basis state $\left| x \right>$. The closely related task of rotating a target qubit by an angle depending on $f(x)$ is also studied. Such operations are key in many quantum subroutines, and frequently $f(x)$ can be well-approximated by a piecewise function; examples range from the application of diagonal Hamiltonian terms (such as the Coulomb interaction) in grid-based many-body simulation, to derivative pricing algorithms. Here we exploit a parallelisation of the piecewise approach so that all constituent elementary rotations are performed simultaneously, that is, we achieve a total rotation depth of one. Moreover, we explore the use of recursive catalyst `towers' to implement these elementary rotations efficiently. We find that strategies prioritising execution speed can achieve circuit depth as low as $O(\log{n}{+}\log{S})$ for a register of $n$ qubits and a piecewise approximation of $S$ sections (presuming prior preparation of enabling resource states), albeit total qubit count then scales with $S$. In the limit of multiple repetitions of the oracle, we find that catalyst tower approaches have an $O(S\cdot n)$ T-count.

Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schrödinger's equation and the second law of thermodynamics. Despite its ubiquity and conceptual significance, the precise conditions that give rise to quantum thermalization are still not well understood. After nearly a century of efforts, we have yet to find a complete mathematical proof that an effective statistical description naturally emerges the underlying quantum dynamics in generic settings. Here, we prove that quantum thermalization must occur in any qubit system with local interactions under three conditions: (i) high effective temperature, (ii) translation invariance, and (iii) no perfect resonances in the energy spectrum. Specifically, we show that a typical, low-complexity pure state drawn from any ensemble with large entropy and well-defined effective temperature becomes locally indistinguishable from a Gibbs state upon unitary evolution. In this setting, our rigorous results prove the widely anticipated notion that statistical physics should be understood as an emergent phenomenon, explicitly derived from the first principles of quantum mechanics.

Embezzlement of entanglement refers to the task of extracting entanglement from an entanglement resource via local operations and without communication while perturbing the resource arbitrarily little. Recently, the existence of embezzling states of bipartite systems of type III von Neumann algebras was shown. However, both the multipartite case and the precise relation between embezzling states and the notion of embezzling families, as originally defined by van Dam and Hayden, was left open. Here, we show that finite-dimensional approximations of multipartite embezzling states form multipartite embezzling families. In contrast, not every embezzling family converges to an embezzling state. We identify an additional consistency condition that ensures that an embezzling family converges to an embezzling state. This criterion distinguishes the embezzling family of van Dam and Hayden from the one by Leung, Toner, and Watrous. The latter generalizes to the multipartite setting. By taking a limit, we obtain a multipartite system of commuting type III$_1$ factors on which every state is an embezzling state. We discuss our results in the context of quantum field theory and quantum many-body physics. As open problems, we ask whether vacua of relativistic quantum fields in more than two spacetime dimensions are multipartite embezzling states and whether multipartite embezzlement allows for an operator-algebraic characterization.

We study the Hamiltonian of two isotropic oscillators with weak coupling from an algebraic approach. We write the Hamiltonian of this problem in terms of the boson generators of the $SU(1,1)$ and $SU(2)$ groups. This allows us to apply two tilting transformations based on both group similarity transformations to obtain its energy spectrum and eigenfunctions. Then, we obtain the Mandel $Q$-parameter and the second-order correlation function $g^2(0)$ of the photon numbers $n_a$ and $n_b$. It is important to note that in our procedure we consider the case of weak coupling.

Solid-state spin systems hold great promise for quantum information processing and the construction of quantum networks. However, the considerable inhomogeneity of spins in solids poses a significant challenge to the scaling of solid-state quantum systems. A practical protocol to individually control and entangle spins remains elusive. To this end, we propose a hybrid spin-phonon architecture based on spin-embedded SiC optomechanical crystal (OMC) cavities, which integrates photonic and phononic channels allowing for interactions between multiple spins. With a Raman-facilitated process, the OMC cavities support coupling between the spin and the zero-point motion of the OMC cavity mode reaching 0.57 MHz, facilitating phonon preparation and spin Rabi swap processes. Based on this, we develop a spin-phonon interface that achieves a two-qubit controlled-Z gate with a simulated fidelity of $96.80\%$ and efficiently generates highly entangled Dicke states with over $99\%$ fidelity, by engineering the strongly coupled spin-phonon dark state which is robust against loss from excited state relaxation as well as spectral inhomogeneity of the defect centers. This provides a hybrid platform for exploring spin entanglement with potential scalability and full connectivity in addition to an optical link, and offers a pathway to investigate quantum acoustics in solid-state systems.

The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-1/2 XXZ model. These circuits represent a unitary formulation of the standard algebraic Bethe Ansatz, expressed using matrix-product states that act on both the spin chain and an auxiliary space. In this work, we systematize these previous results, and show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. The new basis, identical to the "F-basis" known from the theory of quantum-integrable models, generates the linear superposition of plane waves that is characteristic of the coordinate Bethe Ansatz. We explain this connection, highlighting that certain properties of the F-basis (namely, the exchange symmetry of the spins) are crucial for the construction of algebraic Bethe circuits. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-1/2 XXZ model.

In this article the weakest possible theorem giving a foundation behind the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelled out in detail. It is argued that, from this approach, a general epistemic interpretation of quantum mechanics is natural. Some applications to the Bell experiment and to decision theory are briefly discussed. The article represents the conclusion of a series of articles and books on quantum foundations.

The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of the supports of logical operators, can give rise to non-Clifford $T$ and $CCZ$ gates. Here we present a color code with a logical control-$S$ gate that is accomplished with transversal $T$ and $T^\dagger$ rotations on its physical qubits.

Machine learning offers a promising methodology to tackle complex challenges in quantum physics. In the realm of quantum batteries (QBs), model construction and performance optimization are central tasks. Here, we propose a cavity-Heisenberg spin chain quantum battery (QB) model with spin-$j (j=1/2,1,3/2)$ and investigate the charging performance under both closed and open quantum cases, considering spin-spin interactions, ambient temperature, and cavity dissipation. It is shown that the charging energy and power of QB are significantly improved with the spin size. By employing a reinforcement learning algorithm to modulate the cavity-battery coupling, we further optimize the QB performance, enabling the stored energy to approach, even exceed its upper bound in the absence of spin-spin interaction. We analyze the optimization mechanism and find an intrinsic relationship between cavity-spin entanglement and charging performance: increased entanglement enhances the charging energy in closed systems, whereas the opposite effect occurs in open systems. Our results provide a possible scheme for design and optimization of QBs.

Multipartite entangled states, particularly Greenberger--Horne--Zeilinger (GHZ) and other graph states, are important resources in multiparty quantum network protocols and measurement-based quantum computing. We consider the problem of generating such states from networks of bipartite entangled (Bell) pairs. We adopt the perspective that, in practice, unlike the traditional information-theoretic setting, local operations and classical communications are not free. Consequently, protocols should not only be efficient with respect to the number of consumed Bell pairs, as typically considered, but also efficient with respect to the number of (local) gates, number of Bell-pair sources, and computational complexity. In this work, we present a protocol for producing GHZ states in arbitrary Bell-pair networks that is efficient with respect to all of these figures of merit. We prove that our protocol: (1) requires $O(N)$ gates in a network with $N$ nodes, independent of the topology of the network; (2) has time complexity $O(N^2)$, thereby avoiding finding a Steiner tree or solving any other computationally hard problem; and (3) maintains nearly the optimal number of consumed Bell pairs. We prove that the minimal Bell-pair source cost is equivalent to the graph-theoretic dominating set problem, and via numerical simulations on real-world network models, we demonstrate that our protocol is nearly optimal with respect to Bell-pair source cost. Numerically, our protocol also outperforms existing protocols based on (approximate) Steiner trees with respect to both number of gates and Bell-pair sources. Finally, we provide a detailed analysis of the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.

TThe organization and structure of bipartite mixed-state quantum entanglement (QE) are more complex and less well understood compared to bipartite pure-state QE. Bipartite mixed-state QEs and their measures play a crucial role in both theory and practical applications. Some existing measures involve quantifying the minimum QE and reflect the inherently complex nature of their computation, while others are only applicable to highly limited-dimensional quantum systems. In this context, we propose a method termed Reduction-induced Variation of Partial Von Neumann Entropy to quantify QE in any bipartite states, particularly focusing on bipartite mixed states. Partial Von Neumann Entropy is merely a special case of this method,Its intuitive and clear physical representation, along with easy computation and wide applicability, facilitates exploring its potential applications. Furthermore, we present examples to demonstrate the superiorities of this method in identifying bipartite QE by comparing with other existing bipartite mixed-state QE measures through both their physical implications and mathematical structures.

We consider the dynamics in the one-dimensional quantum Ising model in which each spin coherently interacts with its phononic mode. The model is motivated by quantum simulators based on Rydberg atoms in tweezers or trapped ions. The configuration of two domain walls simulates the particle-antiparticle connecting string. We concentrate on the effect the local vibrations have on the dynamics of this initial state. Our study supplements recent investigations of string breaking, traditionally studied within quantum chromodynamics (QCD), to quantum many-body systems. Two regimes are identified depending on the strength of the coupling with local vibrations. For weak coupling, the string breaking is slowed down as compared to the dynamics in an isolated Ising string. The strong coupling leads to complicated dynamics in which the domain wall character of excitation is dissolved among many coupled states.

Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents Tile Trotterization, a generalization of plaquette Trotterization (PLAQ), which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The Tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of Tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of Tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that Tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.

Quantum information scrambling (QIS) describes the rapid spread of initially localized information across an entire quantum many-body system through entanglement generation. Once scrambled, the original local information becomes encoded globally, inaccessible from any single subsystem. In this work, we introduce a protocol that enables information scrambling into the past, allowing decoding even before the original information is generated. This protocol is achieved by simulating a closed timelike curve (a theoretical construct in which particles can traverse backward in time) using postselection methods. Remarkably, the postselected outcome corresponds to a paradox-free trajectory that enables consistent time travel and reliable information recovery. Furthermore, the success probability is governed by out-of-time-ordered correlations, which is a standard measure of QIS. We present a quantum circuit design and experimentally implement our protocol on cloud-based Quantinuum and IBM quantum processors. Our approach illuminates a unique quantum task: retrieving information encoded in the future without altering the past.

Leakage errors are unwanted transfer of population outside of a defined computational subspace and they occur in almost every platform for quantum computing. While prevalent, leakage is often overlooked when measuring and reporting the fidelity of quantum gates with standard methods. In fact, when leakage is substantial it can cause a large overestimation of fidelity from the typical method used to measure fidelity, randomized benchmarking. We provide several methods for properly estimating fidelity in the presence of leakage errors that are applicable in different error regimes with carefully chosen sequence lengths. Then, we numerically demonstrate the methods for two-qubit randomized benchmarking, which often have the largest errors. Finally, we reanalyze previously shared data from Quantinuum systems with some of the methods provided.

We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched Rényi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version, and more generally, additive across tensor products of channels. For the purposes of cryptography, applying our chain rule to sequences of channels yields a new variant of Rényi entropy accumulation, in which we can impose some specific forms of marginal-state constraint on the input states to each individual channel. This generalizes a recently introduced security proof technique that was developed to analyze prepare-and-measure QKD with no limitations on the repetition rate. In particular, our generalization yields ``fully adaptive'' protocols that can in principle update the entropy estimation procedure during the protocol itself, similar to the quantum probability estimation framework.

Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator scrambling via Holevo information of operators, by taking its capacity to distinguish operator information locally. We show that the operator size is closely related to a special kind of Holevo information of operators. Moreover, we propose a feasible protocol for measuring Holevo information of operators on digital quantum simulators based on random states. \textcolor{black}{For the mixed-field Ising model,} our numerical simulations show that the integrable system can be told apart from the chaotic system by measuring the spatial-temporal patterns of Holevo information. Furthermore, we find that error mitigation is required to restore the time-oscillation behavior of Holevo information for the integrable system, a crucial feature distinct from the chaotic one. Our work provides a new perspective to understand the information scrambling and quantum chaos from aspects of Holevo information of operators.

Quantum kernels (QK) are widely used in quantum machine learning applications; yet, their potential to surpass classical machine learning methods on classical datasets remains uncertain. This limitation can be attributed to the exponential concentration phenomenon, which can impair generalization. A common strategy to alleviate this is bandwidth tuning, which involves rescaling data points in the quantum model to improve generalization. In this work, we numerically demonstrate that optimal bandwidth tuning results in QKs that closely resemble radial basis function (RBF) kernels, leading to a lack of quantum advantage over classical methods. Moreover, we reveal that the size of optimal bandwidth tuning parameters further simplifies QKs, causing them to behave like polynomial kernels, corresponding to a low-order Taylor approximation of a RBF kernel. We thoroughly investigate this for fidelity quantum kernels and projected quantum kernels using various data encoding circuits across several classification datasets. We provide numerical evidence and derive a simple analytical model that elucidates how bandwidth tuning influences key quantities in classification tasks. Overall, our findings shed light on the mechanisms that render QK methods classically tractable.

These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by the topology of spaces that are used as modules to build the quantum mechanical model, while expectation values and probabilities are given by topological invariants of spaces, knots and links. The notes focus on the specific way the topology encodes quantum mechanical features, or, equivalently, on how these features can be controlled through the topology. A topological classification of entanglement is discussed, as well as properties of entanglement entropy and basic quantum protocols. The primary aim is to build a less conventional diagrammatic intuition about quantum mechanics, expanding the paradigm of ``Quantum Picturalism".

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers), when co-designed with hardware to implement powerful Monte Carlo algorithms, provide a compelling and scalable classical pathway for solving hard optimization problems. We focus on two key algorithms applied to 3D spin glasses: discrete-time simulated quantum annealing (DT-SQA) and adaptive parallel tempering (APT). We benchmark these methods against the performance of a leading quantum annealer on the same problem instances. For DT-SQA, we find that increasing the number of replicas improves residual energy scaling, in line with expectations from extreme value theory. We then show that APT, when supported by non-local isoenergetic cluster moves, exhibits a more favorable scaling and ultimately outperforms DT-SQA. We demonstrate these algorithms are readily implementable in modern hardware, projecting that custom Field Programmable Gate Arrays (FPGA) or specialized chips can leverage massive parallelism to accelerate these algorithms by orders of magnitude while drastically improving energy efficiency. Our results establish a new, rigorous classical baseline, clarifying the landscape for assessing a practical quantum advantage and presenting p-computers as a scalable platform for real-world optimization challenges.

While the adiabatic exchange of Majorana zero modes (MZMs) enables a non-universal set of geometrically protected gates, realising an experimental implementation of MZM braiding remains challenging. In an alternative proposal, charge-parity measurement of two neighboring MZMs supports braiding by teleportation. Moreover, owing to the lack of definitive evidence of MZMs in semiconducting systems, there have been several simulations of MZMs on NISQ devices which more naturally lend themselves to braiding. In this work, measurement-based braiding about MZM Y-junctions are simulated by multi-qubit Pauli-parity measurements of a logical qubit. Logical single-qubit geometric $S^{(\dagger)}$-gates and entangling two-qubit gates is shown using two-physical-qubit joint measurements alone, whilst partial phase rotations such as a $T^{(\dagger)}$-gates require at least one three-qubit joint measurement. These relatively small scale circuits offer both novel measurement-based geometric gates as well as a measurement-based demonstration of quantum Hamiltonian simulation.

Measurement based quantum computing is preformed by adding non-Clifford measurements to a prepared stabilizer states. Entangling gates like CZ are likely to have lower fidelities due to the nature of interacting qubits, so when preparing a stabilizer state, we wish to minimize the number of required entangling states. This naturally introduces the notion of CZ-distance. Every stabilizer state is local-Clifford equivalent to a graph state, so we may focus on graph states $\left\vert G \right\rangle$. As a lower bound for general graphs, there exist $n$-vertex graphs $G$ such that the CZ-distance of $\left\vert G \right\rangle$ is $\Omega(n^2 / \log n)$. We obtain significantly improved bounds when $G$ is contained within certain proper classes of graphs. For instance, we prove that if $G$ is a $n$-vertex circle graph with clique number $\omega$, then $\left\vert G \right\rangle$ has CZ-distance at most $4n \log \omega + 7n$. We prove that if $G$ is an $n$-vertex graph of rank-width at most $k$, then $\left\vert G \right\rangle$ has CZ-distance at most $(2^{2^{k+1}} + 1) n$. More generally, this is obtained via a bound of $(k+2)n$ that we prove for graphs of twin-width at most $k$. We also study how bounded-rank perturbations and low-rank cuts affect the CZ-distance. As a consequence, we prove that Geelen's Weak Structural Conjecture for vertex-minors implies that if $G$ is an $n$-vertex graph contained in some fixed proper vertex-minor-closed class of graphs, then $\left\vert G \right\rangle$ has CZ-distance at most $O(n\log n)$. Since graph states of locally equivalent graphs are local Clifford equivalent, proper vertex-minor-closed classes of graphs are natural and very general in this setting.

Recently, the synchronization of coupled quantum oscillators has attracted a great deal of interest. Synchronization requires driven constituents, and in such systems, the coupling can be designed to be nonreciprocal. Nonreciprocally coupled oscillators exhibit a rich variety of behavior including active traveling-wave-type states. In this work, we study the interplay of three competing synchronization mechanisms in a setup of two nonreciprocally coupled quantum van der Pol oscillators. One of the oscillators is driven externally which induces phase locking. A dissipative interaction leads to antiphase locking, whereas a coherent interaction nurtures bistable phase locking and active states. We approximate the phase diagram of the quantum case by evaluating the synchronization measure of a perturbation expansion of the steady state. Effective unidirectional interactions lead to synchronization blockades between the undriven oscillator and the external drive as well as between both oscillators. Furthermore, we study the phase diagrams of two and three oscillators in the mean-field limit and find highly nontrivial active states.

Quantum combinatorial optimization algorithms typically face challenges due to complex optimization landscapes featuring numerous local minima, exponentially scaling latent spaces, and susceptibility to quantum hardware noise. In this study, we introduce Direct Entanglement Ansatz Learning (DEAL), wherein we employ a direct mapping from quadratic unconstrained binary problem parameters to quantum ansatz angles for cost and mixer hamiltonians, which improves the convergence rate towards the optimal solution. Our approach exploits a quantum entanglement-based ansatz to effectively explore intricate latent spaces and zero noise extrapolation (ZNE) to greatly mitigate the randomness caused by crosstalk and coherence errors. Our experimental evaluation demonstrates that DEAL increases the success rate by up to 14% compared to the classic quantum approximation optimization algorithm while also controlling the error variance. In addition, we demonstrate the capability of DEAL to provide near optimum ground energy solutions for travelling salesman, knapsack, and maxcut problems, which facilitates novel paradigms for solving relevant NP-hard problems and extends the practical applicability of quantum optimization using noisy quantum hardware.

This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities, the authors establish tighter bounds for information-theoretic security, demonstrating that quantum protocols inherently outperform classical counterparts in balancing privacy and efficiency. Also explores symmetric Quantum Private Information Retrieval (QPIR) protocols that achieve sub-linear communication complexity while ensuring robustness against specious adversaries: A post-quantum cryptography based protocol that can be authenticated for the specious server; A ring-LWE-based protocol for post-quantum security in a single-server setting, ensuring robustness against quantum attacks; A multi-server protocol optimized for hardware practicality, reducing implementation overhead while maintaining sub-linear efficiency. These protocols address critical gaps in secure database queries, offering exponential communication improvements over classical linear-complexity methods. The work also analyzes security trade-offs under quantum specious adversaries, providing theoretical guarantees for privacy and correctness.

We consider a 2D atomic array coupled to different photonic environments, focusing on the half-filled excitation subspace, where strong photon interactions can give rise to complex many-body states. In particular, we demonstrate that the least radiant state in this sector is well described by a coherent superposition of all possible quantum dimer coverings: a resonating valence bond (RVB) liquid state. We discuss possible strategies to probe this exotic state, along with their limitations and challenges. Finally, we show that such a quantum dimer covering can also emerge as the ground state of the coherent Hamiltonian describing a 2D atomic array coupled to a photonic band-gap material.

The Quantum Internet, a network of quantum-enabled infrastructure, represents the next frontier in telecommunications, promising capabilities that cannot be attained by classical counterparts. A crucial step in realizing such large-scale quantum networks is the integration of entanglement distribution within existing telecommunication infrastructure. Here, we demonstrate a real-world scalable quantum networking testbed deployed within Deutsche Telekom's metropolitan fibers in Berlin. Using commercially available quantum devices and standard add-drop multiplexing hardware, we distributed polarization-entangled photon pairs over dynamically selectable fiber paths ranging from 10~m to 60 km, and showed entanglement distribution over up to approximately 100~km. Quantum signals, transmitted at 1324~nm (O-band), coexist with conventional bidirectional C-band traffic without dedicated fibers or infrastructure changes. Active stabilization of the polarization enables robust long-term performance, achieving entanglement Bell-state fidelity bounds between 85-99% and Clauser-Horne-Shimony-Holt parameter $S$-values between 2.36-2.74 during continuous multiday operation. By achieving a high-fidelity entanglement distribution with less than 1.5% downtime, we confirm the feasibility of hybrid quantum-classical networks under real-world conditions at the metropolitan scale. These results establish deployment benchmarks and provide a practical roadmap for telecom operators to integrate quantum capabilities.

All physical theories should obey the second law of thermodynamics. However, existing proposals to describe the dynamics of hybrid classical-quantum systems either violate the second law or lack a proof of its existence. Here we rectify this by studying classical-quantum dynamics that are (1) linear and completely-positive and (2) preserve the thermal state of the classical-quantum system. We first prove that such dynamics necessarily satisfy the second law. We then show how these dynamics may be constructed, proposing dynamics that generalise the standard Langevin and Fokker-Planck equations for classical systems in thermal environments to include back-reaction from a quantum degree of freedom. Deriving necessary and sufficient conditions for completely-positive, linear and continuous classical-quantum dynamics to satisfy detailed balance, we find this property satisfied by our dynamics. To illustrate the formalism and its applications we introduce two models. The first is an analytically solvable model of an overdamped classical system coupled to a quantum two-level system, which we use to study the total entropy production in both quantum system and classical measurement apparatus during a quantum measurement. The second describes an underdamped classical-quantum oscillator system subject to friction, which we numerically demonstrate exhibits thermalisation in the adiabatic basis, showing the relevance of our dynamics for the mixed classical-quantum simulation of molecules.

Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is examined in detail. It has three instanton types or flavors with distinct actions. For weak coupling and subject to there being a single large (or small) parameter, the interactive system can be handled perturbatively. The zero mode problem arising from time translation symmetry is handled via the Fadeev-Popov procedure. A diagrammatic procedure allows corrections to the fluctuation determinant to be calculated systematically. Independent instanton contributions are summed over by extending the dilute gas approximation to three flavors and energy splittings of the lowest four states is calculated. All tunneling amplitudes are concisely expressed in terms of elementary functions. While the model is possibly useful for a variety of physical systems, an application is made here to the tunneling of a composite particle in one dimension.

The Petz recovery map provides a near-optimal reversal of quantum noise, yet proposals for its implementation are only recent. We propose a physical realization of the exact state-specific Petz map in an ion trap for qubit decoherence channels. Our circuit constructions require at most $1 (2)$ ancilla qubits and $3 (20)$ CNOT gates for channels with Kraus rank $2 (>2)$. We analyze typical ion trap errors and construct corresponding Petz maps, simulating their performance under realistic noise modeled by residual spin-motion coupling. Quantum circuits are provided for depolarizing, dephasing, and amplitude damping channels. Focusing on single-shot recovery, suited for present-day devices, we also quantify the precision of prior knowledge required to achieve a recovery error below 0.01 across varying decoherence levels and state purities.

We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical subgraphs with unitary symmetry described by complex conjugate Hamiltonians, that are coupled by a pair of bonds. The results are compared to random-matrix theory predictions obtained on the basis of the Heidelberg approach for the scattering matrix of open quantum-chaotic systems. We demonstrate that deviations from random-matrix theory predictions observed in the distributions may be attributed to the fact that the subgraphs are not fully connected.

Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as pseudo-random generators, leakage-resilient cryptography, and randomness extractors. In the quantum setting, however, computational analogues of entropy remain largely unexplored. In this work, we initiate the study of quantum computational entropy by defining quantum computational unpredictability entropy, a natural generalization of classical unpredictability entropy to the quantum setting. Our definition builds on the operational interpretation of quantum min-entropy as the optimal guessing probability, while restricting the adversary to efficient guessing strategies. We prove that this entropy satisfies several fundamental properties, including a leakage chain rule that holds even in the presence of unbounded prior quantum side-information. We also show that unpredictability entropy enables pseudo-randomness extraction against quantum adversaries with bounded computational power. Together, these results lay a foundation for developing cryptographic tools that rely on min-entropy in the quantum computational setting.

We demonstrate how a single heat exchange between a probe thermal qubit and multi-qubit thermal machine encoding a Boolean function, can determine whether the function is balanced or constant, thus providing a novel thermodynamic solution to the Deutsch-Jozsa problem. We introduce a thermodynamic model of quantum query complexity, showing how qubit thermal machines can act as oracles, queried via heat exchange with a probe. While the Deutsch-Jozsa problem requires an exponential encoding in the number of oracle bits, we also explore the Bernstein-Vazirani problem, which admits a linear thermal oracle and a single thermal query solution. We establish bounds on the number of samples needed to determine the probe temperature encoding the solution for the Deutsch-Jozsa problem, showing that it remains constant with problem size. Additionally, we propose a proof-of-principle experimental implementation to solve the 3-bit Bernstein-Vazirani problem via thermal kickback. This work bridges thermodynamics and complexity theory, suggesting a new test bed for quantum thermodynamic computing.

In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state. However, accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator. In this work, we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap. By utilizing the Choi-Jamiokowski isomorphism, we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian. Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence. Moreover, to address scenarios with degenerate steady states, we introduce an iterative energy-offset scanning technique. Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths. These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.

Widely used in atomic and superconducting qubit systems, the Jaynes-Cummings (JC) Hamiltonian is a simple, yet powerful model for a two-level system interacting with a quantum harmonic oscillator. In this paper, we focus on a system of n qubits, identically coupled to a single oscillator via JC interaction, also known as the Tavis-Cummings (TC) Hamiltonian. We show that all permutationally-invariant unitaries on an arbitrary number of qubits can be realized using this permutationally-invariant Hamiltonian, which couples the qubits to an oscillator initialized in its vacuum state, together with global uniform x and z fields on all qubits. This includes useful gates, such as controlled-Z gate with an arbitrary number of control qubits. As a corollary, we find that all permutationally invariant states -- including useful entangled states such as GHZ and Dicke states -- can be prepared using this interaction and global fields. We also characterize unitaries that can be realized on the joint Hilbert space of the qubits and oscillator with the TC interaction and global z field, and develop new methods for preparing the state of the oscillator in an arbitrary initial state. We present various examples of explicit circuits for the case of n=2 qubits. In particular, we develop new methods for implementing controlled-Z, SWAP, iSWAP, and $\sqrt{i\text{SWAP}}$ gates using only the TC interaction and a global z field. Our work also reveals an accidental symmetry in the TC Hamiltonian and shows that it can be explained using Schwinger's oscillator model of angular momentum.

The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational quantum mechanics from well known inference principles -- probability, entropy and information geometry. Although only partially relational -- the absolute structures of simultaneity and Euclidean geometry are still retained -- these models provide a useful testing ground for ideas that will prove useful in the context of more realistic relativistic theories. The fact that in ED the positions of particles have definite values, just as in classical mechanics, has allowed us to adapt to the quantum case some intuitions from Barbour and Bertotti's classical framework. Here, however, we propose a new measure of the mismatch between successive states that is adapted to the information metric and the symplectic structures of the quantum phase space. We make explicit that ED is temporally relational and we construct non-relativistic quantum models that are spatially relational with respect to rigid translations and rotations. The ED approach settles the longstanding question of what form should the constraints of a classical theory take after quantization: the quantum constraints that express relationality are to be imposed on expectation values. To highlight the potential impact of these developments, the non-relativistic quantum model is parametrized into a generally covariant form and we show that the ED approach evades the analogue of what in quantum gravity has been called the problem of time.

We establish and analyse the performance and resource requirements of an end-to-end fault-tolerant quantum algorithm for computing the absorption spectrum and population dynamics of photoexcited pyrazine. The quantum circuit construction consists of initial state preparation using uniformly controlled rotations, the time-dependent Hamiltonian propagation based on the grid-based Split Operator Quantum Fourier Transform (SO-QFT) method, and cost-effective measurements including statistical and canonical phase estimation. We use classical emulations to validate the quantum resources required for the task, and propose generalised formulae for the qubit count and gate depth calculation. Simulating the vibronic dynamics of pyrazine in a low-dimensional abstraction requires 17-qubit circuits with a gate depth of $\mathcal{O}(10^4)$, whereas a full-dimensional simulation of pyrazine in 24 modes requires at least 97-qubit circuits with a gate depth of $\mathcal{O}(10^6)$. Our work provides a foundational framework for understanding high-dimensional wavepacket-based quantum simulations of photo-induced dynamics and vibronic spectra, anticipating future applications in the simulation of even larger molecular systems on fault-tolerant quantum computers.

Magnetic resonance imaging (MRI) is a foundational tool in the physical and life sciences, yet conventional implementations are typically limited to macroscopic spatial resolution. Here, we introduce a method for nanoscale MRI by combining strong, time-dependent magnetic field gradients with global coherent control over a dense ensemble of electron spins in diamond. This approach enables spatially structured manipulation of spin dynamics, allowing us to generate and track nanoscale spin textures - patterns of spin polarization - that evolve under engineered many-body dipolar interactions. By tuning the rotational symmetry of the dipolar exchange interactions, we observe pronounced sensitivity of the spin dynamics to the microscopic structure of the polarization, which we resolve through nanoscale MRI. Our results open the door for robust control of metrologically useful entanglement and nanoscale imaging of materials and biological systems under ambient conditions.

Quantum physics exhibits an intrinsic and private form of randomness with no classical counterpart. Any setup for quantum randomness generation involves measurements acting on quantum states. In this work, we consider the following question: Given a quantum measurement, how much randomness can be generated from it? In real life, measurements are noisy and thus contain an additional, extrinsic form of randomness due to ignorance. This extrinsic randomness is not private since, in an adversarial model, it takes the form of quantum side information held by an eavesdropper who can use it to predict the measurement outcomes. Randomness of measurements is then quantified by the guessing probability of this eavesdropper, when minimized over all possible input states. This optimization is in general hard to compute, but we solve it here for any two-outcome qubit measurement and for projective measurements in arbitrary dimension mixed with white noise. We also construct, for a given measured probability distribution, different realizations with (i) a noisy state and noiseless measurement (ii) a noiseless state and noisy measurement and (iii) a noisy state and measurement, and we show that the latter gives an eavesdropper significantly higher guessing power.

We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a new generalization of symmetry for open quantum systems. For abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has non-trivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.

We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices, which frequently arise in the numerical solution of partial differential equations (PDEs). While LCU is a foundational primitive in both variational and fault-tolerant quantum algorithms, conventional approaches based on the Pauli basis can require a number of terms that scales quadratically with matrix size. We introduce the Sigma basis, a compact set of simple, non-unitary operators that can better capture sparsity and structure, enabling decompositions with only polylogarithmic scaling in the number of terms. We develop both numerical and semi-analytical methods for computing Sigma basis decompositions of arbitrary matrices. Given this new basis is comprised of non-unitary operators, we leverage the concept of unitary completion to design efficient quantum circuits for evaluating observables in variational quantum algorithms and for constructing block encodings in fault-tolerant quantum algorithms. We compare our method to related techniques like unitary dilation, and demonstrate its effectiveness through several PDE examples, showing exponential improvements in decomposition size while retaining circuit efficiency.

In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998. By choosing the optimal input distribution, we recover the optimal error exponent (i.e., the reliability function) of classical-quantum channels for rates above the critical rate. Our result extends to various quantum packing-type problems, including classical communication over any fully quantum channel with or without entanglement-assistance, constant composition codes, and classical data compression with quantum side information via fixed-length or variable-length coding. Our technical ingredient is to establish an operator layer cake theorem - the directional derivative of an operator logarithm admits an integral representation of certain projections. This shows that a kind of pretty-good measurement is equivalent to a randomized Holevo-Helstrom measurement, which provides an operational explanation of why the pretty-good measurement is pretty good.

Substitutional nitrogen atoms in a diamond crystal (P1 centers) are, on one hand, a resource for creation of nitrogen-vacancy (NV) centers, that have been widely employed as nanoscale quantum sensors. On the other hand, P1's electron spin is a source of paramagnetic noise that degrades the NV's performance by shortening its coherence time. Accurate quantification of nitrogen concentration is therefore essential for optimizing diamond-based quantum devices. However, bulk characterization methods based on optical absorption or electron paramagnetic resonance often overlook local variations in nitrogen content. In this work, we use a helium ion microscope to fabricate nanoscale NV center ensembles at predefined sites in a diamond crystal containing low concentrations of nitrogen. We then utilize these NV-based probes to measure the local nitrogen concentration on the level of 230 ppb (atomic parts per billion) using the double electron-electron resonance (DEER) technique. Moreover, by comparing the DEER spectra with numerical simulations, we managed to determine the concentration of other unknown paramagnetic defects created during the ion implantation, reaching 15 ppb depending on the implantation dose.

We present a detailed theoretical treatment of four-wave mixing (FWM) in a quantized paraxial framework, capturing the multi-spatial-mode nature of the biphoton state generated in the process. By analyzing the biphoton state both in position and momentum representations, we identify the conditions under which these descriptions become equivalent. We also highlight formal and physical similarities between FWM and spontaneous parametric down-conversion (PDC), showing that the transfer of pump structure to the spatial coincidence profile, an important and well-known characteristic of the biphoton state, carries over naturally to FWM. In addition, our treatment captures the transition from position correlations in the near field to momentum correlations in the far field, reflecting the underlying spatial entanglement. The measures of entanglement, including the spiral bandwidth and the Schmidt rank, are discussed. Our work consolidates known and new results on spatial correlations in FWM and provides a theoretical framework that may support future studies in nonlinear and quantum optics with structured light.

Simulating nuclear matter described by quantum chromodynamics using quantum computers is notoriously inefficient because of the assortment of quark degrees of freedom such as matter/antimatter, flavor, color, and spin. Here, we propose to address this resource efficiency challenge by encoding three qubits within individual ytterbium-171 atoms of a neutral atom quantum processor. The three qubits are encoded in three distinct sectors: an electronic "clock" transition, the spin-1/2 nucleus, and the lowest two motional states in one radial direction of the harmonic trapping potential. We develop a family of composite sideband pulses and demonstrate a universal gate set and readout protocol for this three-qubit system. We then apply it to single-flavor quantum chromodynamics in 1+1D axial gauge for which the three qubits directly represent the occupancy of quarks in the three colors. We show that two atoms are sufficient to simulate both vacuum persistence oscillations and string breaking. We consider resource requirements and connections to error detection/correction. Our work is a step towards resource-efficient digital simulation of nuclear matter and opens new opportunities for versatile qubit encoding in neutral atom quantum processors.

In this paper we study the $(2+1)$-dimensional Klein-Gordon oscillator coupled to an external magnetic field, in which we change the standard partial derivatives for the Dunkl derivatives. We find the energy spectrum (Landau levels) in an algebraic way, by introducing three operators that close the $su(1,1)$ Lie algebra and from the theory of unitary representations. Also we find the energy spectrum and the eigenfunctions analytically, and we show that both solutions are consistent. Finally, we demonstrate that when the magnetic field vanishes or when the parameters of the Dunkl derivatives are set zero, our results are adequately reduced to those reported in the literature.

Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby operators are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a resolvent formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory.

We study a free open fermionic string theory within a non-commutative target phase-space, considering non-commutativity in both the spatial and momentum components. The altered commutation relations are expressed in terms of mode oscillators. We derive modified super-Virasoro algebras for both the Ramond and Neveu-Schwarz sectors, which include new anomaly terms arising from non-commutativity. This non-commutativity breaks Lorentz covariance and leads to a non-diagonal mass operator in the conventional Fock space. To address this, we propose a redefinition of the Fock space that diagonalizes the matrices of non-commutativity parameters, thereby yielding a diagonal mass operator. To eliminate the anomalies in the Virasoro algebra caused by non-commutativity and recover the standard mass spectrum, certain constraints are imposed on the non-commutativity parameters. Under these conditions, the GSO projection becomes viable, allowing for the emergence of space-time supersymmetry. Additional constraints on the zero modes of the non-commutativity parameters are introduced to restore Lorentz covariance.

Rydberg atom array experiments have demonstrated the ability to act as powerful quantum simulators, preparing strongly-correlated phases of matter which are challenging to study for conventional computer simulations. A key direction has been the implementation of interactions on frustrated geometries, in an effort to prepare exotic many-body states such as spin liquids and glasses. In this paper, we apply two-dimensional recurrent neural network (RNN) wave functions to study the ground states of Rydberg atom arrays on the kagome lattice. We implement an annealing scheme to find the RNN variational parameters in regions of the phase diagram where exotic phases may occur, corresponding to rough optimization landscapes. For Rydberg atom array Hamiltonians studied previously on the kagome lattice, our RNN ground states show no evidence of exotic spin liquid or emergent glassy behavior. In the latter case, we argue that the presence of a non-zero Edwards-Anderson order parameter is an artifact of the long autocorrelations times experienced with quantum Monte Carlo (QMC) simulations, and we show that autocorrelations can be systematically reduced by increasing numerical effort. This result emphasizes the utility of autoregressive models, such as RNNs, in conjunction with QMC, to explore Rydberg atom array physics on frustrated lattices and beyond.

We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ Majorana fermions with $q$-body fermion interaction with $q=4,6,8$ for a range of sparse parameter $k$ that controls the number of remaining terms in the original SYK model after sparsification. The critical value of $k$ below which the model ceases to be holographic, denoted $k_c$, has been subject of several recent investigations. Using Krylov complexity as a probe, we find that the peak value of complexity does not change as we increase $k$ beyond $k \ge k_{\text{min}}$ at large temperatures. We argue that this behavior is related to the change in the holographic nature of the Hamiltonian in the sparse SYK-type models such that the model is holographic for all $k \ge k_{\text{min}} \approx k_c$. Our results provide a novel way to determine $k_c$ in SYK-type models.

High-quality potential energy surfaces (PES) are a prerequisite for quantitative atomistic simulations, with both quantum and classical dynamics approaches. The ultimate test for the validity of a PES are comparisons with judiciously chosen experimental observables. Here we ask whether cold collision measurements are sufficiently informative to validate and distinguish between high-level, state-of-the art PESs for the strongly interacting Ne-H$_2^+$ system. We show that measurement of the final state distributions for a process that involves only several metastable intermediate states is sufficient to identify the PES that captures the long-range interactions properly. Furthermore, we show that a modest increase in the experimental energy resolution will allow for resolving individual Feshbach resonances and enable a quantitative probe of the interactions at short and intermediate range.

Frequency-based synthetic dimensions are a promising avenue for expanding the dimensionality of photonic systems. In this work, we show how a tilted synthetic lattice is naturally realised by periodically modulating a single-mode resonator under a coherent monochromatic drive. We theoretically study the Bloch wave dynamics in the tilted synthetic lattice, which gives rise to peculiar features in the spectral distribution of the cavity field. Our predictions are experimentally confirmed using a planar tunable superconducting microwave resonator.

We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in physically relevant random quadratic Hamiltonians, is typical for large systems ($N \gg 1$) with initial conditions drawn from the microcanonical distribution. Moreover, we show that thermalization can also arise from non-typical initial conditions, where only a finite fraction of the normal modes is excited. A different choice of initial conditions, such as all the initial energy localized in a single particle, instead leads to energy equipartition without thermalization. Since the models we consider are integrable, our findings provide a general dynamical basis for an approach to thermalization that bypasses chaos and ergodicity, focusing instead on the physical requirement that thermodynamic observables depend on a large number of normal modes, and build a bridge between the classical and quantum theories of thermalization.

The Fermi surface topology of a triple non-hermitian (NH) Weyl semimetal (WSM) driven by bi-circularly polarized light is presented in this study. A NH WSM in particular has remarkable outlines. Bi-circular light, however, modifies the symmetry features of non-hermitian triple Weyl and causes an unusual new kind of band swapping. We observe swapping between the imaginary bands (with or without exceptional degenaracies), which causes unique Fermi surfaces in the form of double rings and knots. This is something never discussed before phase transition between Weyl and knotted phases. We also discuss the corresponding changes in the Berry curvature as well.

In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provide greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of ``the advantage of maximally entangled steering in the relativistic framework" and provides a new perspective for understanding the Hawking effect of the black hole.

We prove that the generalised second law (GSL), with an appropriate modification, holds in perturbative gravity to all orders beyond the semiclassical limit and without a UV cutoff imposed on the fields. Our proof uses algebraic techniques and builds on the recent work of Faulkner and Speranza, which combined Wall's proof of the GSL with the identification of generalised entropy as the von Neumann entropy of a boost-invariant crossed product algebra. The key additional step in our approach is to further impose invariance under null translations. Doing so requires one to describe horizon exterior regions in a relational manner, so we introduce `dynamical cuts': quantum reference frames which give the location of a cut of the horizon. We use idealised dynamical cuts, but expect that our methods can be generalised to more realistic models. The modified GSL that we prove says that the difference in generalised entropies of the regions outside two dynamical cuts is bounded below by the free energy of the degrees of freedom giving the location of the later cut. If one takes a semiclassical limit, imposes a UV cutoff, and requires the cuts to obey certain energy conditions, then our result reduces to the standard GSL.

Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.

We argue that rotation of a thin superconducting cylinder in the presence of a magnetic field can increase the critical temperature of the superconducting phase transition substantially. The phenomenon originates from interaction energy of the dipole magnetic moment of the normal component with the background magnetic field, which encourages the formation of condensate that decouples from mechanical rotation. We give quantitative estimates for a thin cylinder of aluminum.

We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N^{-1} v(x)$. The system is studied at inverse temperatures of order $N^{-2/3}$, which corresponds to the temperature scale of the Bose--Einstein condensation phase transition. We show that spontaneous $U(1)$ symmetry breaking occurs if and only if the system exhibits Bose--Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.

We investigate deterministic identification over arbitrary memoryless channels under the constraint that the error probabilities of first and second kind are exponentially small in the block length $\mathbf{n}$, controlled by reliability exponents $\mathbf{E_1,E_2 \geq 0}$. In contrast to the regime of slowly vanishing errors, where the identifiable message length scales linearithmically as $\mathbf{\Theta(n\log n)}$, here we find that for positive exponents linear scaling is restored, now with a rate that is a function of the reliability exponents. We give upper and lower bounds on the ensuing rate-reliability function in terms of (the logarithm of) the packing and covering numbers of the channel output set, which for small error exponents $\mathbf{E_1,E_2>0}$ can be expanded in leading order as the product of the Minkowski dimension of a certain parametrisation the channel output set and $\mathbf{\log\min\{E_1,E_2\}}$. These allow us to recover the previously observed slightly superlinear identification rates, and offer a different perspective for understanding them in more traditional information theory terms. We also show that even if only one of the two errors is required to be exponentially small, the linearithmic scaling is lost. We further illustrate our results with a discussion of the case of dimension zero, and extend them to classical-quantum channels and quantum channels with tensor product input restriction.

We derive a universal thermodynamic uncertainty relation for Fermionic coherent transport, which bounds the total rate of entropy production in terms of the mean and fluctuations of a single particle current. This bound holds for any multi-terminal geometry and arbitrary chemical and thermal biases, as long as no external magnetic fields are applied. It can further be saturated in two-terminal settings with boxcar-shaped transmission functions and reduces to its classical counterpart in linear response. Upon insertion of a numerical factor, our bound also extends to systems with broken time-reversal symmetry. As an application, we derive trade-off relations between the figures of merit of coherent thermoelectric heat engines and refrigerators, which show that such devices can attain ideal efficiency only at vanishing mean power or diverging power fluctuations. To illustrate our results, we work out a model of a coherent conductor consisting of a chain of quantum dots.

A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that emerge from bosonic abelian Chern-Simons theories, playing the role of a symmetry topological field theory, by imposing topological boundary conditions. Our construction includes the fermionic generalization of code CFTs. When the Chern-Simons theory is associated with the root lattice of a simply laced Lie algebra, this approach yields a fermionic CFT with a level-one affine Lie algebra symmetry. As an application, we consider the Chern-Simons theories corresponding to a class of supersymmetric vertex operator algebras studied by Johnson-Freyd and classify their fermionic topological boundary conditions that give rise to supersymmetric CFTs.

Diamond lattice magnets, formed by a framework of corner-sharing tetrahedra of magnetic cations, offer unique opportunities to realize novel states of matter for potential utility in information technology. However, research has mostly focused on AB2X4 spinels with Td magnetic ions. This hinders the atomically enabled tunability of competing interactions at different energy scales and the ability to harness many-body electronic states in quantum materials, making the discovery of quantum fluctuations and spin dynamics less accessible. We discover a new material CaCo2TeO6 featuring a diamond lattice of two distinct Oh-Co2+ sites. This material displays strong quantum fluctuations, increased competing magnetic exchange interactions, and field-induced tunability of magnetic structures. The results demonstrate how simple, fundamental refinements in ligand fields can profoundly influence the phase space of quantum matter.

The direct bonding process of a diamond-on-insulator (DOI) substrate enables monolithic integration of diamond photonic structures for quantum computing by improving photon collection efficiency and entanglement generation rate between emitters. It also addresses key fabrication challenges, such as robustness, bonding strength, and scalability. This study investigates strain effects in DOI substrates following direct bonding. Strain generation is expected near the diamond-SiO$_2$/Si interface due to thermal expansion coefficient mismatch between the bonded materials. Strain-induced lattice distortions are characterized using nitrogen-vacancy (NV) centers in diamond via optically detected magnetic resonance (ODMR) and photoluminescence (PL) mapping. PL mapping reveals interference fringes in unbonded regions, indicating bonding irregularities. Depth-resolved ODMR measurements show a volumetric strain component increase of $\approx$0.45 MHz and a shear component increase of $\approx$0.71 MHz between the top surface and the DOI interface. However, ODMR signal contrast and peak linewidth remain largely unaffected, suggesting no visible deterioration in the optical properties of the emitters. By combining ODMR and PL mapping, this work establishes a robust methodology for assessing bonding quality and strain impact on NV centers, an essential step toward advancing scalable quantum technologies and integrated photonic circuits.

We report the experimental observation of discrete bright matter-wave solitons with attractive interaction in an optical lattice. Using an accordion lattice with adjustable spacing, we prepare a Bose-Einstein condensate of cesium atoms across a defined number of lattice sites. By quenching the interaction strength and the trapping potential, we generate both single-site and multi-site solitons. Our results reveal the existence and characteristics of these solitons across a range of lattice depths and spacings. We identify stable regions of the solitons, based on interaction strength and lattice properties, and compare these findings with theoretical predictions. The experimental results qualitatively agree with a Gaussian variational model and match quantitatively with numerical simulations of the three-dimensional Gross-Pitaevskii equation, extended with a quintic term to account for the loss of atoms. Our results provide insights into the quench dynamics and collapse mechanisms, paving the way for further studies on transport and dynamical properties of matter-wave solitons in lattices.

Solid-state spin-based quantum systems have emerged as popular platforms for quantum networking applications due to their optical interfaces, their long-lived quantum memories, and their natural compatibility with semiconductor manufacturing. Photonic crystal cavities are often used to enhance radiative emission; however, fabrication of the necessary subwavelength cavities is typically limited to small batch electron beam lithography. In this work, we demonstrate high quality factor, small mode volume nanobeam cavities fabricated on a scalable silicon photonic foundry platform. The foundry fabricated cavities are then interfaced with single erbium ions through backend deposition of TiO2 thin films lightly doped with erbium. Single ion lifetime measurements indicate Purcell enhancement up to about 500, thereby demonstrating a route toward manufacturable deterministic single photon sources in the telecom C-band.

The momentum of light in dielectric media has been a century-long controversy that continues to attract significant interest. In a linear dielectric medium with refractive index n, the momentum is predicted to be smaller by a factor of n according to Max Abraham, and larger by the same factor according to Hermann Minkowski. By studying the coupled dynamics of electromagnetic waves and dipoles in a dielectric medium, we show that the change in momentum of the dipole, expressed by the Lorentz force, corresponds to the Abraham momentum. On the other hand, the Minkowski momentum arises as the eigenvalue of the Hamiltonian and determines the direction of refraction in accordance with Snell's law. Our model also predicts a zitterbewegung-like oscillation due to helicity mixing between left- and right-handed wave components, mediated by dipole oscillation. These internal wave dynamics may be observable via wavepacket motion or polarization-sensitive measurements.

The dynamics of the outer electron in an alkali atom in the presence of structured electromagnetic waves is described. The interaction of the alkali Rydberg atom with twisted radiowaves is considered. The two schemes for Rydberg-atom based detector of twisted radiowaves are proposed. According to the theoretical model for these detectors, they can record a source of twisted radiowaves with power down to several nW. The first scheme of the detector employs the nondipole transitions between Rydberg states induced by twisted radio photons. The second scheme involves the array of Rydberg-atom based antennas, every antenna measuring the dipole transitions excited by plane radiowaves comprising the twisted one.

Relativistic, quantum electrodynamics, as well as non-adiabatic corrections and couplings, are computed for the b $^3\Pi_\mathrm{g}$ and c $^3\Sigma_\mathrm{g}^+$ electronic states of the helium dimer. The underlying Born-Oppenheimer potential energy curves are converged to 1 ppm ($1:10^6$) relative precision using a variational explicitly correlated Gaussian approach. The quantum nuclear motion is computed over the b $^3\Pi_\mathrm{g}$-c $^3\Sigma_\mathrm{g}^+$ (and B $^1\Pi_\mathrm{g}$-C $^1\Sigma_\mathrm{g}^+$) 9-(12-)dimensional electronic-spin subspace coupled by non-adiabatic and relativistic (magnetic) interactions. The electron's anomalous magnetic moment is also included; its effect is expected to be visible in high-resolution experiments. The computed rovibronic energy intervals are in excellent agreement with available high-resolution spectroscopy data, including the rovibronic b $^3\Pi_\mathrm{g}$-state fine structure. Fine-structure splittings are also predicted for the c $^3\Sigma_\mathrm{g}^+$ levels, which have not been fully resolved experimentally, yet.

In Jackiw-Teitelboim (JT) gravity, which is dual to a random matrix ensemble, the annealed entropy differs from the quenched entropy at low temperatures and goes negative. However, computing the quenched entropy in JT gravity requires a replica limit that is poorly understood. To circumvent this, we define an intermediate quantity called the semi-quenched entropy, which has the positivity properties of the quenched entropy, while requiring a much simpler replica trick. We compute this in JT gravity in different regimes using i) a bulk calculation involving wormholes corresponding to the Airy limit of the dual matrix integral and ii) a boundary calculation involving one-eigenvalue instanton saddles proposed by Hernández-Cuenca, demonstrating consistency between these two calculations in their common regime of validity. We also clarify why similar one-eigenvalue instanton saddles cannot be used to compute the quenched entropy due to a breakdown of the saddle-point approximation for the one-eigenvalue instanton in the replica limit.

Long, human-generated passwords pose significant challenges to both classical and quantum attacks due to their irregular structure and large search space. In this work, we propose an enhanced classical-quantum hybrid attack specifically designed for this scenario. Our approach constructs rainbow tables using dictionary-based password generation augmented with transformation rules that better capture real-world user behavior. These tables are organized into buckets, enabling faster lookup and reduced space complexity. For the search within each bucket, we employ a distributed exact variant of Grover's algorithm. This method provides deterministic success and significantly lower circuit depth, enhancing robustness against noise-particularly depolarizing errors common in near-term quantum devices. Overall, our hybrid framework improves the efficiency and practicality of password recovery for long, human-readable passwords in realistic adversarial settings.

Here, we demonstrate that vacuum fluctuations can induce lateral forces on a small particle positioned near a translation-invariant uniform non-Hermitian substrate with chiral gain. This type of non-Hermitian response can be engineered by biasing a low-symmetry conductor with a static electric field and is rooted in the quantum geometry of the material through the Berry curvature dipole. The chiral-gain material acts as an active medium for a particular circular polarisation handedness, while serving as a passive, dissipative medium for the other polarisation handedness. Owing to the nonreciprocity and gain characteristics, momentum is continuously exchanged in a preferred direction parallel to the surface between the test particle and the surrounding electromagnetic field, giving rise to lateral forces. Interestingly, the force can be viewed as a fluctuation-induced drag linked to the nonlinear Hall current. Indeed, although the gain is driven by an electric current, the resulting force acts perpendicular to the bias -- unlike conventional current-drag effects. This effect stems from the skewed propagation characteristics of surface modes and gain-momentum locking. Our theory reveals a Hall-like asymmetry in the field correlations and establishes a novel link between quantum geometry and fluctuation-induced phenomena, offering new possibilities for nanoscale control via tailored electromagnetic environments.