We address the problem of detecting initial system--environment correlations when the environment is not directly accessible. Most existing approaches rely on full state tomography or multiple system preparations, which can be experimentally demanding. We show that, for a known interaction, it can be sufficient to monitor a single expectation value of the system. Focusing on a qubit interacting with an environment via isotropic Heisenberg exchange, we derive exact bounds on the signal $z(t)=\langle\sigma_z^S\rangle(t)$ that hold for all factorized initial states. These bounds define a \emph{factorized envelope}: if an observed trajectory exits this envelope at any time, initial system--environment correlations are certified. From a reduced-dynamics perspective, the envelope admits a clear operational interpretation as the admissible region generated by the standard product assignment (embedding) map, which serves as a null model for uncorrelated preparations. Envelope violations therefore rule out the entire product-assignment class using only a single calibrated observable. We illustrate the method using three families of correlated initial states and observe clear envelope violations, including cases in which the reduced system state is maximally mixed. We further show that the same single-observable logic extends to an exactly solvable pure-dephasing spin--boson model with an infinite environment, where factorized initial states generate a simple coherence envelope whose violation certifies initial correlations. Overall, our results demonstrate that single-axis measurements, combined with a one-time calibration of $\rho_S(0)$, can certify initial system--environment correlations without tomography or environment access.

Organic molecules embedded in an organic matrix exhibit lifetime-limited optical coherence and bright emission at cryogenic temperatures below 3 K. Here we present a simple vapor-phase growth method for synthesizing optically thin DBT-doped anthracene crystals that are compatible with integrated nanophotonics. The crystals are ~200 nm thick with sub-nm surface roughness and a tunable lateral dimension of up to 200 $\mu$m. The molecular transitions remain narrow and spectrally stable, with inhomogeneous broadening below 100 GHz, comparable to DBT in bulk anthracene. The dopant density is tunable up to several hundred molecules per $\mu$m$^2$, ensuring emitters within the near-field of nanophotonic structures. We demonstrate that the crystals can be micropositioned onto integrated photonic devices with the molecular dipole aligned to the optical mode. This approach opens a path toward on-chip single-photon sources and collective many-emitter effects.

High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.

Understanding emergent phenomena in out-of-equilibrium interacting many-body systems is an exciting frontier in physical science. While quantum simulators represent a promising approach to this long-standing problem, in practice it can be challenging to directly realize the required interactions, measure arbitrary observables, and mitigate errors. Here we use coherent mapping between the Rydberg and hyperfine qubits in a neutral atom array simulator to engineer and probe complex quantum dynamics. We combine efficient analog dynamics with fully programmable state preparation and measurement, leverage non-destructive readout for loss information and atomic qubit reuse, and use an atom reservoir for replacing lost atoms. With this analog-digital approach, we first demonstrate dynamical engineering of ring-exchange and particle hopping dynamics via Floquet driving and measure the spectral function of single excitations by evolving initial superposition states. Extending these techniques to a 271-site kagome lattice, we employ closed-loop optimization to target an out-of-equilibrium critical quantum spin liquid of the Rokhsar-Kivelson type. We observe the key features of such a state, including the absence of local order, many-body coherences between nearly equal-amplitude dimer configurations over up to 18 sites, and universal correlations consistent with predictions from field theory. Together, these results pave the way for using dynamical control in analog-digital quantum simulators to study complex quantum many-body systems.

Symmetry constraints provide a powerful means to control the dynamics of open quantum systems. However, the set of accessible control parameters is often limited. Here, we show that a tunable phase in the collective light-matter coupling of a cavity QED system induces a phase-dependent strong symmetry of the Liouvillian, enabling dynamical control of the open quantum system evolution. We demonstrate that tuning this phase substantially reduces the critical driving strength for dissipative phase transitions between stationary and non-stationary phases. We illustrate this mechanism in two experimentally relevant cavity QED settings: a two-species ensemble of two-level atoms and a single-species ensemble of three-level atoms. Our results establish phase control as a versatile tool for engineering dissipative phase transitions, with implications for quantum state preparation.

We experimentally demonstrate transitions between electronic angular momentum states with a difference in magnetic quantum numbers $\Delta \mathrm{m_J} = $ 3, 4, and 5 via resonant four- and six-photon stimulated Raman transitions in a single trapped atom. Derivation of the corresponding Rabi frequencies, which are verified experimentally, follows the standard treatment of two-photon transitions including the adiabatic elimination of intermediate states. Finally, we discuss pathways to increase the observed multi-photon transition fidelities to $>99.99\%$, providing a tool for efficient, high-fidelity control of qu\textit{d}its and single-atom logical qubits.

With fault-tolerant quantum computing on the horizon, there is growing interest in applying quantum computational methods to data-intensive scientific fields like remote sensing. Quantum machine learning (QML) has already demonstrated potential for such demanding tasks. One area of particular focus is quantum data fusion -- a complex data analysis problem that has attracted significant recent attention. In this work, we introduce an automated QML (AQML) approach for addressing data fusion challenges. We evaluate how AQML-generated quantum circuits perform compared to classical multilayer perceptrons (MLPs) and manually designed QML models when processing multisource inputs. Furthermore, we apply our method to change detection using the multispectral ONERA dataset, achieving improved accuracy over previously reported QML-based change detection results.

We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order bipartite processes and higher-order bipartite states. In category-theoretic terms, these laws are expressed using enrichment and cotensors in symmetric polycategories, along with a frobenius-like coherence between them. We describe how these laws capture the salient features of higher-order quantum theory, and discover an upper bound for higher-order circuits: any higher-order circuit theory embeds into the theory of strong profunctors.

We develop a thermodynamic characterization of multimode entanglement in pure continuous-variable systems by quantifying the gap between globally and locally extractable work (ergotropy). For arbitrary pure multimode Gaussian states, we prove that the $2$-local ergotropic gap is a faithful entanglement monotone across any bipartition and constitutes a functionally independent upper bound to the Renyi-2 entanglement entropy. We further introduce the $k$-ergotropic score, the minimum $k$-local ergotropic gap, and show that it faithfully quantifies multimode entanglement across $k$ partitions. For pure three-mode Gaussian states, we derive its closed-form relation with the geometric measure for genuine multimode entanglement $(k=2)$, and total Gaussian multimode entanglement $(k=3)$. For systems with more than three modes, the $k$-ergotropic score becomes a functionally independent measure of multimode entanglement to the standard geometric measures. Our results reveal a direct operational hierarchy linking Gaussian multimode entanglement to work extraction under locality constraints, and provide a computable and experimentally accessible thermodynamic framework for characterizing quantum correlations.

We investigate the decomposition of ergotropy into incoherent and coherent contributions for quantum systems subject to typical Markovian noise channels. The incoherent part originates from population inversion in the energy eigenbasis after dephasing, while the coherent part captures the role of quantum coherence in work extraction. For single-qubit systems, we derive explicit conditions for freezing and enhancement of coherent ergotropy and obtain an analytical upper bound, showing that it cannot exceed one half of the state's quantum coherence. We then study two classes of separable two-qubit states under local noise. For Bell-diagonal states, which are locally completely passive and possess no local coherence, we prove that the total extractable work equals the average of geometric quantum and classical correlations. In this case, coherent ergotropy cannot be enhanced, although freezing occurs under specific noise conditions. By contrast, for separable states with local coherence, coherent ergotropy can increase under all considered noise channels, including phase-flip and depolarizing noise. Extending the analysis to multipartite systems, we show that both the magnitude and range of noise-induced enhancement grow with the number of qubits, indicating collective reinforcement. Finally, we demonstrate through an explicit example that entanglement does not prevent this enhancement: coherent ergotropy may increase under noise even for entangled states. Our results reveal that noise can assist energy storage, challenging the conventional view of noise as purely detrimental and suggesting compatibility between noise-assisted enhancement and fast entanglement-based charging mechanisms in quantum batteries.

Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.

Quantum computation with Trotter product formulae is straightforward and requires little overhead in terms of logical qubits. The choice of the orbital basis significantly affects circuit depth, with localised orbitals yielding lowest circuit depths. However, literature results point to large Trotter errors incurred by localised orbitals. Here, we therefore investigate the effect of orbital transformations on Trotter error. We consider three strategies to reduce Trotter error by orbital transformation: (i) The a priori selection of an orbital basis that produces low Trotter error. (ii) The derivation of an orbital basis that produces a ground state energy free of Trotter error (as we observed that the Trotter error is a continuous function in the Givens-rotation parameter, from which continuity of this error upon orbital transformation can be deduced). (iii) Application of propagators that change the computational basis between Trotter steps. Our numerical results show that reliably reducing Trotter error by orbital transformations is challenging. General recipes to produce low Trotter errors cannot be easily derived, despite analytical expressions which suggest ways to decrease Trotter error. Importantly, we found that localised orbital bases do not produce large Trotter errors in molecular calculations, which is an important result for efficient QPE set-ups.

In this letter we explore how full frequency conversion can be performed in shorter, integrable devices by using a STIRAP-like protocol modified by the time rescaling shortcut to adiabaticity. We show how the coupled equations for two simultaneous three-wave mixing processes can be written in terms of a STIRAP-like system, which creates robust conversion, albeit requiring long propagation distances inside a bulk crystal or waveguide. We then discuss how the time rescaling (TR) method can be modified to be applied in optical systems, then apply it in the conversion process to create a TR-STIRAP protocol, showing that full conversion is also obtained, but at a fraction of the propagation distance. We also show how the original shaping of the coupling coefficients required by the TR-STIRAP can be approximated by gaussian functions with high conversion fidelity, thus simplifying the experimental implementation. This protocol has the potential to be used in several areas, including the integration of photon sources and efficient detectors for quantum key distribution.

The nonstabilizerness of quantum states is a necessary resource for universal quantum computation, yet its characterization is notoriously demanding. Quantifying nonstabilizerness typically requires an exponential number of measurements and a doubly exponential classical post-processing cost to evaluate its standard monotones. In this work, we show that nonstabilizerness is, to a large extent, in the eyes of the beholder: it can be witnessed and quantified using any set of $m$ $n$-qubit Pauli measurements, provided the set contains anti-commuting pairs. We introduce a general framework that projects the stabilizer polytope onto the subspace defined by these observables and provide an algorithm that estimates magic from Pauli expectation values with runtime exponential in the number of measurements $m$ and polynomial in the number of qubits $n$. By relating the problem to a stabilizer-restricted variant of the quantum marginal problem, we also prove that deciding membership in the corresponding reduced stabilizer polytope is NP-hard. In particular, unless $\mathrm{P} = \mathrm{NP}$, no algorithm polynomial in $m$ can solve the problem in full generality, thus establishing fundamental complexity-theoretic limitations. Finally, we employ our framework to compute nonstabilizerness in different Hamiltonian ground states, demonstrating the practical performance of our method in regimes beyond the reach of existing techniques.

The co-propagation of quantum and classical signals through shared optical fibers is crucial for scalable quantum networks. However, this coexistence is fundamentally limited by spontaneous Raman scattering (SpRS) from the bright classical light, which generates overwhelming noise that disrupts the single-photon-level quantum signals. Here, we overcome this long-standing challenge by leveraging the inherently ultralow nonlinearity of hollow-core fiber (HCF) to suppress SpRS noise. By operating both the quantum time synchronization (QTS) and classical optical frequency transfer (OFT) signals within the telecom C-band, separated by only ~10 nm, we successfully demonstrate their simultaneous transmission over a 122-km HCF link. With a classical OFT power of 1 mW, the QTS performance shows negligible degradation, maintaining sub-picosecond time stability at 2000 s, while the OFT achieves a fractional frequency instability of 10^-20. Near-sub-picosecond QTS stability is preserved even when the classical power is increased to 3 mW. Furthermore, simulations based on our experimental data indicate that with next-generation low-loss HCF, the platform can tolerate classical powers beyond 10 mW and extend the QTS range to over 500 km. By realizing a unified quantum-classical time-frequency distribution framework, this work establishes HCF as a highly capable and practical platform for future scalable quantum networks.

Achieving superradiant lasing with an ultranarrow linewidth is crucial for enhancing atomic clock stability in quantum precision measurement. By employing the exceptional point (EP) property of the system, we demonstrate theoretically superradiant lasing with linewidths in the $\mu$Hz range, sustained at the high-power level. This is achieved by incoherently pumping optical lattice clock transitions with ultracold alkaline-earth strontium-87 atoms in the EP of a $\mathcal{PT}$-symmetric system. Physically, the atomic coherence reaches a maximum in the EP, significantly amplifying the superradiance effect and resulting in superradiant lasing with an ultranarrow linewidth. This linewidth is even three orders of magnitude smaller than that of superradiant lasing in the systems without EP. Our work extends the realm of superradiant lasing by introducing the EP property, and offers promising applications for developing atomic clocks with exceptional stability and accuracy.

Quantum error correction (QEC) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can conflict with an encoded subspace, and QEC performance is governed by the errors that survive decoding, not necessarily those DD suppresses. We analyze a hybrid memory cycle where DD is implemented logically (LDD) using normalizer elements of an $[[n,k,d]]$ stabilizer code, followed by a round of syndrome measurement and recovery (or, in the detection setting, postselection on a trivial syndrome). In an effective Pauli model with physical error probability $p$, LDD suppression factor $p_{DD}$, and recovery imperfection rate $p_{QEC}$ (or $p_{QED}$), we derive closed-form entanglement-fidelity expressions for QEC-only, LDD-only, physical DD, and the hybrid LDD+QEC protocol. The formulas are expressed via a small set of code-dependent weight enumerator polynomials, making the role of the decoder and the LDD group explicit. For ideal recovery LDD+QEC outperforms QEC-only iff the conditional fraction of uncorrectable Pauli errors is larger in the LDD-suppressed sector than in the unsuppressed sector. In the low-noise regime, a sufficient design rule guaranteeing hybrid advantage is that LDD suppresses at least one minimum-weight uncorrectable Pauli error for the chosen recovery map. We show how stabilizer-equivalent choices of LDD generators can be used to enforce this condition. We supplement our analysis with numerical results for the $[[7,1,3]]$ Steane code and a $[[13,1,3]]$ code, mapping regions of hybrid-protocol advantage in parameter space beyond the small-$p$ regime. Our work illustrates the need for co-design of the code, decoder, and logical decoupling group, and clarifies the conditions under which the hybrid LDD+QEC protocol is advantageous.

Directional codes, recently introduced by Gehér--Byfield--Ruban \cite{Geher2025Directional}, constitute a hardware-motivated family of quantum low-density parity-check (qLDPC) codes. These codes are defined by stabilizers measured by ancilla qubits executing a fixed \emph{direction word} (route) on square- or hex-grid connectivity. In this work, we develop a comprehensive \emph{word-first} analysis framework for route-generated, translation-invariant CSS codes on rectangular tori. Under this framework, a direction word $W$ deterministically induces a finite support pattern $P(W)$, from which we analytically derive: (i)~a closed-form route-to-support map; (ii)~the odd-multiplicity difference lattice $L(W)$ that classifies commutation-compatible $X/Z$ layouts; and (iii)~conservative finite-torus admissibility criteria. Furthermore, we provide: (iv)~a rigorous word equivalence and canonicalization theory (incorporating dihedral lattice symmetries, reversal/inversion, and cyclic shifts) to enable symmetry-quotiented searches; (v)~an ``inverse problem'' criterion to determine when a translation-invariant support pattern is realizable by a single route, including reconstruction and non-realizability certificates; and (vi)~a quasi-cyclic (group-algebra) reduction for row-periodic layouts that explains the sensitivity of code dimension $k$ to boundary conditions. As a case study, we analyze the word $W=\texttt{NE$^2$NE$^2$N}$ end-to-end. We provide explicit stabilizer dependencies, commuting-operator motifs, and an exact criterion for dimension collapse on thin rectangles: for $(L_x, L_y) = (2d, d)$ with row alternation, we find $k=4$ if $6 \mid d$, and $k=0$ otherwise.

Achieving high fidelity of quantum teleportation (QT) in a noisy environment is an essential requirement for its real-world applications. To this end, we devise a distinctive protocol for ensuring teleportation fidelity {\it close to unity}, hinging essentially on the timing of Alice's Bell-basis measurement (BM) dependent on the choice of Bob's local noise parameters, but is independent of Alice's local noise. Our scheme is enabled by Alice communicating to Bob only two of the BM outcomes corresponding to the states that are decoherence-free under common dephasing at Alice's wing. On the other hand, Bob is asked to discard the states of his qubit for the other two BM outcomes in order to maximize fidelity of the teleported state. This ensures the teleportation fidelity's independence of noise parameters in Alice's wing. We formulate the protocol in terms of a generic two-level quantum system, subjected to non-Markovian dephasing noise, applicable for any pure maximally/non-maximally entangled state as well as a Werner-type mixed state as resource. Notably, we show that high fidelity is achievable even using resource states with small values of the entanglement measure. Remarkably, even within the local regime of Werner states, where Bell-CHSH inequalities are not violated, the teleportation fidelity remains significantly high. Finally, we discuss the empirical feasibility of our scheme using photonic qubits.

This paper introduces the Kaiwu-PyTorch-Plugin (KPP) to bridge Deep Learning and Photonic Quantum Computing across multiple dimensions. KPP integrates the Coherent Ising Machine into the PyTorch ecosystem, addressing classical inefficiencies in Energy-Based Models. The framework facilitates quantum integration in three key aspects: accelerating Boltzmann sampling, optimizing training data via Active Sampling, and constructing hybrid architectures like QBM-VAE and Q-Diffusion. Empirical results on single-cell and OpenWebText datasets demonstrate KPPs ability to achieve SOTA performance, validating a comprehensive quantum-classical paradigm.

In a previous paper [S. Mudli {\it et al.} Phys. Rev. A 110, 062618 (2024)], it was shown that a trapped ion can mediate interaction between two largely separated Rydberg atoms, and this mediated interaction can be leveraged to perform a universal two-qubit gate operation between neutral atom qubits in optical tweezers. In this paper, we demonstrate the universal two-qubit CNOT gate with high fidelity between an ionic and an atomic qubit relying on Rydberg excitation of the atom and the resulting phonon blockade in the motional states of the harmonically trapped ion. The phonon blockade arises due to strong ion-atom interaction when the atom is excited to a Rydberg state. These demonstrations suggest that an ion-atom hybrid system can serve as a resourceful platform or module for quantum computing and quantum networking as it can utilize the best features of charged as well as neutral atom qubits.

Controlled unitary gates are a basic element in many quantum algorithms. Converting a general unitary $U$ with a known decomposition into its controlled version, controlled-$U$, can introduce a large overhead in terms of the depth of the circuit. We present a general method to take any unitary $U$ into controlled-$U$ using a fixed circuit with 4 CNOT gates and 2 Toffoli gates per qubit. For $n$-qubit unitaries and one control qubit, we require $2n+1$ qubits and a circuit that can generate an eigenstate of $U$, for which there are many cost-effective known algorithms. The method also works for any black block implementation of $U$, achieving a constant-depth realization independent of its decomposition. We illustrate its use in the Hadamard test and discuss applications to variational and quantum machine-learning algorithms.

Motivated by Johnson--Lindenstrauss dimension reduction, amplitude encoding, and the view of measurements as hash-like primitives, one might hope to compress an $n$-point approximate nearest neighbor (ANN) data structure into $O(\log n)$ qubits. We rule out this possibility in a broad quantum sketch model, the dataset $P$ is encoded as an $m$-qubit state $\rho_P$, and each query is answered by an arbitrary query-dependent measurement on a fresh copy of $\rho_P$. For every approximation factor $c\ge 1$ and constant success probability $p>1/2$, we exhibit $n$-point instances in Hamming space $\{0,1\}^d$ with $d=\Theta(\log n)$ for which any such sketch requires $m=\Omega(n)$ qubits, via a reduction to quantum random access codes and Nayak's lower bound. These memory lower bounds coexist with potential quantum query-time gains and in candidate-scanning abstractions of hashing-based ANN, amplitude amplification yields a quadratic reduction in candidate checks, which is essentially optimal by Grover/BBBV-type bounds.

We consider physical Hamiltonians that can be represented by the multiparametric Gaussian ensembles, theoretically derive the state ensembles for its eigenstates and analyze the effect of varying system conditions on its bipartite entanglement entropy. Our approach leads to a single parametric based common mathematical formulation for the evolution of the entanglement statistics of different states of a given Hamiltonian or different Hamiltonians subjected to same symmetry constraints. The parameter turns out to be a single functional of the system parameters and thereby reveals a deep web of connection hidden underneath different quantum states.

We analyze a time-continuous version of a cellular automaton decoder for the toric code in the form of a Lindblad master equation. In this setting, a self-correcting quantum memory becomes a thermodynamical phase of the steady state, which manifests itself through the steady state being topologically ordered. We compute the steady state phase diagram, finding a competition between the error correction rate and the update rate for the classical field of the cellular automaton. Strikingly, we find that self-correction of errors is possible even in situations where conventional quantum error correction does not have a finite threshold.

We analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.

Higher-dimensional quantum systems are attracting interest for improving quantum protocol performance by increasing memory space. Characterizing quantum resources of such systems is fundamental but experimentally costly. We tackle the first non-trivial example: a qubit-ququart system, focusing on partial-transpose spectral classification. Entanglement distillation extracts maximally entangled states from noisy resources, but determining distillability typically requires full state tomography, experimentally prohibitive for high-dimensional systems. We explore a machine learning framework to classify distillable bipartite quantum states using fewer measurements than complete tomography. Our approach employs the PPT criterion, categorizing states by negative eigenvalues in the partial transpose. We use various ML algorithms, including Support Vector Machines, Random Forest, and Artificial Neural Networks, with features from fixed measurements and learnable observables. Results show learnable observables consistently outperform Collective Measurement Witnesses methods. While all models distinguish between non-distillable (PPT) and distillable (NPT) states, differentiating NPT subclasses remains challenging, underscoring the intricate Hilbert space geometry. This work provides an experimentally friendly tool for distillability verification in high-dimensional quantum systems without full state reconstruction

The Gravitational Poissonian Spontaneous Localization (GPSL) model is a hybrid classical-quantum framework in which Newtonian gravity emerges from stochastic collapses of a smeared mass-density operator. Consistency of the hybrid dynamics entails momentum diffusion and, hence, spontaneous heating. Without smearing, which enters both the collapse (measurement) and gravitational-feedback components of the dynamics, the heating rate would be divergent. Previous work assumed identical smearings for both components. Here, we treat the general case of distinct spatial smearings $g_{r_C} (\mathbf{x})$ and $g_{r_G} (\mathbf{x})$, characterized, respectively, by length scales $r_C$ and $r_G$. We characterize the spontaneous heating rate for arbitrary $g_{r_C} (\mathbf{x})$ and $g_{r_G} (\mathbf{x})$, and then discuss which smearing profiles minimize the spontaneous heating rate in relevant physical situations. Remarkably, there are situations in which, while the measurement noise remains the same, allowing $g_{r_G} (\mathbf{x}) \neq g_{r_C} (\mathbf{x})$ may reduce the feedback-induced spontaneous heating by more than 60 orders of magnitude already for $r_G = 10 r_C$. Finally, we use our results to estimate the spontaneous heating rate of neutron stars and to set new lower bounds on the model's parameters by comparing the theoretical predictions with astronomical data on temperature, radius, and mass of neutron stars.

Variational quantum circuits (VQCs) constitute a central building block of near-term quantum machine learning (QML), yet the principled design of expressive and trainable architectures remains a major open challenge. The VQC design space grows combinatorially with the number of qubits, layers, entanglement structures, and gate parameterizations, rendering manual circuit construction inefficient and often suboptimal. We introduce an autonomous agent-based framework for VQC architecture search that integrates high-level reasoning with a quantum simulation environment. The agent proposes candidate circuit architectures, evaluates them through fully automated training and validation pipelines, and iteratively improves its design strategy via performance-driven feedback. Empirically, we show that the agent autonomously evolves circuit architectures from simple initial ansätze toward increasingly expressive designs, progressively trying to improve task performance. This demonstrates that agentic AI can effectively navigate and refine the VQC design landscape with minimal human intervention, providing a scalable methodology for automated quantum model development in the Noisy Intermediate-Scale Quantum (NISQ) regime.

Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit contextuality-enhanced success probabilities that surpass classical bounds, offering significant advantages for quantum sensing and communication. However, in practice, both error and failure outcomes can occur, suggesting the need for a unified strategy that incorporates both aspects while exploring the potential for contextuality enhancement. In this work, we theoretically demonstrate contextuality enhancement in quantum state discrimination under a fixed failure probability. We show that this enhancement disappears within a certain intermediate range of failure probabilities--a phenomenon absent in conventional strategies, where both minimum-error and unambiguous discrimination consistently outperform the noncontextual bound for equal priors. Moreover, we analyze how the existence of this non-enhancement region depends on the confusability of the quantum states, which corresponds to their fidelity in a quantum model. We further extend the discussion to the noisy state discrimination, which even encompasses the maximal-confidence discrimination. In this extended discussion, we observe that the non-enhancement region tends to disappear with increasing noise strength.

Preparing high-fidelity Greenberger-Horne-Zeilinger (GHZ) states on noisy quantum hardware remains challenging due to cumulative gate errors and decoherence. We introduce Group-Majority-Voting (Group-MV), a dynamic-circuit protocol that partitions arbitrary coupling graphs, prepares local GHZ states in parallel, and fuses them via majority-voted mid-circuit measurements. The majority vote over redundant boundary links mitigates measurement errors that would otherwise propagate through classical feedforward. We evaluate Group-MV on simulated Heavy-hex and Grid topologies for 30 through 60 qubits under a realistic noise regime. Group-MV generalizes to arbitrary GHZ sizes on arbitrary coupling topologies, achieving 2.4x higher fidelity than the Line Dynamic method while tracking the unitary baseline within 3%.

We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of random quantum states, providing a unified finite-size description of full-system, subsystem, and conditional statistics. In the presence of depolarizing noise, these distributions are scaled and shifted by the noise strength, producing a noise-induced gap in their support. Remarkably, we prove that random states exhibit exact conditional self-similarity: the distribution of subsystem bit-string probabilities conditioned on specific outcomes of the complementary subsystem is identical to that of the full system. This hidden scale invariance enables the exact restoration of the full-system statistics from the marginalized Beta distribution via post-selection, and persists under depolarizing noise. Our results uncover a fundamental symmetry of Hilbert space and provide a scalable, rigorous framework for validating random circuit sampling via subsystem or conditional cross-entropy benchmarking.

We present a new Hamiltonian-learning framework based on time-resolved measurement data from a fixed local IC-POVM and its application to inferring gene regulatory networks. We introduce the quantum Hamiltonian-based gene-expression model (QHGM), in which gene interactions are encoded as a parameterized Hamiltonian that governs gene expression evolution over pseudotime. We derive finite-sample recovery guarantees and establish upper bounds on the number of time and measurement samples required for accurate parameter estimation with high probability, scaling polynomially with system size. To recover the QHGM parameters, we develop a scalable variational learning algorithm based on empirical risk minimization. Our method recovers network structure efficiently on synthetic benchmarks and reveals novel, biologically plausible regulatory connections in Glioblastoma single-cell RNA sequencing data, highlighting its potential in cancer research. This framework opens new directions for applying quantum-like modeling to biological systems beyond the limits of classical inference.

The deterministic preparation of quantum many-body ground states is essential for advanced quantum simulation, yet optimal algorithms often require prohibitive hardware resources. Here, we propose a highly efficient, non-variational protocol for ground state preparation using a Power-Cosine quantum signal processing (QSP) filter. By eschewing complex block-encoding techniques, our method directly utilizes coherent time-evolution operators controlled by a single ancillary qubit. The integration of mid-circuit measurement and reset (MCMR) drastically minimizes spatial overhead, translating iterative non-unitary filtering into deep temporal coherence. We analytically demonstrate that this approach achieves exponential suppression of excited states with a circuit depth scaling of $\mathcal{O}(\Delta^{-2}\log(1/\epsilon))$, prioritizing implementational simplicity over optimal asymptotic complexity. Numerical simulations on the 1D Heisenberg XYZ model validate the theoretical soundness and shot-noise resilience of our method. Furthermore, an advantage analysis reveals that our protocol exponentially outperforms standard Trotterized Adiabatic State Preparation (TASP) at equivalent circuit depths. This single-ancilla framework provides a highly practical and deterministic pathway for many-body ground state preparation on Early Fault-Tolerant (EFT) quantum architectures.

Calderbank-Shor-Steane (CSS) codes are a versatile quantum error-correcting family built out of commuting $X$- and $Z$-type checks. We introduce CSS-like codes on $G$-valued qudits for any finite group $G$ that reduce to qubit CSS codes for $G = \mathbb{Z}_2$ yet generalize the Kitaev quantum double model for general groups. The $X$-checks of our group-CSS codes correspond to left and/or right multiplication by group elements, while $Z$-checks project onto solutions to group word equations. We describe quantum-double models on oriented two-dimensional CW complexes (which need not cellulate a manifold) and prove that, when $G$ is non-Abelian and simple, every $G$-covariant group-CSS code with suitably upper-bounded $Z$-check weight and lower-bounded $Z$-distance reduces to a CW quantum double. We describe the codespace and logical operators of CW quantum doubles via the same intuition used to obtain logical structure of surface codes. We obtain distance bounds for codes on non-Abelian simple groups from the graph underlying the CW complex, and construct intrinsically non-Abelian code families with asymptotically optimal rate and distances. Adding "ghost vertices" to the CW complex generalizes quantum double models with defects and rough boundary conditions whose logical structure can be understood without reference to non-Abelian anyons or defects. Several non-invertible symmetry-protected topological states, both with ordinary and higher-form symmetries, are the unique codewords of simply-connected CW quantum doubles with a single ghost vertex.

Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in $d$-dimensional Hilbert spaces using Dirac notation, where $d$ is a prime integer strictly greater than 2. We establish a new algebraic relation connecting these operators and present the cases $d=3$ and $d=5$ as illustrative examples.

The stability of motional-mode frequency is essential for realizing high-fidelity quantum gates in trapped-ion quantum computing. While broadband Gaussian noise has been extensively studied and mitigated using pulse shaping techniques, the impact of coherent periodic noise has remained largely unexplored. Here we report a systematic investigation of 60-Hz power-line noise and its effect on the secular frequencies of a single ${}^{171}\mathrm{Yb}^{+}$ ion. Using spin-echo Ramsey spectroscopy, we characterize the amplitude and phase of the resulting secular-frequency modulation and validate this characterization via passive phase correction of the Ramsey sequence. Building on this, we implement active cancellation by injecting a compensation tone into the set-point of a PI controller that stabilizes the trap RF drive amplitude. A phasor-fitting procedure optimizes the amplitude and phase of the compensation signal, enabling near-complete suppression of the 60-Hz component. With active cancellation engaged, the coherence time of a radial motional mode is extended from approximately 10 ms to 35 ms, consistent with the limit set by motional heating. Our results provide both a clear characterization of periodic motional-mode noise and a practical framework for its suppression in trapped-ion quantum computing platforms.

Squeezed states, crucial for quantum metrology and emerging quantum technologies, have been demonstrated in various platforms, but quantum squeezing of magnons in macroscopic spin systems remains elusive. Here we report the experimental observation of quantum-level magnon squeezing in a millimeter-scale yttrium iron garnet (YIG) sphere. By engineering a strong dispersive magnon-superconducting qubit coupling via a microwave cavity, we implement a significant self-Kerr nonlinearity to generate squeezed magnon states with their mean magnon number less than one. Harnessing a magnon-assisted Raman process, we perform Wigner tomography, revealing quadrature variances of $\sim\!0.8$ ($\sim\!1.0$~dB squeezing) relative to the vacuum. These results lay the groundwork for quantum nonlinear magnonics and promise potential applications in quantum metrology.

Quantum reservoir computing (QRC) exploits fixed quantum dynamics and a trainable linear readout to process temporal data, yet reversing the transformation -- reconstructing the input from the reservoir output -- has been considered intractable owing to the recursive nonlinearity of sequential quantum state evolution. Here we propose a four-equation encode-decode protocol with cross-key pairing and constructively show that quantum reservoir and key combinations satisfying all four equations exist. Using a full XYZ Hamiltonian reservoir with 10 data qubits, we expand the feature dimension to 76 without increasing qubit count and achieve machine-precision reconstruction (mean-squared error $\mathrm{MSE} \sim 10^{-17}$) for data lengths up to 30 under ideal conditions; the rank condition $\mathrm{dim}(V) \geq N_c$ is identified as a necessary criterion. A comprehensive noise analysis across seven conditions and four baseline methods reveals a clear hierarchy: shot noise dominates, depolarizing noise adds a moderate factor, and asymmetric resource allocation -- 10 shots for encoding, $10^5$ for decoding -- yields approximately two orders of magnitude MSE improvement by exploiting the asymmetric noise roles of the encryption and decryption feature matrices. Under realistic noise the MSE degrades to $10^{-3}$-$10^{-1}$, indicating that error mitigation is needed before practical deployment, but our results establish the feasibility of bidirectional reversible information transformation within QRC.

We introduce a method for the measurement of the lower bound on the initial polarization of spinful nuclei in a diamond by following the coherence evolution of an NV center spin qubit after a simple scheme is operated on the qubit to facilitate the transfer of information from the environment into the qubit state. Current polarization measurement techniques are challenging to implement due to the need for direct access to the environment. In our method, information is obtained by measuring the difference of the evolution of the qubit coherence resulting from preparation phase when the environment evolution is conditional on the qubit pointer state. We find that the method does not depend strongly on the applied magnetic field, but rather on the number of spinfull nuclei that lead to decoherence, and gives a reasonable estimate if the environment is polarized. The key advantage of this approach is its simplicity and minimal experimental requirements, allowing the inference of initial nuclear polarizations without direct access to the environment. We demonstrate the efficacy of this method using a simulated environment of up to fifteen randomly placed nuclear spins.

Accurate noise estimation is essential for fault-tolerant quantum computing, as decoding performance depends critically on the fidelity of the circuit-level noise parameters. In this work, we introduce a differentiable Maximum Likelihood Estimation (dMLE) framework that enables exact, efficient, and fully differentiable computation of syndrome log-likelihoods, allowing circuit-level noise parameters to be optimized directly via gradient descent. Leveraging the exact Planar solver for repetition codes and a novel, simplified Tensor Network (TN) architecture combined with optimized contraction path finding for surface codes, our method achieves tractable and fully differentiable likelihood evaluation even for distance 5 surface codes with up to 25 rounds. Our method recovers the underlying error probabilities with near-exact precision in simulations and reduces logical error rates by up to 30.6(3)% for repetition codes and 8.1(2)% for surface codes on experimental data from Google's processor compared to previous state-of-the-art methods: correlation analysis and Reinforcement Learning (RL) methods. Our approach yields provably optimal, decoder-independent error priors by directly maximizing the syndrome likelihood, offering a powerful noise estimation and control tool for unlocking the full potential of current and future error-corrected quantum processors.

Spin-boson models are the canonical benchmark for quantum dissipation. We show the symmetry structure of general spin-boson Hamiltonians and obtain their spectra explicitly by exploiting the symmetry. As an illustration of the general case, we numerically demonstrate the exact solution for the two-mode case.

We develop a spectral-resolvent framework for computing the quantum Fisher information (QFI) using Krylov subspace methods, extending the notion of the Krylov distribution. By expressing the QFI as a resolvent moment of the superoperator $\mathcal{K}_\rho$ associated with a density matrix, the Krylov distribution quantifies how the QFI weight is distributed across Krylov levels in operator space and provides a natural measure for controlling the truncation error in Krylov approximations. Leveraging orthogonal polynomial theory, we identify two universal convergence regimes: exponential decay when the Liouville-space spectrum is gapped away from zero, and algebraic decay governed by hard-edge (Bessel) universality when small eigenvalues accumulate near zero. This framework establishes a direct connection between quantum metrology, spectral geometry, and Krylov dynamics, offering both conceptual insight and practical tools for efficient QFI computation in high-dimensional and many-body systems.

Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size. Even on fault-tolerant quantum computers, quantum algorithms with convergence guarantees -- such as quantum phase estimation and quantum subspace methods -- require an initial state with sufficiently large overlap with the true ground state to be effective. Variational quantum eigensolvers (VQEs) are natural candidates for preparing such states; however, standard VQEs typically exhibit poor generalization, requiring retraining for each Hamiltonian instance, and often suffer from barren plateaus, where gradients can vanish exponentially with circuit depth and system size. To address these limitations, we propose an end-to-end representation learning framework that combines a graph autoencoder with a classical neural network to generate VQE parameters that generalize across Hamiltonian instances. By encoding interaction topology and coupling structure, the proposed model produces high-overlap initial states without instance-specific optimization. Through extensive numerical experiments on families of one- and two-local Hamiltonians, we demonstrate improved generalization and trainability, manifested as reduced test error and a significantly milder decay of gradient variance. We further show that our method substantially accelerates convergence in quantum subspace-based eigensolvers, highlighting its practical impact for downstream quantum algorithms.

We present a quantum optical scheme for imaging transversely displaced thermal sources of arbitrary intensities by employing multiphoton interference with a reference single-photon Fock state at a beamsplitter. Obtaining an analytical form for transverse momenta-resolved $L$-photon probabilities in either output, we show via Fisher information analysis that separation estimators built using interference sampling of multiphoton events exhibit significantly enhanced precision vis-à-vis existing imaging schemes over a wide range of separations and brightness. Even-photon-number coincidences exhibit constant precision in the sub-Rayleigh regime, demonstrating quantum superresolution of our scheme beyond the diffraction limit. For sources emitting on average $N_s\sim1$ photon per frame (such as in IR emission of thermal sources), precision bounds for our scheme scale linearly in $N_s$, exemplifying an enhanced precision of estimators in relation to weak sources $N_s\ll1$, and matching the ultimate quantum scaling. Finally, transverse momenta resolution in the Fourier plane produces finite imaging precisions for intermediate and large source separations using coarse pixel sizes of order $\delta y\sim100\,\mu \mathrm{m}$ for exemplary image spot sizes $\sigma_x \sim 0.1\, \mu \mathrm{m}$, in contrast with existing schemes of diffraction-limited direct imaging and superresolved inversion interferometric imaging that are severely degraded by coarse pixel sizes and have limited use. Combining the relatively straightforward sensing operation of Hong-Ou-Mandel interferometers with multiphoton coincidence detection of arbitrarily bright thermal sources and inner variable resolution of transverse photonic momenta, our scheme offers a robust alternative to non-invasive single-particle tracking and imaging of bright sources in nanoscopic chemical and biological systems.

To operate quantum sensors at their quantum limit in real time, it is crucial to identify efficient data inference tools for rapid parameter estimation. In photodetection, the key challenge is the fast interpretation of click-patterns that exhibit non-classical statistics -- the very features responsible for the quantum enhancement of precision. We achieve this goal by comparing Bayesian likelihood-free methods with ones based on deep learning (DL). While the former are more conceptually intuitive, the latter, once trained, provide significantly faster estimates with comparable precision and yield similar predictions of the associated errors, challenging a common misconception that DL lacks such capabilities. We first verify both approaches for an analytically tractable, yet multiparameter, scenario of a two-level system emitting uncorrelated photons. Our main result, however, is the application to a driven nonlinear optomechanical device emitting non-classical light with complex multiclick correlations; in this case, our methods are essential for fast inference and, hence, unlock the possibility of distinguishing different photon statistics in real time. Our results pave the way for dynamical control of quantum sensors that leverage non-classical effects in photodetection.

Local Hilbert spaces with large dimension are of key interest for quantum information with applications in quantum computing and memories, quantum simulations and metrology. Thanks to its weak coupling to external perturbations, the large ground-state nuclear spin manifold of fermionic alkaline-earth atoms is an exciting resource to explore for quantum information. Simultaneous single atom and state-resolved detection however remains an outstanding challenge limiting the development of novel quantum computing and simulation schemes beyond qubits. Here, we report on a new imaging technique enabling the simultaneous detection of up to four quantum states encoded in the nuclear spin manifold of a single fermionic strontium atom within 100 microseconds, with state-resolved detection fidelities ranging from 0.936 to 0.997. This technique is further used to track the highly coherent nuclear spin dynamics after a quench highlighting the potential of this system for quantum information. These results offer fascinating perspectives for quantum science with multi-electron atoms ranging from qudit-based quantum computing to quantum simulations of the SU(N) Fermi-Hubbard model.

We provide a theoretical model for the non-equilibrium steady state heat flow through a quantum heat valve. The model is based on a master equation approach, where the partial secular approximation has been carefully performed in order to obtain accurate results. Our study assumes an ohmic spectral density for the two thermal baths of the model. This is in contrast with previous treatments of the quantum heat valve, where the baths have been assumed as being structured with a peaked spectral density near the resonance frequency of the resonator. These studies have also taken the resonator to be a part of the open quantum system of interest, which results in double counting of the resonator, as the latter appears both in the spectral density of the bath and as a part of the open system. Although this model accounts for the observations in a satisfactory way, it raises issues regarding its physical interpretation. Our method solves this conceptual problem. We apply it to describe an experiment on a quantum heat valve, showing that it successfully captures the experimental results and improves upon the previous theoretical model, which suffered from the resonator double-counting issue. Our findings confirm that the careful application of the master equation approach, in particular when it comes to the secular approximation, is a useful tool for explaining realistic experimental setups.

We show that, in the relativistic regime, scalar bosons satisfy a quantum wave equation which is quite analogous to the Dirac equation. In contrast with the Klein-Gordon equation it is first order with respect to time derivation. It leads in a regular way to the standard Schrödinger equation in the non-relativistic limit. There are two components for the wave function in this representation for the scalar boson, in a way completely analogous to the four components for the spin $1/2$ fermion in the Dirac equation.

GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix $\rho$ there is a unique measure GAP$_\rho$. We describe and prove a property of these measures that was not recognized so far: If a wave function $\Psi$ is GAP$_\rho$ distributed and a collapse occurs, then the collapsed wave function $\Psi'$ is again GAP distributed (relative to the appropriate $\rho'$). This fact applies to collapses due to a quantum measurement carried out by an observer, as well as to spontaneous collapse theories such as CSL or GRW. More precisely, it is the conditional distribution of $\Psi'$, given the measurement outcome (respectively, the noise in CSL or the collapse history in GRW), that is GAP$_{\rho'}$.

Layering, the protocol organization principle underpinning the classical Internet, is ill-suited to the Quantum Internet, built around entanglement, which is non-local and stateful. This paper proposes a quantum-native organizational principle based on dynamic composition, which replaces static layering with a distributed orchestration fabric driven by the node local state and in-band control. Each node runs a Dynamic Kernel that i) constructs a local PoA of candidate steps to advance a service intent, and ii) executes the PoA by composing atomic micro-protocols into context-aware procedures (the meta-protocols). Quantum packets carry an in-band control-field (the meta-header) containing the service intent and an append-only list of action-commit records, termed as stamps. Successive nodes exploit this minimal, authoritative history to construct their local PoAs. As quantum packets progress, these local commits collectively induce a network-wide, direct acyclic graph that certifies end-to-end service fulfillment, without requiring global synchronization. In contrast to classical encapsulation, the proposed suite enforces order by certification: dependency-aware local scheduling decides what may run at a certain node, stamps certify what did run and constrain subsequent planning. By embedding procedural control within the quantum packet, the design ensures coherence and consistency between entanglement-state evolution and control-flow, preventing divergence between resource state ad protocol logic, while remaining MP-agnostic and implementation-decoupled. The resulting suite is modular, adaptable to entanglement dynamics, and scalable. It operates correctly with or without optional control-plane hints. Indeed, when present, hints can steer QoS policies, without changing semantics. We argue that dynamic composition is the organizing principle required for a truly quantum-native Internet.

Josephson junctions are a key element of superconducting quantum technology, serving as the core building blocks of superconducting qubits. We present an experimental study on room-temperature electrical tuning of aluminum junctions, showing that voltage pulses can controllably increase their resistance and adjust the Josephson energy while maintaining qubit quality factors above 1 million. We find that the rate of resistance increase scales exponentially with pulse amplitude during manipulation, after which the spontaneous resistance increase scales proportionally to the amount of manipulation. We show that this spontaneous increase halts at cryogenic temperatures, and resumes again at room temperature. Using our stepwise protocol, we achieve up to a 270% increase in junction resistance, corresponding to a reduction of nearly 2 GHz of the qubit transition frequency. These results establish the achievable range, relaxation behavior, and practical limits of electrical tuning, enabling post-fabrication mitigation of frequency crowding in quantum processors.

We investigate the behaviors of thermal entanglement, quantum correlation beyond entanglement namely, measurement-induced nonlocality (MIN) and coherence in a nickel radical molecular magnet (Et3NH)[Ni(hfac)2L], whose spin-spin interactions are well described by the Heisenberg model. Using experimentally estimated coupling parameters, we compute the thermal state of the system and analyze the dependence of quantum resources on temperature and magnetic field. The results indicate that the quantum resources of the nickel-radical molecular magnet persist even at room temperature. We show that while negativity (the entanglement measure) rapidly vanishes with increasing temperature and magnetic field, measurement-induced nonlocality and quantum coherence remain comparatively more stable and persist in regions where entanglement is absent. These results highlight the significance of nonclassical correlations beyond entanglement in thermally activated spin systems and suggest that such molecular magnets could serve as viable platforms for quantum information processing in realistic conditions.

We study theoretically the level shift of the Dirac oscillator perturbed by any sharply peaked potential approaching a surface delta potential. A Green function method is used to obtain closed expressions for all partial waves and parities.

In this work, the entanglement generation between two hexagonal-lattice layers embedded in a microcavity is studied, accounting for both electromagnetic coupling and intrinsic spin-orbit interaction (SOI). Utilizing a short-time dynamical approach, we perform a perturbative Taylor expansion of the reduced density matrix to characterize the bipartite quantum correlations between the hexagonal layers. We demonstrate that the system undergoes a rapid transition from a localized product state in the conduction bands at t = 0 to a coherent superposition of valence and conduction band states. Our results indicate that the degree of entanglement is highly sensitive to the interlayer photon propagator, which contains the geometric ratios of the layer positions and the height cavity, and the specific Fermi energy and SOI signatures of the respective layers. We show the emergence of spacelike-separated quantum correlations in the ultra-short evolution regime, suggesting that heterostructures in cavities may be suitable to develop experiments for a deep understanding of spacelike-separated quantum effects.

We study a Fano-mirror optomechanical system in the quantum nonlinear regime. In this system, two strongly lossy optical modes hybridize through both coherent and dissipative couplings to form an effective optical mode with a drastically reduced linewidth. This linewidth reduction enables the system to access the single-photon strong-coupling and sideband-resolved regimes simultaneously. We formulate the system dynamics using an effective master-equation approach and benchmark it against quantum Langevin and dressed-state master-equation descriptions. With experimentally realistic parameters, we predict clear quantum signatures, including photon blockade and the generation of mechanical cat states. Our work establishes the Fano-mirror architecture as a promising platform for harnessing single-photon optomechanical nonlinearities for quantum state engineering under achievable experimental conditions.

The quantum tunneling time remains the subject of heated debate, and one of its most curious features is faster-than-light or superluminal tunneling. Our tunnel-ionization model of the time-delay, presented in previous work, shows good agreement with the attoclock measurement in the adiabatic and nonadiabatic field calibrations, which also enables the determination of the barrier time-delay. In the present work, we show that the tunnel-ionization for H-like atoms with large nuclear charge can be superluminal (quantum superluminality), which in principle can be investigated experimentally using the attoclock scheme. We discuss the quantum superluminality in detail for the different regimes of the tunnel-ionization. Our result shows that quantum tunneling faster-than-light is indeed possible, albeit only under somewhat extreme conditions.

Quantum computers show promise to solve select problems otherwise intractable on classical computers. However, noisy intermediate-scale quantum (NISQ) era devices are currently prone to various sources of error. Quantum error correction (QEC) shows promise as a path towards fault tolerant quantum computing. Surface codes, in particular, have become ubiquitous throughout literature for their efficacy as a quantum error correcting code, and can execute quantum circuits via lattice surgery operations. Lattice surgery also allows for logical qubits to maneuver around the architecture, if there is space for it. Hardware used for near-term demonstrations have both spatially and temporally varying error results in logical qubits. By maneuvering logical qubits around the topology, an average logical error rate (LER) can be enforced. We propose cyclic qubit mappings (CQM), a dynamic remapping technique implemented during compilation to mitigate hardware heterogeneity by expanding and contracting logical qubits. In addition to LER averaging, CQM shows initial promise given it's minimal execution time overhead and effective resource utilization.

Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian this http URL relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped $^{40}$Ca$^+$ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.

We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.

We present a general framework for simulating quantum systems in the Heisenberg picture on quantum hardware. Based on the vectorization map, our framework fully exploits the mapping between operators and quantum states, allowing any task defined on Heisenberg operators to be mapped to standard Schrödinger-picture tasks that are naturally accessible via quantum computers and simulators. This yields new or improved protocols for tasks such as operator sampling, the computation of OTOCs/superoperator expectation values and their higher order moments, two-point correlators, and operator stabilizer and entanglement entropies. Our approach is also amenable to implementation, as it inherits the structure and resource requirements of the (forward and time-reversed) Schrödinger-picture quantum simulation problem. We demonstrate this by proposing implementations of our framework for a 2D problem on digital and analog quantum simulators, taking into account device connectivity constraints.

We study two-dimensional translation-invariant CSS stabilizer codes over prime-dimensional qudits on the square lattice under twisted boundary conditions, generalizing the Kitaev $\mathbb{Z}_p$ toric code by augmenting each stabilizer with two additional qudits. Using the Laurent-polynomial formalism, we adapt the Gröbner basis to compute the logical dimension $k$ efficiently, without explicitly constructing large parity-check matrices. We then perform a systematic search over various stabilizer realizations and lattice geometries for $p\in\{3,5,7,11\}$, identifying qudit low-density parity-check codes with the optimal finite-size performance. Representative examples include $[[242,10,22]]_3$ and $[[120,6,20]]_{11}$, both achieving $k d^{2}/n=20$. Across the searched regime, the best observed $k d^{2}$ at fixed $n$ increases with $p$, with an empirical relation $k d^{2} = 0.0541 \, n^{2}\ln p + 3.84 \, n$, compatible with a Bravyi--Poulin--Terhal-type tradeoff when the interaction range grows with system size.

Sensing of the geomagnetic field direction by many living organisms is commonly thought to involve radical pairs, such as those formed photochemically between the flavin and tryptophan radicals in the cryptochrome proteins. Previous theoretical studies have shown that strongly axial hyperfine couplings in the cryptochrome radicals greatly enhance the formation of a signaling state of the protein when the magnetic field is directed perpendicular to the hyperfine axis of either of the radicals. However, further analysis led to the conclusion that sharpness of detecting those magnetic directions is strongly suppressed by the inter-radical electron spin coupling. Here, we perform theoretical simulations of the compass function for a set of arrangements of the intra- and inter-radical spin couplings in the idealized cryptochrome radical pair, and find certain arrangements that preserve the sharpness in detecting the direction of the geomagnetic field. One particular arrangement, with the hyperfine axes of the radicals orthogonal to the symmetry axis of inter-radical coupling, provides even sharper field-direction sensitivity than that contributed solely by the anisotropy of the hyperfine coupling.

In April 2024, the White House directed NASA to establish Coordinated Lunar Time (LTC) by December 2026. The programme assumes that a unified time standard can be constructed by deploying atomic clocks on the lunar surface, computing relativistic corrections, and distributing synchronized time via LunaNet. This paper argues that the entire enterprise rests on a category mistake in the sense introduced by Ryle and developed by Spekkens in quantum foundations: it treats "synchronized time" as an ontic entity -- something that exists independently and can be transmitted from authoritative sources to dependent receivers -- when it is in fact an epistemic construct: a model-dependent representation of observer-relative clock relationships. We analyze the cislunar time programme through the lens of Forward-In-Time-Only (FITO) assumptions, Spekkens' Leibnizian operationalism, the Wood-Spekkens fine-tuning argument, and the distinction between ontic and epistemic interpretations that has dissolved long-standing puzzles in quantum mechanics. We show that the same conceptual move that dissolves quantum "mysteries" -- recognizing what is epistemic versus what is ontic -- dissolves the apparent coherence of the cislunar time programme and reveals it as an engineering project built on a philosophical confusion. We sketch a transactional alternative grounded in bilateral atomic interactions rather than unidirectional time distribution.

The foundational impossibility results of distributed computing -- the Fischer-Lynch-Paterson theorem, the Two Generals Problem, the CAP theorem -- are widely understood as discoveries about the physical limits of coordination. This paper argues that they are nothing of the sort. They are consequences of a category mistake: treating Forward-In-Time-Only (FITO) information flow as a law of nature rather than recognizing it as a design choice inherited from Shannon's channel model and Lamport's happened-before relation. We develop this argument in six steps. First, we introduce the category mistake framework from Ryle through Spekkens' ontic/epistemic distinction in quantum foundations. Second, we identify FITO as the hidden axiom that unifies the classical impossibility results. Third, we apply Spekkens' Leibnizian principle to show that FITO-based models contain surplus ontological structure. Fourth, we develop the counterfactual: what changes when FITO is dropped. Fifth, we demonstrate that the impossibility theorems are theorems about FITO systems, not about physics. Sixth, we sketch the transactional alternative -- bilateral interactions that dissolve the apparent impossibilities by replacing unidirectional message passing with atomic bilateral transactions. The implication is that distributed computing has spent fifty years optimizing within the wrong design space.

The idea that topologically protected quantum states, such as anyons, may be attached to super/semiconductor heterostructures has received enormous attention, but experimental signatures in 1D systems remain elusive. Here we revisit theoretical underpinnings of anyons in 2D fractional quantum Hall (FQH) systems, whose signatures have been experimentally observed by independent groups. Invoking novel theorems about the Hopfion or $\mathbb{C}P^1$-model understood as flux quantization in 2-Cohomotopy, we demonstrate a robust prediction for possibly nonabelian anyonic states induced by superconducting islands.

We present a systematic evaluation of large language models on quantum mechanics problem-solving. Our study evaluates 15 models from five providers (OpenAI, Anthropic, Google, Alibaba, DeepSeek) spanning three capability tiers on 20 tasks covering derivations, creative problems, non-standard concepts, and numerical computation, comprising 900 baseline and 75 tool-augmented assessments. Results reveal clear tier stratification: flagship models achieve 81\% average accuracy, outperforming mid-tier (77\%) and fast models (67\%) by 4pp and 14pp respectively. Task difficulty patterns emerge distinctly: derivations show highest performance (92\% average, 100\% for flagship models), while numerical computation remains most challenging (42\%). Tool augmentation on numerical tasks yields task-dependent effects: modest overall improvement (+4.4pp) at 3x token cost masks dramatic heterogeneity ranging from +29pp gains to -16pp degradation. Reproducibility analysis across three runs quantifies 6.3pp average variance, with flagship models demonstrating exceptional stability (GPT-5 achieves zero variance) while specialized models require multi-run evaluation. This work contributes: (i) a benchmark for quantum mechanics with automatic verification, (ii) systematic evaluation quantifying tier-based performance hierarchies, (iii) empirical analysis of tool augmentation trade-offs, and (iv) reproducibility characterization. All tasks, verifiers, and results are publicly released.

Our goal is to provide precise effective operators for monolayer graphene at Fermi energy. We consider the microscopic potential created by a lattice, and add a macroscopic potential with the same periodicity but varying at a scale $\varepsilon^{-1} \in \mathbb{N}$, creating a superlattice. Our approach consists in coupling the variational approximation, perturbation theory together with a multiscale method. At the effective level the usual massless Dirac operator is replaced by other operators, and we provide simulations in the case of graphene.

We investigate the global well-posedness and modified scattering for the one-dimensional Schrödinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we establish global existence of solution together with persistence of the localization of the associated profile. We further provide a rigorous derivation of the asymptotic expansion at arbitrary order of such solutions, taking into account long-range effects induced by the cubic component of the nonlinearity. Our analysis relies on the space-time resonance method.

To overcome the limit of diffraction while achieving the superresolution technique, solid immersion lenses are the key optical elements for data storage and nanophotonics applications. Recent demonstrations have shown how different nanostructures (such as elliptical SILs) are used in diverse fields of increasing resolution in the presence of a structured Gaussian beam. By applying twisted beams such as angular momentum beams (Laguerre- Gaussian) and spatial higher-order Gaussian beams (Hermite- Gauss), we can attain a sharp (FWHM = 27 nm) near-field focal spot pattern, which is considerably better than the conventional macroscopic SIL. By numerical simulations, tolerance has been confirmed with a slight variation in beam size and geometrical modification to make the model compatible with fabrication errors. This narrow bandwidth intensity distribution can be utilized for scanning the sample with higher resolution, especially in the field of quantum technology.

By combining genetic algorithm and a spatial light modulator we theoretically analyse how to improve a two-photon cascade absorption in atomic ensembles, inspecting the impact of various configurations and parameters in the optimized phase mask. At low atomic densities, we compare the cases of sequential transitions with the two photons coming from the same pulse or from two different pulses. For the former, we predict an enhancement by a factor of $9.5$, similar to what was previously reported in the literature [Phys. Rev. Lett. {\bf 86}, 47 (2002)]. For the later, on the other hand, we obtain an enhancement factor of $26$ times. This absorption of two photons by different pulses is of particular interest for the storage of ultra-broadband single photons by atomic ensembles, in which case the second photon would come from a control pulse. We investigate this process as a function of the atomic density, demonstrating enhancements by factors up to 3 for the two-photon absorption after propagating through large optical depths. However, for the experimental conditions considered in the previous work by Carvalho {et al.} [Phys. Rev. A {\bf 101}, 053426 (2020)], in terms of control power and optical depths, we show that this enhancement in two-photon absorption would still result in just a modest increase of the absorption of a weak probe pulse.

A temporal magnon-qubit Mach-Zehnder (MZ) interferometer is proposed. The interferometer is based on controllable entanglement of a microwave qubit and a magnonic state, achieved by application of a pulsed magnetic field playing the role of a magnon-qubit temporal "beam splitter". Analogous to a typical MZ interferometer, the generated interference pattern of the final qubit population carries information about the magnon dynamics. One important application of the proposed scheme is the study of single magnon decoherence. Interestingly, this scheme allows one to independently determine rates of two possible decoherence channels. This may help enable single magnon state applications and answer fundamental questions of quasi-particle decoherence at single quantum levels.

The mechanisms by which isolated interacting quantum systems evade thermalization extend beyond disorder-induced many-body localization, encompassing a growing class of interaction-driven phenomena. We investigate a spin-1/2 ladder with asymmetric XY leg couplings and tunable Ising interactions on the rungs, and identify the microscopic origin of many-body localization (MBL) in this setting. Through a suite of diagnostics -including entanglement dynamics, fidelity susceptibility, adiabatic gauge potential norms, level-spacing statistics and entropy of eigenstates- we uncover a reentrant progression of dynamical regimes as the rung coupling Jz is varied: integrable behavior at Jz=0, quantum chaos at intermediate Jz, and a robust nonthermal regime at strong coupling. In the latter regime, we demonstrate the emergence of a reversed quantum disentangled liquid (reversed-QDL), where the light species thermalizes while the heavy species remains localized. The strong-coupling limit further yields emergent local integrals of motion anchored in a fixed-point structure, providing a microscopic origin of the observed quasi-MBL dynamics. These results establish reversed-QDL as a distinct, disorder-free route to nonergodicity and broaden the classification of dynamical phases in quantum matter.

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive noise. We introduce Spectral Phase Encoding (SPE), a hybrid construc- tion combining a discrete Fourier transform (DFT) front-end with a diagonal phase-only embedding aligned with the geometry of diagonal quantum maps. Within a unified framework, we compare QK-DFT against alternative quantum variants (QK-PCA, QK-RP) and classi- cal SVM baselines under identical clean-data hyperparameter selection, quantifying robustness via dataset fixed-effects regression with wild cluster bootstrap inference across heterogeneous real-world datasets. Across the quantum family, DFT-based preprocessing yields the smallest degradation rate as noise increases, with statistically sup- ported slope differences relative to PCA and RP. Compared to classical baselines, QK-DFT shows degradation comparable to linear SVM and more stable than RBF SVM under matched tuning. Hardware exper- iments confirm that SPE remains executable and numerically stable for overlap estimation. These results indicate that robustness in quan- tum kernels depends critically on structure-aligned preprocessing and its interaction with diagonal embeddings, supporting a robustness-first perspective for NISQ-era quantum machine learning.

We study whether latent motivation signals in short Spanish admission responses predict engagement and performance in an early quantum computing pathway run by QuantumHub Peru. We analyze N=241 applicants' open responses and link them to outcomes from two selective modules: Module 1 (secondary; mathematics and computing foundations; n=23) and Module 2 (secondary + early undergraduate; quantum fundamentals; n=36, including M1 continuers). To ensure baseline comparability, the M2 university entrance exam matched the difficulty of the M1 final. Final grades followed the program's official cohort-specific weightings (attendance/assignments/exam), which we retain to preserve ecological validity. Methodologically, we model text with Latent Dirichlet Allocation (LDA, k=8) and, for robustness, with sentence embeddings from a small multilingual language model, EmbeddingGemma-300M, projected via UMAP and clustered with HDBSCAN. This combination leverages the transparency of bag-of-words topics and the semantic richness of small language model embeddings. Descriptively, curiosity/learning topics show higher grades and attendance than technology/career-oriented topics; inferential tests are underpowered (e.g., linear R2 ~ 0.03; logistic pseudo-R2 ~ 0.04) so effect-size estimates should be viewed as preliminary rather than confirmatory. Embedding-based clustering yields seven clusters with 11.2% noise and modest agreement with LDA (ARI=0.068; NMI=0.163). Results suggest that brief motivation responses encode promising signals that could support early mentoring in rigorous STEM pipelines, while highlighting the need for larger, pre-registered studies.

Recently, Fendley et al. (2025) [arXiv:2511.04674] revealed a new way to demonstrate the integrability of XYZ Heisenberg model by constructing a one-parameter family of integrals of motion in the matrix product operator (MPO) form. In this short note, I report on the discovery of two-parameter families of MPOs that commute with with the Heisenberg spin chain Hamiltonian in the XXX, XXZ, and XYZ cases. I describe a symbolic algebra approach for finding such integrals of motion and speculate about possible applications.

Lasers serve as the fundamental workhorses of photonic quantum technologies, with perfectly coherent light fields being essential for many protocols that generate nonclassical light, implement coherent control schemes, and initialize qubits. However, no laser is absolutely ideal and the implications of deviations from perfect coherence in quantum technological tasks remain unclear. In this study, we theoretically and experimentally explore the quantum coherence properties of lasers from a resource theory perspective, establishing a significant connection between photonics, quantum optics, and quantum information science. We demonstrate that the maximum achievable quantum coherence for laser light is constrained by spontaneous emission and the purity of the dephased laser field state. As a critical example application in quantum information protocols, we show that the quantum coherence of a laser field with a given mean photon number directly governs the maximum purity attainable when initializing a qubit in a superposition state through resonant driving. Our findings are highly relevant for bridging applied physics and engineering with integrated photonic quantum technologies and resource theories, paving the way for reliable benchmarking of various coherent light sources for applications in photonics and quantum protocols.

We study the robustness of the Floquet quantum Ising model against integrability-breaking perturbations, focusing on the phase hosting both Majorana zero and $\pi$ modes. A recent work [Phys. Rev. B 110, 075117, (2024)] observed that the Floquet product mode, a composite edge mode constructed from both Majorana operators, is considerably more robust than the individual Majorana edge modes. We analyze these strong modes from the point of view of the eigenphase order present in finite chains with open boundary conditions. As a result of the Majorana modes, all Floquet eigenstates come in quadruplets in the integrable limit. We show that the robustness of the various modes as well as the behavior of the boundary spin correlation functions can be understood in terms of the spectral statistics of these quadruplets in the presence of integrability-breaking perturbations.

Highly excited Rydberg states of lanthanides are a promising, yet largely unexplored, playground for quantum studies. Here, we report on the first high-resolution spectroscopy of 162Dy obtained by two-color trap depletion spectroscopy in a magneto-optical trap. The absolute excitation frequency of over 700 states with effective principal quantum number n between 21 and 130 is measured with an accuracy of 20 MHz. Most states are assigned to the 8 different series converging to the first 4f10(5I8)6s(2S1/2) J = 17/2 ionization potential. This energy is measured at EIP = 47901.8265 +/- 0.0008 cm-1, improving the precision of the literature value by over an order of magnitude. A multichannel quantum defect theory approach is used to benchmark and refine the assignments and to characterize six observed perturbing states belonging to higher ionization limits. These results pave the way for using dysprosium in Rydberg-based quantum architectures, leveraging the unique properties arising from its complex electronic structure. They also represent a compelling benchmark for ab-initio calculations of open-shell atomic systems.

When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality.

The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap $\Delta$ encountered at quantum phase transitions. We investigate the scaling of $\Delta$ with system size $N$ for two paradigmatic quantum spin-glass models: the two-dimensional Edwards-Anderson (2D-EA) and the all-to-all Sherrington-Kirkpatrick (SK) models. Utilizing a newly proposed unbiased energy-gap estimator for continuous-time projection quantum Monte Carlo simulations, complemented by high-performance sparse eigenvalue solvers, we characterize the gap distributions across disorder realizations. It is found that, in the 2D-EA case, the inverse-gap distribution develops a fat tail with infinite variance as $N$ increases. This indicates that the unfavorable super-algebraic scaling of $\Delta$, recently reported for binary couplings [Nature 631, 749 (2024)], persists for the Gaussian disorder considered here, pointing to a universal feature of 2D spin glasses. Conversely, the SK model retains a finite-variance distribution, with the disorder-averaged gap following a rather slow power law, close to $\Delta \propto N^{-1/3}$. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity.

Information causality (IC) was one of the first principles that have been invoked to bound the set of quantum correlations. For some families of correlations, this principle recovers exactly the boundary of the quantum set; for others, there is still a gap. We close some of these gaps using a new quantifier for IC, based on the notion of ``redundant information''. This progress was made possible by the recognition that the principle of IC can be captured without referring to the success criterion of random access codes. We give strong numerical evidence that the new definition is still obeyed by quantum correlations in the same scenario.

We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local constraint satisfaction problems ($k$-CSP). We show that either (a) the algorithm finds the optimal solution in time $O^*(2^{(0.5-c)n})$ for an $n$-independent constant $c$, a $2^{cn}$ advantage over Grover's algorithm; or (b) there are sufficiently many low-cost solutions such that classical random guessing produces a $(1-\eta)$ approximation to the optimal cost value in sub-exponential time for arbitrarily small choice of $\eta$. Additionally, we show that for a large fraction of random instances from the $k$-spin model and for any sufficiently close-to-regular, fully satisfiable (or slightly frustrated) $k$-CSP formula, statement (a) is the case. The algorithm and its analysis is largely inspired by Hastings' short-path algorithm [$\textit{Quantum}$ $\textbf{2}$ (2018) 78].

The quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. It is not easy to achieve in practice. The original idea of PST depends on the fundamentals of the continuous-time quantum walk. A path graph with at most three vertices allows PST based on continuous-time quantum walk. Based on the Markovian quantum walk, we introduce a significantly powerful method for PST in this article. We establish PST between the extreme vertices of a path graph of arbitrary length. Moreover, any pair of symmetric vertices in a path graph allows PST under Markovian quantum walks. We extend our investigations for the cycle graphs. The cycle graphs with more than $4$ vertices do not allow the PST based on the continuous-time quantum walk. In contrast, a cycle graph with $2m$ vertices exhibits PST based on Markovian quantum walk between the vertices $j$ and $j + m$ for $j = 0, 1, \dots (m - 1)$, where $m > 0$ is an integer.

We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are defined. Such non-commutative polynomial optimization (NPO) problems are routinely solved through hierarchies of semidefinite programming (SDP) relaxations. By formulating the general NPO problem in Lagrangian terms, we heuristically derive first-order optimality conditions via small variations in the problem variables. Although the derivation is not rigorous, it gives rise to two types of optimality conditions -- state and operator -- which are rigorously analyzed in the paper. Both types of conditions can be enforced through additional positive semidefinite constraints in the SDP hierarchies. State optimality conditions are shown to be satisfied by all NPO problems. For NPO problems with optimal solutions (such as, e.g., Archimedean ones) they allow enforcing a new type of constraints: namely, restricting the optimization over states to the set of common ground states of an arbitrary number of operators. Operator optimality conditions are the non-commutative analogs of the Karush--Kuhn--Tucker (KKT) conditions, which are known to hold in many classical optimization problems. In this regard, we prove that a weak form of operator optimality holds for all NPO problems; stronger versions require the problem constraints to satisfy some qualification criterion, just like in the classical case (e.g.: Mangasarian--Fromovitz constraint qualification). We test the power of the new optimality conditions by computing local properties of ground states of many-body spin systems and the maximum quantum violation of Bell inequalities.

The transfer of information from one part of a quantum system to another is fundamental to the understanding and design of quantum information processing devices. In the realm of discrete systems such as spin chains, inhomogeneous networks have been engineered that allow for the perfect transfer of qubits from one end to the other. Here, by contrast, we investigate the perfect transfer of information in continuous systems, phrased in terms of wave propagation. A remarkable difference is found between systems that possess conformal invariance and those that do not. Systems in the first class enjoy perfect wave transfer (PWT), explicitly shown for one-particle excitations and anticipated in general. In the second class, those that exhibit PWT are characterized as solutions to an inverse spectral problem. As a concrete example, we demonstrate how to formulate and solve this problem for a prototypical class of bosonic theories, showing the importance of conformal invariance for these theories to enjoy PWT. Using bosonization, our continuum results extend to theories with interactions, broadening the scope of perfect information transfer to more general quantum systems.

Quantum Convolutional Neural Networks (QCNNs) are widely regarded as a promising model for Quantum Machine Learning (QML). In this work we tie their heuristic success to two facts. First, that when randomly initialized, they can only operate on the information encoded in low-bodyness measurements of their input states. And second, that they are commonly benchmarked on "locally-easy'' datasets whose states are precisely classifiable by the information encoded in these low-bodyness observables subspace. We further show that the QCNN's action on this subspace can be efficiently classically simulated by a classical algorithm equipped with Pauli shadows on the dataset. Indeed, we present a shadow-based simulation of QCNNs on up-to $1024$ qubits for phases of matter classification. Our results can then be understood as highlighting a deeper symptom of QML: Models could only be showing heuristic success because they are benchmarked on simple problems, for which their action can be classically simulated. This insight points to the fact that non-trivial datasets are a truly necessary ingredient for moving forward with QML. To finish, we discuss how our results can be extrapolated to classically simulate other architectures.

Conveyor-mode shuttling is a key approach for implementing intermediate-range coupling between electron-spin qubits in quantum dots. Initial implementations are encouraging; however, long shuttling trajectories are guaranteed to encounter regions of low conduction-band valley energy splittings, due to the presence of random-alloy disorder in Si/SiGe quantum wells. Here, we theoretically explore two schemes for avoiding valley-state excitations at these valley-splitting minima, by allowing the electrons to detour around them. A multichannel shuttling scheme allows electrons to tunnel between parallel channels, while a two-dimensional (2D) shuttler provides full omnidirectional control. Using simulations, we estimate shuttling fidelities in these two schemes, obtaining a clear preference for the 2D shuttler. Based on such encouraging results, we propose a modular qubit architecture based on 2D shuttling, which enables all-to-all connectivity within qubit plaquettes and high-fidelity communication between different plaquettes.

Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing quantum technologies. Some quantum algorithms simulate Lindblad dynamics exponentially accurately, i.e., they achieve logarithmically short circuit depth in terms of accuracy, but they need to coherently encode all possible jump operators with a large ancilla consumption. Minimizing the gate and ancilla counts while achieving such a logarithmic scaling in accuracy remains an important challenge. In this work, we present two randomized quantum algorithms for simulating general Lindblad dynamics with multiple jump operators aimed at an observable estimation that achieve a circuit depth with not only logarithmic scaling in accuracy but also either partial or complete independence from the parameters specifying the Lindbladian. This is based on a novel random circuit compilation method that leverages dissipative processes with only a single jump operator, leading to the proposed methods using minimal ancilla qubits -- $4+\lceil\log_2 M\rceil$ in the first case and $7$ in the other, where each single jump operator has at most $M$ Pauli strings. In addition, we numerically demonstrate the practical advantage over existing approaches by providing a detailed analysis of the required gate and ancilla counts. This work represents a significant step towards making open quantum system simulations more feasible on early fault-tolerant quantum computing devices.

Efficient and scalable decoding of quantum codes is essential for high-performance quantum error correction. In this work, we introduce Reliable Subset Reduction (RSR), a reliability-driven preprocessing framework that leverages belief propagation (BP) statistics to identify and remove highly reliable qubits, substantially reducing the effective problem size. Additionally, we identify a degeneracy condition that allows high-order OSD to be simplified to order-0 OSD. By integrating these techniques, we present an ADOSD algorithm that significantly improves OSD efficiency. Our BP+RSR+ADOSD framework extends naturally to circuit-level noise and can handle large-scale codes with more than $10^4$ error variables. Through extensive simulations, we demonstrate improved performance over MWPM and Localized Statistics Decoding for a variety of CSS and non-CSS codes under the code-capacity noise model, and for rotated surface codes under realistic circuit-level noise. At low physical error rates, RSR reduces the effective problem size to as little as 1\% (e.g., for $\epsilon=0.001$ in surface-code DEM), enabling higher-order OSD with drastically reduced computational complexity. These results highlight the practical efficiency and broad applicability of the BP+ADOSD framework for both theoretical and realistic quantum error correction scenarios.

One of the key steps in quantum algorithms is to prepare an initial quantum superposition state with different kinds of features. These so-called state preparation algorithms are essential to the behavior of quantum algorithms, and complicated state preparation algorithms are difficult to develop correctly and effectively. This paper presents Pqasm: a high-assurance framework implemented with the Coq proof assistant, allowing us to certify our Pqasm tool to correctly reflect quantum program behaviors. The key in the framework is to reduce the program correctness assurance of a program containing a quantum superposition state to the program correctness assurance for the program state without superposition. The reduction allows the development of an effective testing framework for testing quantum state preparation algorithm implementations on a classical computer - considered to be a hard problem with no clear solution until this point. We utilize the QuickChick property-based testing framework to test state preparation programs. We evaluated the effectiveness of our approach over 5 case studies implemented using Pqasm; such cases are not even simulatable in the current quantum simulators.

Preparing quantum states is a fundamental task in various quantum algorithms. In particular, state preparation in quantum harmonic oscillators (HOs) is crucial for the creation of qudits and the implementation of high-dimensional algorithms. In this work, we develop a methodology for preparing quantum states in HOs. The HO is coupled to an auxiliary qubit to ensure that any state can be prepared in the oscillator [J. Math. Phys. 59, 072101]. By applying a sequence of square pulses to both the qubit and the HO, we drive the system from an initial state to a target state. To determine the required pulses, we use a neural network that predicts the pulse parameters needed for state preparation. Specifically, we present results for preparing qubit and qutrit states in the HO, achieving average fidelities of 99.9% and 97.0%, respectively.

Understanding and mitigating noise in quantum systems is a fundamental challenge in achieving scalable and fault-tolerant quantum computation. Error modeling for quantum systems can be formulated in many ways, some of which are very fundamental, but hard to analyze (evolution by general dynamical map) and others perhaps too simplistic to represent physical reality. In this paper, we present an intermediate approach, introducing the random Schrödinger equation, with a noise term given by a time-varying random Hermitian matrix as a means to model noisy quantum systems. We derive bounds on the error of the synthesized unitary in terms of bounds on the norm of the noise, and show that for certain noise processes these bounds are tight. We then show that in certain situations, minimizing the error is equivalent to finding a geodesic on SU(n) with respect to a Riemannian metric encoding the coupling between the control pulse and the noise process, thus connecting our work to the complexity geometry pioneered by Michael Nielsen.

Current superconducting quantum computing platforms face significant scaling challenges, as individual signal lines are required for control of each qubit. This wiring overhead is a result of the low level of integration between control electronics at room temperature and qubits operating at millikelvin temperatures, which raise serious doubts among technologists about whether utility-scale quantum computers can be built. A promising alternative is to utilize cryogenic, superconducting digital control electronics that coexist with qubits. Here, we report the first multi-qubit system integrating this technology. The system utilizes digital demultiplexing, breaking the linear scaling of control lines to number of qubits. We also demonstrate single-qubit fidelities above 99%, and up to 99.9%. This work is a critical step forward in realizing highly scalable chip-based quantum computers.

The development of prototype quantum information processors has progressed to a stage where small instances of logical qubit systems perform better than the best of their physical constituents. Advancing towards fault-tolerant quantum computing will require an understanding of the underlying error mechanisms in logical primitives as they relate to the performance of quantum error correction. In this work we demonstrate the novel capability to characterize the physical error properties relevant to fault-tolerant operations via cycle error reconstruction. We illustrate this diagnostic capability for a transversal CNOT, a prototypical component of quantum logical operations, in a 16-qubit register of a trapped-ion quantum computer. Our error characterization technique offers three key capabilities: (i) identifying context-dependent physical layer errors, enabling their mitigation; (ii) contextualizing component gates in the environment of logical operators, validating the performance differences in terms of characterized component-level physics, and (iii) providing a scalable method for predicting quantum error correction performance using pertinent error terms, differentiating correctable versus uncorrectable physical layer errors. The methods with which our results are obtained have scalable resource requirements that can be extended with moderate overhead to capture overall logical performance in increasingly large and complex systems.

Accurate prediction and stabilization of blast furnace temperatures are crucial for optimizing the efficiency and productivity of steel production. Traditional methods often struggle with the complex and non-linear nature of the temperature fluctuations within blast furnaces. This paper proposes a novel approach that combines hybrid quantum machine learning with pulverized coal injection control to address these challenges. By integrating classical machine learning techniques with quantum computing algorithms, we aim to enhance predictive accuracy and achieve more stable temperature control. For this we utilized a unique prediction-based optimization method. Our method leverages quantum-enhanced feature space exploration and the robustness of classical regression models to forecast temperature variations and optimize pulverized coal injection values. Our results demonstrate a significant improvement in prediction accuracy over 25 percent and our solution improved temperature stability to +-7.6 degrees of target range from the earlier variance of +-50 degrees, highlighting the potential of hybrid quantum machine learning models in industrial steel production applications.

Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting that enables both global inconsistency and local consistency. Our approach builds upon pairwise consistent families of K-relations, i.e, relations with tuples annotated with elements of some positive commutative monoid. The framework covers, e.g., families of probability distributions arising from quantum experiments and their possibilistic counterparts. As a first step, we investigate the entailment problem for functional dependencies (FDs) in this setting. Notably, the transitivity rule for FDs is no longer sound, but can be replaced by two novel axiom schemas. We provide a complete axiomatisation for, and establish NL-completeness of, the entailment problem of unary FDs, and demonstrate that even this restricted case exhibits context-dependent subtleties. In addition, we explore when contextual families over the Booleans have realisations as contextual families over various monoids.

We present new generalizations of Cauchy-Schwarz (CS) inequalities to multiple vectors and use them to derive multi-operator quantum uncertainty relations and propose multi-operator squeezing.

We present results from co-designed quantum simulations of the neutrinoless double-beta decay of a simple nucleus in 1+1D quantum chromodynamics using IonQ's Forte-generation trapped-ion quantum computers. Electrons, neutrinos, and up and down quarks are distributed across two lattice sites and mapped to 32 qubits, with an additional 4 qubits used for flag-based error mitigation. A four-fermion interaction is used to implement weak interactions, and lepton-number violation is induced by a neutrino Majorana mass. Quantum circuits that prepare the initial nucleus and time evolve with the Hamiltonian containing the strong and weak interactions are executed on IonQ Forte Enterprise. Enabled by tuned model parameters, lepton-number violation is observed in real time, providing a clear signal of neutrinoless double-beta decay. This was made possible by co-designing the simulation to maximally utilize the all-to-all connectivity and native gate-set available on IonQ's quantum computers. Quantum circuit compilation techniques and co-designed error-mitigation methods, informed from executing benchmarking circuits with up to 2,356 two-qubit gates, enabled observables to be extracted with high precision. We discuss the potential of future quantum simulations to provide yocto-second resolution of the reaction pathways in these, and other, nuclear processes.

Characterizing quantum processes is essential for unlocking the potential of quantum devices. However, standard quantum process tomography is resource-intensive and becomes infeasible on large-scale systems. Despite alternative approaches have been successfully developed for specific scenarios, they typically rely on multi-qubit gates or extensive prior knowledge, limiting their practicability and scalability. To address these challenges and complement existing approaches, we introduce $\textit{influence sampling}$, an efficient and scalable protocol that quantifies the $\textit{influence}$ of a quantum process on all qubit subsets using only single-qubit test gates, with sample complexity independent of system size. Using a photonic platform, we demonstrate influence sampling to identify high-influence qubits, reduce the full process to a smaller effective process, i.e., a junta approximation, and then learn it. We further confirm scalability by applying the protocol to a 24-qubit system and validate the junta approximation on a two-qubit process. These results establish influence sampling as a critical characterization technique, facilitating process learning and device assessment.

Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.

Access to the time-reverse $U^{-1}$ of an unknown quantum unitary process $U$ is widely assumed in quantum learning, metrology, and many-body physics. The fundamental task of unitary time-reversal dictates implementing $U^{-1}$ to within diamond-norm error $\epsilon$ using black-box queries to the $d$-dimensional unitary $U$. Although the query complexity of this task has been extensively studied, existing lower bounds either hold only for the exact case (i.e., $\epsilon=0$) or are suboptimal in $d$. This raises a central question: does approximation help reduce the query complexity of unitary time-reversal? We settle this question in the negative by establishing a robust and tight lower bound $\Omega((1-\epsilon)d^2)$ with explicit dependence on the error $\epsilon$. This implies that unitary time-reversal retains optimal exponential hardness (in the number of qubits) even when constant error is allowed. Our bound applies to adaptive and coherent algorithms with unbounded ancillas and holds even when $\epsilon$ is an average-case distance error.

We investigate dynamical decoupling operated by $2\pi$-pulses in a two-level subspaces of a multilevel system showing that it may leads to selective decoupling. This provides a flexible strategy for decoupling transitions in a quantum network, when control to directly address them is not available which can be use to control internode interaction or actively suppress decoherence

Global-scale entanglement distribution has been a formidable challenge due to the unavoidable losses in communication channels. Here, we propose a novel backbone channel for quantum network based on balloon-based aerial relays. We demonstrate for the first time that the atmospheric disturbances in balloon-based channels can be almost eliminated through optimizing beam waist positions and employing a series of adaptive optics systems, which boosts the channel efficiency to -21 dB over a 10,000 km distance, outperforming satellite-based relays by 12 dB with same device parameters. We then propose a global-scale quantum networking scheme based on hybrid-channel quantum repeaters that combine ground-based quantum repeaters and balloon-based aerial relays. Servers are interconnected globally via a chain of balloons, while clients link to local servers through fiber connections, facilitating rapid client switching and network scalability. Our simulations, employing state-of-the-art Eu$^{3+}$:Y$_2$SiO$_5$ quantum memories and mature entanglement sources based on spontaneous parametric down-conversion, demonstrate an entanglement distribution rate in the sub-Hertz range between clients separated by 10,000 km. This approach offers a practical path toward global quantum networking in the near future.

Multimode multiphoton states are at the center of many photonic quantum technologies, from photonic quantum computing to quantum sensing. In this work, we derive a procedure to generate exactly, and with a predictable number of steps, any such state by using only multiport interferometers, photon number resolving detectors, photon additions and displacements. We achieve this goal by establishing a connection between photonic quantum state engineering and the algebraic problem of symmetric tensor decomposition. This connection allows us to solve the problem by using corresponding results from algebraic geometry and unveils a mechanism of photon catalysis, where photons are injected and subsequently retrieved in measurements, to generate entanglement that cannot be obtained through Gaussian operations. We also introduce a tensor decomposition, that generalizes our method and allows to construct circuits yielding perfect fidelity, using the minimum number of catalysis photons. As a benchmark, we numerically evaluate our method and compare its performance with state-of-the art results, confirming 100\% fidelity on different classes of states.

Quantum adiabatic dynamics is the crucial element of adiabatic quantum computing and quantum annealing. Shortcuts to adiabaticity enable acceleration of the computational time by suppressing unwanted non-adiabatic processes with designed classical fields. Here, we consider quantum state transfer in the Landau-Zener model, which exemplifies the key elements of quantum adiabatic dynamics. We argue that non-adiabatic transitions can be suppressed by autonomous quantum dynamics, which involves coupling the Landau-Zener qubit to a second quantum system. By tuning the coupling strength, the composite quantum dynamics can reduce the probability of unwanted processes by more than two orders of magnitude. This is a prime example of control where the quantum properties of the control fields are key for implementing shortcuts to adiabaticity.

Multipartite entanglement is an essential aspect of quantum systems, needed to execute quantum algorithms, implement error correction, and achieve quantum-enhanced sensing. In solid-state quantum registers such nitrogen-vacancy (NV) centers in diamond, entangled states are typically created using sequential, pairwise gates between the central electron and individual nuclear qubits. This sequential approach is slow and suffers from crosstalk errors. Here, we demonstrate a parallelized multi-qubit entangling gate to generate a four-qubit GHZ state using a room-temperature NV center in only 14.8 $\mu$s $-$ 10 times faster than using sequences of two-qubit gates and close to the fundamental limit set by the hyperfine coupling frequencies. Parallel three-qubit gates are also realized with all nuclear-qubit subsets. The entangled states are verified by measuring multiple quantum coherences. The four-qubit parallel gate has a fidelity of 0.92(4), whereas the sequential four-qubit gate fidelity is only 0.69(3). The approach is generalizable to other solid-state platforms, and it lays the foundation for scalable generation and control of entanglement in practical devices.

We analyze the conditional quantum state of a mechanical mirror in an optomechanical system subject to continuous measurement, feedback control, and quantum filtering. We identify a parameter regime in which the mirror exhibits momentum squeezing beyond the standard quantum limit, achieved through an appropriate choice of the homodyne detection angle. In this regime, we show that optimal filtering effectively realizes a free-particle-like conditional state. When this mechanism is applied to a configuration consisting of two optomechanical systems, the resulting momentum squeezing significantly enhances the signal of gravity-induced entanglement (GIE). This enhancement arises because the momentum squeezing not only amplifies the distinction between the common and differential modes, but also, in the high-purity regime, increases the position uncertainty in accordance with the uncertainty principle, thereby enlarging the spatial extent of the quantum superposition. Our results provide new insights into experimental strategies for probing the quantum nature of gravity using optomechanical platforms.

Nonclassical states of bosonic modes, especially the large number states, are valuable resources for quantum information processing and quantum metrology. It is however intricate to generate a desired Fock state of bosonic systems by unitary protocols due to their uniform energy spectrum. We here propose a nonunitary protocol that is based on the resonant Jaynes-Cummings interaction of the bosonic mode with an ancillary two-level atom and sequential projective measurements on the atom. Using the generalized parity-measurement operator constructed by several rounds of free evolution with stepwise halved intervals and measurement, we can efficiently filter out the unwanted population and push the target resonator conditionally toward the desired Fock state. In the ideal situation, a Fock state $|n_t\approx2000\rangle$ can be prepared with a fidelity over $98\%$ using only eight rounds of measurements. Under qubit dissipation and dephasing and cavity decay in the current circuit-QED platforms, a Fock state $|n_t\approx100\rangle$ can be prepared with a fidelity of about $80\%$ by six measurements. It is found that the number of measurement rounds for preparing a large Fock state $|n_t\rangle$ scales roughly as $\log_2\sqrt{n_t}$, which is similar to the number of ancillary qubits required in the state preparation via the quantum phase estimation algorithm and yet costs much less in gate operations. Our protocol can also be used to prepare a large Dicke state $|J\simeq1000,0\rangle$ of a spin ensemble with a sufficiently high fidelity by less than six measurements. It is qualified by the quantum Fisher information approaching the Heisenberg scaling in sensing the rotation phase along the $x$ axis.

In this exploratory numerical study, we assess the suitability of Quantum Linear Solvers(QLSs)toward providing a quantum advantage for Networks-based Linear System Problems (NLSPs). NLSPs naturally arise from graphs, and are of importance as they are connected to real-world applications. The achievable advantage with a QLS for an NLSP depends on the interplay between the scaling of condition number and sparsity of matrices associated with the graph family. We analyze 50 graph families and identify that within the scope of our study, only 21 of them exhibit prospects for an exponential advantage with the Harrow-Hassidim-Lloyd (HHL) algorithm relative to an efficient classical solver. We call graph families that offer advantage with HHL as good graph families. We also compare the performance of the considered 50 graph families with 7 other QLSs. Furthermore, we report that some graph families graduate from offering no advantage with HHL to promising an exponential advantage with improved algorithms such as the Childs-Kothari-Somma algorithm. We also introduce a unified graph superfamily and show the existence of infinite good graph families in it. Since the runtime expressions for linear solvers involve condition number, which in itself is not easy to compute, ascertaining advantage prospects with quantum linear solvers itself is not an easy problem. Thus, we conjecture the conditions under which one may visually examine a graph family and guess the prospects for an advantage. Finally, we very briefly touch upon some practical issues that may arise even if the aforementioned graph theoretic requirements are satisfied, including quantum hardware challenges.

We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $\SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by Sá Earp and Pachos (2005), we overcome key limitations of their method, such as reliance on ill-defined matrix logarithms and the convergence issues of truncated Baker-Campbell-Hausdorff(BCH) series. Our reformulation leverages the algebraic structure of involutive automorphisms and symmetric Lie algebra decompositions to yield a stable and recursive factorization process. We provide a full Python implementation of the algorithm, available in an open-source repository, and validate its performance on matrices in $\SU(8)$ and $\SU(16)$ using random unitary benchmarks. The algorithm produces decompositions that are directly suited to practical quantum hardware, with factors that can be implemented near-optimally using standard gate sets.

Variational quantum algorithms have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of variational quantum algorithms is highly sensitive to the design of the ansatze. To be effective, ansatze must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatze that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatze through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches. This work presents a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.

We propose an iterative variational quantum algorithm to simulate the time evolution of arbitrary initial states within a given subspace. The algorithm compresses the Trotter circuit into a shorter-depth parameterized circuit, which is optimized simultaneously over multiple initial states in a single training process using fidelity-based cost functions. After the whole training procedure, we provide an efficiently computable lower bound on the fidelities for arbitrary states within the subspace, which guarantees the performance of the algorithm in the worst-case training scenario. We also show our cost function exhibits a barren-plateau-free region near the initial parameters at each iteration in the training landscape. The experimental demonstration of the algorithm is presented through the simulation of a 2-qubit Ising model on an IBMQ processor. As a demonstration for a larger system, a simulation of a 10-qubit Ising model is also provided.

We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely tuned irrational rotations, making them difficult to realize on near-term devices. We find that the controlled-$V$ gate, an elementary two-qubit interaction directly implementable on leading hardware, is universal and capable of simulating standard universal gate sets with minimal overhead. Specifically, we use catalytic embeddings to develop a constant-overhead algorithm that simulates standard universal gate sets, including Clifford$+T$ and Clifford$+$Toffoli. We combine this simulation algorithm with existing synthesis results to yield exact and approximate synthesis algorithms for unitaries with and without number-theoretic restrictions. The results highlight how full quantum computational power, complete with algorithms for synthesis and simulation, can emerge from unexpectedly simple ingredients.

We present a model to detect a classical state mixed with an idler photon from a polarization-entangled pair. A weak coherent light with a well-defined polarization, matched in wavelength to the idler photon, is injected into the idler channel. Quantum state tomography is then performed on both the classically mixed idler photon and its entangled signal partner. The reconstructed state is modeled as a combination of an $X-$quantum state and a classical-quantum (CQ) state. In this framework, the weak coherent light acts as a measurement apparatus performing a local polarization measurement on the idler channel, thereby inducing a classical state. The density matrix of the classical state is identified via algorithmic analysis of the diagonal and off-diagonal elements of the reconstructed density matrix. This approach could advance techniques for classical-quantum coexistence in networking applications$\,-\,$such as quantum wrapping$\,-\,$as well as future quantum key distribution protocols based on the coexistence of weak coherent states and entangled photon states.

As a key component of quantum networks, the quantum router distributes quantum information among different quantum nodes. The silicon-vacancy (SiV) center in diamond offers a promising platform for quantum technology due to its strong strain-induced coupling with phonons. However, the development of a practical quantum router faces the challenges of achieving long-range entanglement and suppressing decoherence. Here, we propose a non-Markovian quantum router based on a diamond waveguide embedded with an array of SiV centers as the quantum nodes. Unlike conventional channel-switching methods, our design enables parallel quantum-state transfer from a single input node to multiple target nodes, analogous to a classical WiFi router. We demonstrate that persistent entanglement and suppressed decoherence of the SiV centers over long distances are achievable when bound states are present in the energy spectrum of the total system formed by the SiV centers and the phonon waveguide. Our scheme enriches the implementation of quantum routing and prompts the development of solid-state quantum networks.

Preparing magnon nonclassical states is a central topic in the study of quantum magnonics. Here we propose to generate magnon squeezed states in a hybrid cavity-magnon-qubit system by engineering an effective Rabi-type magnon-qubit interaction. This is achieved by adiabatically eliminating the cavity mode and driving the qubit with two microwave fields, of which the driving frequencies and amplitudes are properly selected. By operating the system around the critical point associated with the ground-state superradiant phase transition in the normal phase, a magnon parametric amplification-like interaction is induced, leading to a dynamical magnon squeezing. We further analyze the effects of the dissipation, dephasing, and thermal noise on the magnon squeezing. Our results indicate that a moderate degree of squeezing can be produced using currently available parameters in the experiments.

The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched Rényi relative entropy. In this paper, we present a comprehensive study of the estimation of the quantum Tsallis relative entropy. We show that for any constant $\alpha \in (0, 1)$, the $\alpha$-Tsallis relative entropy between two quantum states of rank $r$ can be estimated with sample complexity $\operatorname{poly}(r)$, which can be made more efficient if we know their state-preparation circuits. As an application, we obtain an approach to tolerant quantum state certification with respect to the quantum Hellinger distance with sample complexity $\widetilde{O}(r^{3.5})$, which exponentially outperforms the folklore approach based on quantum state tomography when $r$ is polynomial in the number of qubits. In addition, we show that the quantum state distinguishability problems with respect to the quantum $\alpha$-Tsallis relative entropy and quantum Hellinger distance are $\mathsf{QSZK}$-complete in a certain regime, and they are $\mathsf{BQP}$-complete in the low-rank case.

We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a fundamental fact that underpins electronic-structure Hamiltonians in quantum chemistry and condensed matter. We prove that fermionic Gaussian states achieve an approximation ratio of at least 1/3 for such Hamiltonians, independent of sparsity. This shows that classical interactions are sufficient to prevent the vanishing Gaussian approximation ratio observed in SYK-type models. We also give efficient semi-definite programming algorithms for Gaussian approximations to several families of traceless and positive-semidefinite classically interacting Hamiltonians, with the ability to enforce a fixed particle number. The technical core of our results is the concept of a Gaussian blend, a construction for Gaussian states via mixtures of covariance matrices.

The Marcus theory expression for the rate of non-adiabatic electron transfer is widely used across a range of physical conditions. Although Marcus theory defines the reorganization energy classically, here we show that the reorganization parameter governing the activation barrier for normal-region electron transfer is most generally a quantum mechanical object that depends on the electronic coupling, coinciding with the Marcus picture only in the limit of vanishing electronic coupling. This result unifies the physical description of electron-transfer activation barriers across the adiabatic and non-adiabatic regimes and formally predicts that Marcus-like rate expressions remain accurate beyond their traditional non-adiabatic domain of validity. These insights allow us to derive a closed-form expression for the curvature of the current-overpotential relation for electron-transfer-limited reactions at the electrochemical interface, now formally applicable to both inner-sphere and outer-sphere processes.

Quantum thermometry plays a critical role in the development of low-temperature sensors and quantum information platforms. In this work, we propose and theoretically analyze a hybrid circuit quantum electrodynamics architecture in which a superconducting qubit is dispersively coupled to two distinct bosonic modes: one initialized in a weak coherent state and the other coupled to a thermal environment. We show that the qubit serves as a sensitive readout of the probe mode, mapping the interference between thermal and coherent photon-number fluctuations onto measurable dephasing. This mechanism enables enhanced sensitivity to sub-millikelvin thermal energy fluctuations through Ramsey interferometry. We derive analytic expressions for the qubit coherence envelope, compute the quantum Fisher information for temperature estimation, and demonstrate numerically that the presence of a coherent reference amplifies the qubit's sensitivity to small changes in thermal photon occupancy. Our results establish a new paradigm for quantum-enhanced thermometry and provide a scalable platform for future calorimetric sensing in high-energy physics and quantum metrology.

With the continued scaling of quantum processors, holistic benchmarks are essential for extensively evaluating device performance. Layer fidelity is a benchmark well-suited to assessing processor performance at scale. Key advantages of this benchmark include its natural alignment with randomized benchmarking (RB) procedures, crosstalk awareness, fast measurements over large numbers of qubits, high signal-to-noise ratio, and fine-grained information. In this work, we extend the analysis of the original layer fidelity manuscript to optimize parameters of the benchmark and extract deeper insights of its application. We present a robust protocol for identifying optimal qubit chains of arbitrary length N, demonstrating that our method yields error per layered gate (EPLG) values 40% - 70% lower than randomly selected chains for N=100 qubits. We further establish layer fidelity as an effective performance monitoring tool, capturing both edge-localized and device-wide degradation by tracking optimal chains of length 50 and 100, and fixed chains of length 100. Additionally, we refine error analysis by proposing parameter bounds on the number of randomizations and Clifford lengths used in direct RB fits, minimizing fit uncertainties. Finally, we use layer fidelity to analyze the impact of varying gate durations on layered two-qubit (2Q) errors, showing that prolonged gate times leading to idling times significantly increase these quantities. These findings extend the applicability of the layer fidelity benchmark and provide practical guidelines for optimizing quantum processor evaluations.

The issue of separating Schrödinger-type quantum time evolution into a product of holonomic and dynamical parts in the non-adiabatic non-Abelian case is examined. We identify all special cases in which this kind of separation is possible, and we prove that separability is a gauge invariant property of quantum time evolution. The general analysis is implemented in a three-level system with $\Lambda$-type coupling structures. The typical case where the holonomic and dynamical parts do not separate is illustrated by means of two non-commuting $\Lambda$-type Hamiltonians.

Simulating hybrid magnonic quantum systems remains a challenge due to the large disparity between the timescales of the two systems. We present a massively parallel GPU-based simulation framework that enables fully coupled, large-scale modeling of on-chip magnon-photon circuits. Our approach resolves the dynamic interaction between ferromagnetic and electromagnetic fields with high spatiotemporal fidelity. To accelerate design workflows, we develop a physics-informed machine learning surrogate trained on the simulation data, reducing computational cost while maintaining accuracy. This combined approach reveals real-time energy exchange dynamics and reproduces key phenomena such as anti-crossing behavior and the suppression of ferromagnetic resonance under strong electromagnetic fields. By addressing the multiscale and multiphysics challenges in magnon-photon modeling, our framework enables scalable simulation and rapid prototyping of next-generation quantum and spintronic devices.

The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in quantum learning theory. Here we give a remarkably simple construction of this channel, making its known properties -- and several new ones -- immediately transparent. In particular, we show that the channel also purifies non-i.i.d. states: it transforms any permutationally symmetric state into a uniform convex combination of permutationally symmetric purifications, each differing only by a tensor-product unitary acting on the purifying system. We then apply the channel to give a one-line proof of (a stronger version of) the recently established Uhlmann's theorem for quantum divergences.

The fundamental question of when a static or dynamic system should be deemed intrinsically quantum remains a challenge to address in absolute terms. In this regard, a critical requirement lies in the certification (ideally, in real-time) of the emergence and persistence of genuine quantum features, principally entanglement and quantum superposition. Quantum Non-Demolition Measurements (QNDM) serve as the appropriate instrument for this certification, both from a theoretical and experimental standpoint. In this review paper, we explain, with accessible clarity, how the implementation of QNDM can be directly linked to a necessary and sufficient condition for the presence of genuinely quantum features in the system's state monitored over time in finite-dimensional systems, establishing a conceptual parallel with Leggett-Garg inequalities. Using concrete examples that detail the detection of negative terms in the quasi-probability density function resulting from QNDM, we introduce the core concepts for quantumness certification. As specific examples, we discuss an application where the quantum-to-classical transition due to the interaction with an environment can be tracked by QNDM. Moreover, we argue about the robustness of QNDM protocols in the presence of noise sources and their advantages with respect to standard Leggett-Garg inequalities defined by two-time correlators.

We develop a variational regularisation framework that enables analytical solutions of the stationary de Broglie Bohm wave equation. The formulation begins with a Fisher-information augmented action functional for the probability density and phase fields, yielding the Madelung (Hamilton--Jacobi and continuity) equations and, upon complex recombination, a Schrodinger-type equation with a parametric information coupling mu. Beyond the density-based formulation, we introduce a reduced (shell) variational principle for the local momentum field, obtained by imposing stationary flux closure. This reduction isolates the regularisation mechanism at the level of spatial momentum flow and leads to constrained Euler Lagrange equations governing admissible amplitude configurations. The resulting first integral possesses an elliptic (Weierstrass) structure, whose admissible asymptotic branch enforces a universal canonical relation px=mu over 2 near amplitude zeros. This canonical product emerges dynamically from amplitude regularity and conserved flux, rather than being postulated. The framework yields closed-form analytical solutions for standard potentials and reveals a systematic inverse square regularising term in the effective potential. The associated elliptic discriminant defines a geometric length scale which, under physical identification mu=hbar naturally reduces to the reduced Compton wavelength. Thus, canonical Bohmian regularisation is interpreted as a variational admissibility condition on density dynamics, providing structurally stable analytical branches and modified yet consistent energy spectra within stationary dBB mechanics.

Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schrödinger and Klein-Gordon equations. By assuming that the angular momentum of an irrotational vortex in an inviscid, barotropic, isothermal fluid with sound speed c is equal in magnitude to the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity equations of an Euler-Korteweg vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is formally equivalent to Schrödinger's equation. The model is shown to yield analogues to de Broglie wavelength, the Einstein-Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wave field of a vortex in convection requires the Lorentz transformation and yields a wave equation mathematically equivalent to the Klein-Gordon equation, with Schrödinger's equation appearing as the low-Mach-number limit.

Bias-tailored codes such as the XZZX surface code and the domain wall color code achieve high dephasing-biased thresholds because, in the infinite-bias limit, their $Z$ syndromes decouple into one-dimensional repetition-like chains; the $X^3Z^3$ Floquet code shows an analogous strip-wise structure for detector events in spacetime. We capture this common mechanism by defining strip-symmetric biased codes, a class of static stabilizer and dynamical (Floquet) codes for which, under pure dephasing and perfect measurements, each elementary $Z$ fault is confined to a strip and the Z-detector--fault incidence matrix is block diagonal. For such codes the Z-detector hypergraph decomposes into independent strip components and maximum-likelihood $Z$ decoding factorizes across strips, yielding complexity savings for matching-based decoders. We characterize strip symmetry via per-strip stabilizer products, viewed as a $\mathbb{Z}_2$ 1-form symmetry, place XZZX, the domain wall color code, and $X^3Z^3$ in this framework, and introduce synthetic strip-symmetric detector models and domain-wise Clifford constructions that serve as design tools for new bias-tailored Floquet codes.

As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem: universal dynamics can be achieved using only a static qubit array and global control operations. Despite an extensive history of theoretical explorations and proposals, QCAs have not been experimentally explored in the context of highly-scalable globally-controlled systems. Here we realize QCAs on a dual-species Rydberg array of rubidium and cesium atoms, leveraging independent global control of each species to perform multiple quantum protocols. Seeding an automaton with different initial states, we explore many-body dynamics of quasiparticles and grow GHZ states across both species, highlighting the flexibility of our approach. We further develop a second automaton using a novel mediated entangling gate, enabling generation of 96.7(1.7)%-fidelity Bell states, 17-qubit cluster states, and high-connectivity graph states. Our results demonstrate that simple global controls enable access to a rich variety of applications through the QCA framework. The versatility and scalability of QCAs present compelling opportunities for the development of quantum information systems, as well as new perspectives on quantum many-body dynamics.

Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any system at finite characteristic energy $E_c = k_B T$ continuously emits thermal radiation and cools unless energy input compensates these losses. What thermodynamics calls ``thermal equilibrium'' is, at the microscopic level, a dynamically sustained steady state maintained by continuous photon exchange. We derive that the average photon energy required to sustain a Planck distribution is $\langle h\nu \rangle = \pi^4 E_c/[30\,\zeta(3)] \approx 2.701\,E_c$, quantifying the energetic throughput that any real system must sustain to maintain a given temperature. We resolve the apparent contradiction with the purely mechanical Maxwell velocity distribution: billiard-ball kinetics correctly describe the \emph{shape} of the distribution at a given $E_c$, but cannot account for how $E_c$ is established or maintained against radiative losses in any real system of charged particles. We further show that every finite thermal reservoir is itself maintained by photon exchange at a larger scale, organizing physical systems into a natural hierarchy from individual samples through cryostats, laboratories, and planetary surfaces to stellar interiors, with the classical infinite reservoir emerging as the large-capacity limit within that hierarchy rather than a fundamental physical entity. We also comment on the relation between thermodynamic entropy $S = k_B \ln W$ and the dimensionless entropy $\mathcal{S} = \ln W$, emphasizing that $k_B$ primarily fixes units (J/K) rather than introducing new statistical content. These results do not modify thermodynamics but provide its mechanistic interpretation in terms of quantum electrodynamics.

Quantum chaos is commonly assessed through probe-dependent signatures that need not coincide. Recently, a dissipative signature was proposed for chaotic Floquet systems, where infinitesimal bulk dissipation induces a non-zero constant intrinsic relaxation rate quantified by the Liouvillian gap. This raises a question: what minimal departure from Clifford dynamics is required to generate such intrinsic relaxation? To address this, we study a Floquet two-qubit Clifford circuit doped with Haar-random single-qubit gates and subject to local dissipation of strength $\gamma$. We find a structure-dependent crossover. The undoped iSWAP-class circuit exhibits a weak-dissipation singularity, with a gap that grows with $N$ for any $\gamma>0$. Haar doping preserves this undoped-like growth for any subextensive doping pattern. At finite doping density, there exist patterns that yield an $\mathcal{O}(1)$ gap for any fixed $\gamma$ as $N\to\infty$, yet remain singular as $\gamma\to0^+$. Because our bounds depend only on the spatial doping pattern, they remain valid even when the Haar rotations are independently redrawn each Floquet period. Overall, our findings provide a circuit-level perspective on intrinsic relaxation, and thus irreversibility, in open many-body systems.

Answering a question of Claudet, we prove that the uniformly random graph $G\sim \mathbb G(n, 1/2)$ is $\Omega(\sqrt n)$-vertex-minor universal with high probability. That is, for some constant $\alpha\approx 0.911$, any graph on any $\alpha\sqrt n$ specified vertices of $G$ can be obtained as a vertex-minor of $G$. This has direct implications for quantum communications networks: an $n$-vertex $k$-vertex-minor universal graph corresponds to an $n$-qubit $k$-stabilizer universal graph state, which has the property that one can induce any stabilizer state on any $k$ qubits using only local operations and classical communications. We further employ our methods in two other contexts. We obtain a bipartite pivot-minor version of our main result, and we use it to derive a universality statement for minors in random binary matroids. We also introduce the vertex-minor Ramsey number $R_{\mathrm{vm}}(k)$ to be the smallest value $n$ such that every $n$-vertex graph contains an independent set of size $k$ as a vertex-minor. Supported by our main result, we conjecture that $R_{\mathrm{vm}}(k)$ is polynomial in $k$. We prove $\Omega(k^2) \leq R_{\mathrm{vm}}(k) \leq 2^k - 1$.

Tensor network methods leverage the limited entanglement of quantum states to efficiently simulate many-body systems. Alternatively, Clifford circuits provide a framework for handling highly entangled stabilizer states, which have low magic and are thus also classically tractable. Clifford tensor networks combine the benefits of both approaches, exploiting Clifford circuits to reduce the classical complexity of the tensor network description of states, with promising effects on simulation approaches. We study the disentangling power of Clifford transformations acting on tensor networks, with a particular emphasis on entanglement cooling strategies. We identify regimes where exact or heuristic Clifford disentanglers are effective, explain the link between the two approaches, and characterize their breakdown as non-Clifford resources accumulate. Additionally, we prove that, beyond stabilizer settings, no Clifford operation can universally disentangle even a single qubit from an arbitrary non-Clifford rotation. Our results clarify both the capabilities and fundamental limitations of Clifford-based simulation methods.

Accurate in situ calibration of microwave attenuation and amplification-chain noise is essential for superconducting quantum circuits. We demonstrate a compact, self-calibrating cryogenic noise source based on an on-chip chromium attenuator that can be resistively heated with nanowatt-level power and directly integrated into a coaxial microwave line at the mixing-chamber stage. By comparing Johnson-Nyquist noise generated by Joule and microwave heating, measured through the amplification chain, the attenuation of the input line, and hence the gain of the chain, is determined without requiring knowledge of the attenuator temperature. The device exhibits millisecond-scale response times and negligible heating of the cryostat base plate. Using this approach, we determine the gain and added noise of a cryogenic amplification chain over the 4-8 GHz band. Our results provide a simple and accurate method to characterize near-quantum-limited parametric amplifiers used in superconducting-qubit readout.

An industrial-scale adoption of Quantum Key Distribution (QKD) requires the development of practical, stable, resilient and cost-effective hardware that can be manufactured at large scales. In this work we present a high-speed (1.25GHz), field-deployable QKD prototype based on integrated photonics, that is consolidated into standard 19-inch rack compatible units. Through integrated photonics, the system prioritizes autonomous long-term stability in metropolitan settings. The architecture is further simplified by removing the need for chromatic dispersion compensation over metropolitan distances (below 100km). We demonstrate continuous key exchange over more than 4 km of metropolitan optical fiber, where the prototype maintained stable, uninterrupted operation across a measurement spanning more than 12 day-night cycles without manual intervention.

Superposition is the core feature that sets quantum theory apart from classical physics. Here, we investigate whether sets of quantum measurements can be modelled by using only devices that are operationally classical, in the sense that they have no superposition properties. This leads us to propose classical measurement models, which we show to be stronger than commutative measurements but weaker than joint measurability. We determine both the exact depolarisation noise rate and the measurement loss rate at which the all projective measurements in $d$-dimensional quantum theory admit a classical model. For finite sets of quantum measurements we develop methods both for constructing classical models and for falsifying the existence of such model via prepare-and-measure setups. Furthermore, we show that this concept also has operational implications. For that, we consider whether quantum measurements with classical side-information can be implemented in sequence without causing a disturbance and we show that classical models imply an affirmative answer. Our work sheds light on superposition as a resource for quantum measurement devices.

Quantum optimization has gained increasing attention as advances in quantum hardware enable the exploration of problem instances approaching real-world scale. Among existing approaches, variational quantum algorithms and quantum annealing dominate current research; however, both typically rely on one-hot encodings that severely limit scalability. Pauli Correlation Encoding (PCE) was recently introduced as an alternative paradigm that reduces qubit requirements by embedding problem variables into Pauli correlations. Despite its promise, PCE has not yet been studied in the context of constrained optimization. In this work, we extend the PCE framework to constrained combinatorial optimization problems and evaluate its performance across multiple problem sizes. Our results show that the standard PCE formulation struggles to reliably enforce constraints, which motivates the introduction of the Iterative-$\alpha$ PCE. This iterative strategy significantly improves solution quality, achieving consistent constraint satisfaction while yielding better cut sizes across a wide range of instances. These findings highlight both the limitations of current PCE formulations for constrained problems and the effectiveness of iterative strategies for advancing quantum optimization in the NISQ era.

We prove that there exists an absolute constant $\alpha<1$ such that for every finite dimension $d$ and every quantum channel $T$ on $\mathsf{L}(\mathbb{C}^d)$, $\left\|\Theta\circ(\mathrm{id}-T)\right\|_\diamond \le \alpha\,\left\|\Theta\right\|_\diamond\,\left\|\mathrm{id}-T\right\|_\diamond$, where $\Theta$ is the transposition map. In fact we show the explicit choice $\alpha=1/\sqrt{2}$ works.

While most of the existing quantum information engines assisted by Maxwell's demon harness thermal fluctuations, those that rectify only quantum fluctuations have recently been constructed. We propose an alternative type of quantum information engine that harnesses only quantum fluctuations to achieve cumulative energy storage and unidirectional transport of a particle. This unidirectional transport makes a stark contrast with the case without Maxwell's demon where the motion of a particle is confined to a finite region due to Bloch oscillations. We find a trade-off relationship between the maximum power and the maximum velocity. With an improved definition of efficiency that includes all possible energy flows in the engine cycle, we numerically demonstrate the absence of a trade-off relationship among power, efficiency, and power fluctuations that is present for classical heat engines and classical information engines. We also evaluate the influence of experimentally unavoidable measurement imprecision on the performance of the quantum Maxwell's demon.

In this work, we propose a soft covering problem for fully quantum channels using relative entropy as a criterion for operator closeness. We establish covering lemmas by deriving one-shot bounds on the achievable rates in terms of smooth min-entropies. In the asymptotic regime, we show that the infimum of the rate, defined as the logarithm of the minimum rank of the encoded input state, is given by the minimal coherent information between the reference and output systems that yields the target output state. Furthermore, we present a one-shot quantum decoupling theorem that also employs a relative-entropy criterion. Due to the Pinsker inequality, our one-shot results based on the relative-entropy criterion are tighter than the corresponding results based on the trace norm considered in the literature. In addition, we establish achievable error exponents and second-order rates for quantum soft covering under both trace-distance and relative-entropy criteria.

We study global anomalies of nonlocal effective theories proposed to describe symmetry-preserving Luttinger surfaces, i.e., the momentum-space manifolds of Green's function zeros (GFZs) at zero energy, in strongly interacting fermionic systems. In particular, we focus on simplest possible cases associated with a gapless Dirac zero, which is the counterpart of the gapless Dirac quasiparticle in weakly interacting systems. These theories may be derived by integrating out low-energy degrees of freedom that do not couple to the relevant gauge field. We discuss the global anomaly, the bulk-boundary correspondence, and the constraint on phases consistent with the anomaly, such as non-Fermi liquids and emergent gapless quasiparticles on Luttinger surfaces. Failing to avoid a spontaneous symmetry breaking in the thermodynamical limit inevitably leads unstable GFZs. We also provide some perspectives on why the related nonlocal fermionic effective theory studied recently is not a suitable starting point for a symmetrically gapped phase.

Thermal interactions are ubiquitous in the cosmos, driving systems toward equilibrium. In this work, we investigate the evolution of thermal states across the early universe, encompassing the inflationary, radiation-dominated (RD), and matter-dominated (MD) eras, through the lens of Krylov complexity. Utilizing a purification scheme, we map the thermal state to a two-mode pure state, facilitating an open-system analysis of Krylov complexity in contrast to closed-system methodologies. Our numerical results demonstrate that Krylov complexity grows exponentially during inflation, indicating chaotic behavior, before saturating at nearly constant values in the RD and MD eras due to particle production via preheating. Furthermore, we analyze the Krylov entropy, which exhibits an evolutionary trend analogous to that of complexity. Crucially, our analysis reveals a dynamical transition in the universe's dissipative nature: with the universe acting as a strongly dissipative system during inflation and transitioning to a weakly dissipative regime in the subsequent eras. These findings provide a novel quantum information perspective on early universe dynamics.

We consider measurement-induced phase transitions in monitored quantum circuits with a measurement rate that fluctuates in time, remaining spatially uniform at each time. The spatially correlated fluctuations in the measurement rate disrupt the volume-law phase for low measurement rates; at a critical measurement rate, they give rise to an entanglement phase transition with ``ultrafast'' dynamics, i.e., spacetime ($x,t$) scaling $\log x \sim t^{\psi_\tau}$. The ultrafast dynamics at the critical point can be viewed as a spacetime-rotated version of an infinite-randomness critical point; despite the spatial locality of the dynamics, ultrafast information propagation is possible because of measurement-induced quantum teleportation. We identify temporal Griffiths phases on either side of this critical point. We provide a physical interpretation of these phases, and support it with extensive numerical simulations of information propagation and entanglement dynamics in stabilizer circuits. The implications of our results on the general stability of phase transitions and ordered phases to such temporal randomness are discussed.

In Anderson localization physics, eigenstates of disordered quantum systems are commonly classified as extended, localized, or critical, distinguished by their distinct spatial structures in real space. While critical states are known to exhibit multifractal characteristics, a precise and operational criterion for characterizing critical states remains an open challenge. In this work, we address this challenge by revisiting criticality from a dual-spaces perspective that treats position and momentum representations on equal footing. Building on the Liu--Xia criterion, which characterizes critical states by the simultaneous vanishing of Lyapunov exponents ($\gamma=\gamma_m=0$) in both spaces, we show that this dual-spaces characterization captures an essential feature of critical states that is not limited to Lyapunov exponents. In particular, through numerical simulations, we demonstrate that the inverse participation ratio exhibits closely related scaling behavior in position and momentum space for critical states. This position-momentum correspondence clearly distinguishes critical states from extended or localized ones, which instead display a pronounced asymmetry between the two representations. Our results establish a robust and universal framework for precisely characterizing multifractal critical states in disordered quantum systems, and provide practical guidance for their identification in current quantum simulation platforms.

It is generally accepted that phonons in a superfluid Bose gas are Goldstone bosons. This is justified by spontaneous symmetry breaking (SSB), which is usually defined as follows: the Hamiltonian of the system is invariant under the $U(1)$ transformation $\hat{\Psi}(\mathbf{r},t)\rightarrow e^{i\alpha}% \hat{\Psi}(\mathbf{r},t)$, whereas the order parameter $\Psi(\mathbf{r},t)$ is not. However, the strict definition of SSB is different: the Hamiltonian and the boundary conditions are invariant under a symmetry transformation, while the ground state is not. Based on the latter criterion, we study a finite system of spinless, weakly interacting bosons using three approaches: the standard Bogoliubov method, the particle-number-conserving Bogoliubov method, and the approach based on the exact ground-state wave function. Our results show that the answer to the question in the title is ``no''. Thus, phonons in a real-world (finite) superfluid Bose gas are similar to sound in a classical gas: they are not Goldstone bosons, but quantised collective vibrational modes arising from the interaction between atoms. In the case of an infinite Bose gas, however, the picture becomes paradoxical: the ground state can be regarded as either infinitely degenerate or non-degenerate, making the phonon both similar to a Goldstone boson and different from it.

We study (i) Janus deformations and (ii) non-local double trace deformations of a pair of CFTs, as two different ways to construct CFT duals of traversable AdS wormholes. First, we construct a simple model of traversable wormholes by gluing two Poincaré AdS geometries and BTZ black holes and compute holographic two point functions and (pseudo) entanglement entropy. We point out that a Janus gravity solution describes a traversable wormhole when the deformation parameter takes imaginary values. On the other hand, we show that double trace deformations between two decoupled CFTs can reproduce two point functions of traversable AdS wormholes. By considering the case where the double trace deformation is given by a non-local $T\overline{T}$ deformation, we analyze the dual gravity which implies emergence of wormholes. We present toy model of these deformed CFTs by using free scalars and obtain qualitative behaviors expected for them. We argue that the crucial difference between the two constructions is that a global time slice of wormhole is described by a pure state for Janus deformations, while it is a mixed state for the double trace deformations.

Theoretical predictions were made for the steady-state gain of an orthogonally polarized probe field in a degenerate two-level alkali atom system driven by a linearly polarized continuous-wave pump field in [Opt. Mem. Neural Networks 32 (Suppl 3), S443-S446 (2023)]. Employing linear response theory, we computed the probe absorption spectrum under conditions where the pump was detuned from resonance. The results revealed a sub-natural linewidth dispersive feature near the pump resonance, characterized by both gain and absorption. Furthermore, a distinct pure gain peak emerged at a sideband associated with a dressed-state transition. These phenomena are generally absent outside the ultracold regime due to inhomogeneous broadening, primarily from Doppler effects, which obscure the fine spectral structure. In this paper, it is demonstrated that the sideband gain peak is sustained in the warm vapor regime when both the pump Rabi frequency and detuning exceed the Doppler width, $\Omega_P > \Delta_P \gg \Delta_{Dop}$. Our results can enable degenerate mirrorless lasing in thermal alkali atom vapors, offering a significant enhancement in the signal-to-noise ratio for fluoroscopic remote magnetic sensing applications. The theoretical model studied in this paper is also a complete description of atomic vapors with isolated $J = 2 \to J' = 3$ transitions, such as atomic samarium.

Understanding and solving fluid dynamics equations efficiently remains a fundamental challenge in computational physics. Traditional numerical solvers and physics-informed neural networks struggle to capture the full range of frequency components in partial differential equation solutions, limiting their accuracy and efficiency. Here, we propose the Multi-stream Physics Hybrid Network, a novel neural architecture that integrates quantum and classical layers in parallel to improve the accuracy of solving fluid dynamics equations, namely ''Kovasznay flow'' problem. This approach decomposes the solution into separate frequency components, each predicted by independent Parallel Hybrid Networks, simplifying the training process and enhancing performance. We evaluated the proposed model against a comparable classical neural network, the Multi-stream Physics Classical Network, in both data-driven and physics-driven scenarios. Our results show that the Multi-stream Physics Hybrid Network achieves a reduction in root mean square error by 36% for velocity components and 41% for pressure prediction compared to the classical model, while using 24% fewer trainable parameters. These findings highlight the potential of hybrid quantum-classical architectures for advancing computational fluid dynamics.

Dark matter (DM) candidates with very small masses, and correspondingly large number densities, have gained significant interest in recent years. These DM candidates are typically said to behave "classically". More specifically, they are often assumed to reside in an ensemble of coherent states. One notable exception to this scenario is when isocurvature fluctuations of the DM are produced during inflation (or more generally by any Bogoliubov transformation). In such contexts, the ultralight DM instead resides in a squeezed state. In this work, we demonstrate that these two scenarios can be distinguished via the statistics of the DM density fluctuations, such as the matter power spectrum and bispectrum. This provides a probe of the DM state which persists in the limit of large particle number and does not rely on any non-gravitational interactions of the DM. Importantly, the statistics of these two states differ when the modes of the squeezed state are all in-phase, as is the case at the end of inflation. Later cosmological dynamics may affect this configuration. Our work motivates future numerical studies of how cosmological dynamics may impact the initial squeezed state and the statistics of its density fluctuations.

Polygon resonators are promising candidates for nanomechanical applications due to their compact architecture and high force sensitivity. Here, we develop an analytical framework to predict the resonance frequencies and dissipation dilution factors $D_Q$ of polygon perimeter modes by extending the Timoshenko-Gere equation to incorporate the tensile stress. The model identifies two dominant dissipation mechanisms: distributed bending in the polygon sides and torsional deformation in the supporting tethers. We reveal that dissipation dilution in these resonators scales as $1/\lambda^2$, distinct from the conventional $1/\lambda$ dependence associated with boundary bending loss. Furthermore, we demonstrate that the torsional loss can be suppressed by tailoring the torsion angle of the supporting tethers. The analytical predictions are validated by finite element simulations, providing a predictive framework for designing high-$Q$ polygon resonators for cavity optomechanics and precision sensing.

Solving quantum field theories at strong coupling remains a challenging task. The main issue is that the usual perturbative series are asymptotic series which can be useful at weak coupling but break down completely at strong coupling. In this work, we show that if the limits of integration in the path integral are finite, the perturbative series is remarkably an absolutely convergent series which works well at strong coupling. For now, we apply this perturbative approach to $\lambda \phi^4$ theory in 0+0 dimensions (a basic integral) and 0+1 dimensions (quartic anharmonic oscillator). As a further application, we also consider the sextic anharmonic oscillator. For the basic integral, we show that finite integral limits yields a convergent series whose values are in agreement with exact analytical results at any coupling. This worked even when the asymptotic series was not Borel summable. It is well known that the perturbative series expansion in powers of the coupling for the energy of the anharmonic oscillator yields an asymptotic series and hence fails at strong coupling. In quantum mechanics, if one is interested in the energy, it is often easier to use Schrödinger's equation to develop a perturbative series than path integrals. Finite path integral limits are then equivalent to placing infinite walls at positions -L and L in the potential where L is positive, finite and can be arbitrarily large. With walls, the series expansion for the energy is now convergent and approaches the energy of the anharmonic oscillator as the walls are moved further apart. We use the convergent series to calculate the ground state energy at weak, intermediate and strong coupling. At strong coupling, the result from the series agrees with the exact energy to within $0.1\%$, a remarkable result in light of the fact that at strong coupling the usual perturbative series diverges badly immediately.

In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum systems, combining clarity with mathematical precision. Core topics are developed systematically, with detailed derivations and comprehensive proofs that aim to make the material accessible to graduate students and beginning PhD students. Special attention is given to formal consistency and pedagogical structure, so as to guide the reader through both the conceptual and technical aspects of the subject. This work is intended as a reliable starting point for further exploration and research in modern quantum many-body physics.

Neural networks (NNs) have great potential in solving the ground state of various many-body problems. However, several key challenges remain to be overcome before NNs can tackle problems and system sizes inaccessible with more established tools. Here, we present a general and efficient method for learning the NN representation of an arbitrary many-body complex wave function from its N-particle probability density and probability current density and successfully test on (non-Abelian) fractional quantum Hall states and chiral BCS wavefunction. Having reached overlaps as large as 99.9%, we employ our neural wave function for pre-training to effortlessly solve the fractional quantum Hall problem with Coulomb interactions and realistic Landau-level mixing for as many as 25 particles and uncover distinctive features of the edge. Our work demonstrates efficient, scalable and accurate simulation of highly-entangled quantum matter using general-purpose deep NNs enhanced with physics-informed initialization.

Understanding the transport properties of quantum many-body systems is a central challenge in condensed matter and statistical physics. Theoretical studies usually rely on two main approaches: Dynamics of linear-response functions in closed systems and boundary-driven dynamics governed by Markovian master equations for open systems. While the equivalence of their dynamical behavior has been explored in recent studies, a systematic comparison of the transport coefficients obtained from these two classes of approaches remains a largely open question. Here, we address this gap by comparing and contrasting the dc diffusion constant $\mathcal{D}_{\text{dc}}$ according to the two approaches, focusing on the specific example of magnetization transport in the spin-$1/2$ XXZ chain. Using exact numerical simulations for finite system sizes, we find (i) a clear mismatch between the two $\mathcal{D}_{\text{dc}}$ and (ii) a strong dependence of $\mathcal{D}_{\text{dc}}$ on the system-bath coupling strength for the open system, where neither (i) nor (ii) tend to vanish in the thermodynamic limit. These findings suggest limitations of the open-system approach to transport coefficients. To gain insight into the origin of (i) and (ii), we go beyond $\mathcal{D}_{\text{dc}}$ and analyze the full time dependence of the diffusion coefficient $D(t)$ in the open system. In this way, we find that both (i) and (ii) vanish up to a finite time scale. While this time scale gradually increases with system size and tends to be macroscopic in the thermodynamic limit, this increase is still slow compared to the increase of the time to reach the steady state, where (i) and (ii) do not vanish. This observation can be seen as a wrong, yet unavoidable order of limits of long times first and large system sizes afterwards.

We investigate the Sagnac and Mashhoon effects in graphene, taking into account both the pseudospin and intrinsic spin of electrons, within a simplified model of a rotating nanotube or infinitesimally narrow ring. Based on considerations of the relativistic phase of the wave function and employing the effective Larmor theorem, we demonstrate that the Sagnac fringe shift retains a form analogous to that for free electrons, governed by the electron's vacuum mass. In the case of a narrow ring, an additional $\pi$-phase shift arises due to the Berry phase associated with the honeycomb graphene lattice. The Mashhoon fringe shift retains its conventional form, with its dependence on the Fermi velocity.

We show that when a Brownian bridge is physically constrained to satisfy a canonical condition, its time evolution exactly coincides with an m-geodesic on the statistical manifold of Gaussian distributions. This identification provides a direct physical realization of a geometric concept in information geometry. It implies that purely random processes evolve along informationally straight trajectories, analogous to geodesics in general relativity. Our findings suggest that the asymmetry of informational ``distance" (divergence) plays a fundamental physical role, offering a concrete step toward an equivalence principle for information.

Rabi oscillations characterize light-matter hybridization in the waveguide quantum electrodynamics~(WQED) framework, with their associated decay rates reflecting excitation damping, yet their behavior remains unresolved when collective emitters are coupled to a collective waveguide mode. This scenario reveals a conceptually novel collective-light-collective-matter interaction, realizable when a timed-Dicke state~(TDS) of subwavelength emitters couples to a slow, delocalized surface-plasmon mode, forming a hybridized plasmon-polariton~(HPP). The HPP acquires its directionality from the TDS via momentum matching. It also exhibits plasmonic characteristics, with excitation frequencies following the surface-plasmon dispersion relation. We obtain a Rabi oscillation and a long-time decay that describe the HPP and use them to reveal weak- and strong-coupling regimes through the emergence of normal-mode splitting. By performing a finite-time Lyapunov-exponent analysis, we show that the HPP also exhibits instantaneous decay and identify three distinct decay regimes: early-time rapid, transient-time oscillatory, and long-time classical. Finally, by analyzing the emission spectrum, we observe an anticrossing of the peak doublets~(a feature also seen in cavity QED setups) which originates from quantum vacuum effects and the resulting non-Markovian HPP evolution in our WQED.

A result by Gioia and Wang [Phys Rev X 12, 031007 (2022)] showed that translationally symmetric states having nonzero momentum are necessarily long range entangled (LRE). Here, we consider the question: can a notion of momentum for non-translation symmetric states directly encode the nature of their entanglement, as it does for translation symmetric states? We show the answer is affirmative for 1D systems, while higher dimensional extensions and topologically ordered systems require further work. While Gioia and Wang's result applies to states connected via finite depth quantum circuits to a translation symmetric state, it is often impractical to find such a circuit to determine the nature of the entanglement of states that break translation symmetry. Here, instead of translation eigenstates, we focus on the many-body momentum distribution and the expectation value of the translation operator in many-body states of systems having broken translation symmetry. We show that in the continuum limit the magnitude of the expectation value of the translation operator $|<T>|$ necessarily goes to $1$ for delocalized states, a proxy for LRE states in 1D systems. This result can be seen as a momentum-space version of Resta's formula for the localization length. We investigate how accurate our results are in different lattice models with and without well-defined continuum limits. To that end, we introduce two models: a deterministic version of the random dimer model, illustrating the role of the thermodynamic and continuum limits for our result at a lattice level, and a simplified version of the Aubry-Andre model, with commensurate hopping for both momentum and position space. Finally, we use the random dimer model as a test case for the accuracy of $|<T>|$ as a localization (and thus entanglement) probe for 1D periodic lattice models without a well-defined continuum limit.

We introduce a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We then focus on a quantum dimer model on the triangular lattice, with doubly-periodic edge weights. For simplicity we consider a $2\times1$ periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled $\alpha$. We analytically show that the model exhibits a continuous quantum phase transition at $\alpha=3$, changing from a topological $\mathbb{Z}_2$ quantum spin liquid ($\alpha<3$) to a columnar ordered state ($\alpha>3$). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $\xi\propto1/|\alpha-3|$ and as a power-law at criticality. The vison correlator exhibits an exponential decay in the spin liquid phase, but becomes a constant in the ordered phase. We explain the constant vison correlator in terms of loops statistics of the double-dimer model. Using finite-size scaling of the vison correlator, we extract critical exponents consistent with the 2D Ising universality class.

In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can identify the usual Krylov structure. We use this identification to construct families of graphs corresponding to special classes of systems with known complexity features and conversely, to compute Krylov complexity for graphs of physical interest. The two main outcomes are the analytic computation of the Lanczos coefficients for the SYK model for an arbitrary number $q$ of interacting fermions and the complete characterization of Krylov complexity for the hypercube graph in any number of dimensions. The latter serves as the starting point for an in-depth comparison between Krylov and circuit complexities as they purportedly arise in the context of black holes. We find that while under certain conditions Krylov complexity follows the growth and saturation pattern ascribed to such systems, the timescale at which saturation happens can generally be shorter than what is predicted by random unitary circuits, due to the effects of quantum speed-ups commonly occurring when comparing quantum and classical random walks.

Geometry design is a crucial and challenging strategy for improving the performance of type-II superconductors. Topology optimization is one of the most powerful approaches used to determine structural geometries. Therefore, a topology optimization approach is presented to inversely design structural geometries of both low- and high-temperature type-II superconductors with superconductor-dielectric/vacuum interfaces. In the presented approach, the magnetic response of type-II superconductors is modeled using the Ginzburg-Landau theory, where the temporal evolution of the order parameter and vector potential is described by the time-dependent Ginzburg-Landau equations under the Weyl gauge.