Papers

Hybrid systems where a quantum material strongly couples to a nonlocal cavity photon mode have emerged as a new frontier for controlling and probing quantum correlations, yet the structure and scaling of light-matter entanglement produced by the nonlocal coupling remains poorly understood. We address this problem through an exactly solvable framework based on reinterpreting the Power–Zienau–Woolley (PZW) transformation as a light-matter quantum circuit that couples the photonic position quadrature $X \sim a + a^\dagger$ to the many-body dipole $\mathcal{P}$ of a one-dimensional quantum chain. We derive a closed-form expression for the reduced density matrix valid at all coupling strengths, in which off-diagonal elements between matter states of unequal dipole are suppressed by a Gaussian factor encoding the full weak-to-ultrastrong coupling crossover. At weak coupling, the reduced density matrix takes a Lindbladian form with $\mathcal{P}$ as the jump operator, and the entanglement entropy is controlled by the dipole variance. At ultrastrong coupling, the density matrix becomes exactly block-diagonal in dipole sectors, reflecting an emergent dipole symmetry dynamically imposed by the photon field, with entanglement entropy given exactly by the Shannon entropy of the dipole-sector weight distribution. Applying this framework to a half-filled Su–Schrieffer–Heeger chain, we show that, at strong coupling, both the light-matter entanglement and the spatial entanglement of the photon-dressed matter state scale logarithmically with system size, $S_\infty \sim \frac{\alpha}{2}\log L$, robust across the SSH phase diagram. The logarithm originates from the photon resolving a single collective coordinate $\mathcal{P}$ whose fluctuations grow as $L^{\alpha/2}$, a distinct mechanism from the logarithmic entanglement of critical one-dimensional systems.

Single-photon routers in cavity and circuit QED direct photons by the qubit's energy eigenstate – a projective decision that destroys coherence. We propose a different primitive: coherence-gated routing, where the decision depends on the magnitude of the qubit's quantum coherence, estimated in real time from simultaneous weak measurements of $\sigma_x$ and $\sigma_z$. A photon is accepted if the coherence score $S(T) = \sqrt{\langle\sigma_x\rangle_c^2 + \langle\sigma_y\rangle_c^2}$, extracted from the conditional density matrix via the stochastic master equation, exceeds a tunable threshold $S_{\mathrm{th}}$. Certifying coherence at emission enables two applications conventional heralded sources cannot: (i) a quantum random number generator with min-entropy bounded by Bloch-sphere geometry, $H_\infty \geq -\log_2\!\bigl(\frac{1+\sqrt{1-S_{\mathrm{th}}^2}}{2}\bigr)$, and (ii) a phase-tracked photon source whose two-node coherence certification bounds the matter-matter entanglement fidelity after Bell-state measurement. The estimator is itself a security primitive. Benchmarking seven configurations, we find that underestimating detector efficiency ($\eta_{\mathrm{a}} < \eta_{\mathrm{true}}$) both stabilizes the numerics and suppresses overcertification. We trace this via a purity-monotonicity result, identify a geometric loophole amplifying purity undercertification into coherence overcertification by an order of magnitude ($\sim$40$\times$), and prove two complementary tail bounds: an Ornstein-Uhlenbeck comparison giving $4.5\%$ raw overcertification (empirical $3.7\%$ from $10^6$ trajectories) and an exponential supermartingale establishing structural exponential decay.

Preparing correlated quantum states is essential for emerging technologies, but remains challenging in many-body systems. Here we propose a dissipative protocol that engineers nonreciprocal, energy-selective transitions to steer dipolar quantum systems toward desired many-body states. This is realized by introducing two types of controllable dissipative auxiliary atoms that act as nonreciprocal excitation and de-excitation channels, respectively, enabling a directional walk in Hilbert space. This approach enables stabilization of states across the many-body spectrum, not limited to the ground state and requiring no a priori knowledge of the Hamiltonian. Our approach is designed for neutral atoms in dipolar Rydberg arrays, but applies broadly to setups with similar capabilities, providing a flexible and scalable framework for state preparation in programmable platforms.

The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this work, we show internal Hamiltonian dynamics can be "faked“ via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian term but nontraceless jump operators, bounded-norm dissipative generators can approximate Hamiltonian dynamics within $\epsilon$ error in diamond norm using $\mathcal{O}(t^2/\epsilon)$ evolution time. We further prove that for time-independent dynamics this $\mathcal{O}(t^2/\epsilon)$ scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.

AtomTwin$.$jl is an open-source Julia package for developing and simulating quantum protocols, hardware configurations and building digital twins for neutral-atom quantum processors and related atomic quantum devices. AtomTwin operates between mathematical models and physical devices; modeling atoms, optical tweezers, laser fields, atomic motion, interactions, and noise processes natively from physical geometry and parameters, without requiring users to define Hamiltonians manually. The package provides hardware-level instruction sequences, high-performance solvers for coupled quantum and classical dynamics, and a ready-to-use model for ytterbium-171 atoms in an extensible framework designed to accommodate a greater variety of atomic species and hardware components in the future. This paper describes the software architecture, performance benchmarks against existing toolboxes, and a demonstrated end-to-end application: preparation of a logical Bell state in the $[[4,2,2]]$ error-detecting code with four $^{171}$Yb atoms in moveable tweezers.

It is pointed out that the vertex operators of a chiral boson in 1+1 dimensions provide an explicit realization of dichotomic, bounded, Hermitian operators that saturate the Tsirelson bound of the Bell-CHSH inequality in the vacuum state.

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task due to the combined effects of non-commutativity, control complexity, and the exponential growth of the Hilbert space. In this work, we present a physics-informed neural network (PINN) framework to address this problem through the learning of counter-diabatic quantum dynamics. Our approach combines a variational PINN formulation with a Magnus-expansion treatment of time-ordered evolution, enabling the adiabatic gauge potential and the scheduling function to be inferred directly from the underlying physics while enforcing the Euler-Lagrange structure of the protocol. The method is applied to several families of driven spin Hamiltonians, including nearest-neighbor, dipolar, and trapped-ion-inspired interactions, for systems of up to six qubits. The numerical results show that the proposed framework systematically improves over reference solutions based only on the Euler-Lagrange condition, yielding high normalized QFI together with favorable fidelity and extremal-balance metrics while preserving small phsical residuals. The analysis further shows that learning the scheduling function provides a clear performance advantage in most cases, and reveals non-trivial finite-size effects, with $q=3$ emerging as a particularly challenging regime. Although scalability remains limited by the exponential growth of the operator space and by automatic-differentiation costs, the results demonstrate that PINNs constitute a viable and physically grounded route for learning metrologically optimal control strategies in interacting quantum systems.

We simulate a long-range extended Ising model in one dimension using a hybrid quantum algorithm, namely Variational Quantum Eigensolver (VQE). In this quantum simulation, we investigate how quantum resources scale with system size and interaction strength. Three structure-aware ansatze incorporating nearest-neighbor (NN), next-nearest-neighbor (NNN), and next-next-nearest-neighbor (NNNN) entangling blocks are constructed by mimicking the string operators in the Hamiltonian. We show that energy fidelity alone is not a good indicator for finding the ground state of our model. To overcome this problem, we introduce an additional criterion based on pairwise logarithmic negativity as a more reliable way to find the actual ground state by the VQE. We find that the interaction range parameter alpha primarily governs the minimum number of ansatz layers required, rather than proximity to the quantum critical point. In particular, we show that in the non-local regime (alpha <= 1), the NNN and NNNN ansatze reduce the layer scaling rate by factors of 2.5x and 3.8x relative to NN in all phases, including the critical point. The total number of two-qubit gates required for reliable simulation grows quadratically with system size for all three ansatze. This is consistent with the theoretical prediction, as the number of non-local terms in the Hamiltonian also grows quadratically with the system size. In the local regime, however, the number of required two-qubit gates grows linearly with system size. In contrast, in the quasi-local regime, the required number of two-qubit gates for the quantum simulation is more subtle and depends on the phase of the Hamiltonian.

Rydberg atom arrays are powerful platforms for studying quantum many-body systems. We consider the Rydberg-Ising Hamiltonian in a ring geometry and numerically study ensembles of states generated by random global pulse sequences subject to hardware constraints and fixed evolution times. We compare the statistical properties of such states with those of Haar-random states within the relevant lattice symmetry sector. In the strong-interaction regime (short interatomic distance), the dynamics is governed by an effective blockade that restricts Hilbert-space exploration and limits entanglement growth. In this regime, level-spacing statistics of the entanglement spectrum are close to random-matrix predictions, while the distribution of measurement probabilities deviates from Porter-Thomas behavior. For weaker interactions (larger interatomic distance), the system approaches Haar-like statistics at long times, as reflected in entanglement entropy, entanglement-spectrum statistics, and the distribution of measurement probabilities. At intermediate interactions, this behavior is observed on experimentally relevant timescales. Motivated by this observation, we investigate whether individual target states can be efficiently prepared using quantum optimal control in this regime. Employing target states drawn from an ensemble with a broad entropy distribution, we observe high fidelities (infidelities between 10^-5 and 3 x 10^-2 for nine spins). Within this ensemble, the fidelity decreases with the entanglement entropy of the target state, indicating that highly entangled targets are more difficult to prepare under the considered finite-time control constraints.

We analyze vibrational dynamics in a toy model for polaritonic chemistry under collective electronic strong coupling. In a Holstein-Tavis-Cummings model, incoherently excited by a photon, we show that disorder leads to non-Gaussian states of vibrational modes on short time scales at the single-molecule level. Using exact matrix product state simulations, we demonstrate that this effect can remain robust for larger molecule numbers, implying that nuclear wave packets cannot be effectively described by thermal states. Furthermore, we compare simulations of the exact quantum dynamics with semiclassical approximations. We find that the Ehrenfest approximation can only well reproduce ensemble-averaged observables for very large system sizes. Also simulations in the truncated Wigner approximation fail to capture the non-Gaussian effects. Our work highlights the importance of disorder and genuine quantum effects in cavity-modified nuclear dynamics in polaritonic chemistry.

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a nonlinear time-series analysis framework long established for classical dynamical systems - to investigate correlated quantum many-body dynamics. Recurrence plots provide a qualitative fingerprint of simulated or experimental data, while recurrence quantification analysis extracts corresponding numerical descriptors. Applying this framework to quenches from the paramagnetic ground state in the one-dimensional transverse-field Ising model, we observe a clear progression in the recurrence plots of two-site correlations: nearly periodic patterns in the deeply ferromagnetic phase give way to multiscale temporal structures at criticality. Recurrence quantifiers further recover the critical field strength without prior knowledge of the model, establishing recurrence analysis as a versatile tool for characterizing quantum many-body dynamics, including unsupervised detection of quantum phase transitions.

Shortcuts to adiabaticity (STA) were first developed in quantum dynamics to realize rapid transformations with suppressed residual excitations. Here we show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems. Using a coupled $r$-$\theta$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories, obtaining the corresponding force and torque profiles and quantifying how geometric coupling amplifies errors and residual energy. We further compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking, which highlights a trade-off among smoothness, speed, and robustness. Finally, we introduce a single-shot correction based on one mid-course measurement to reduce the effect of early deviations while keeping the inputs nearly smooth. These results provide a practical bridge between quantum STA concepts and their classical counterparts.

Fiber-integrated micro-optical elements promise a scalable approach to photon collection and beam shaping for quantum information processing. Here, we demonstrate single-step micro-machining of micro-spherical, micro-spiral, and micro-axicon structures directly onto the core of single-mode optical fibers using focused-ion beam (FIB) machining with nanometer-scale precision. Atomic force microscopy reveals that micro-concave and micro-convex spherical surfaces achieve shape accuracies of $\lambda/50$ and $\lambda/33$ (at $\lambda = 633$~nm), respectively. Via optical characterization using a He-Ne laser (633~nm), we verify for the micro-spiral and -axicon structures the expected far-field donut beam patterns. Via Mach-Zehnder interferometry, we verify the azimuthal and radial phase structure of the light emitted from the spiral and axicon fibers, respectively. Surface metrology further shows that FIB processing introduces only a small increase in nanoscale roughness while preserving sub-nanometer RMS surface quality. The monolithically integrated fiber micro-optic elements demonstrated here enable broad use in quantum technology, for example, fiber micro-cavities for cavity quantum electrodynamics, beam shaping for neutral atom trapping, and the generation of structured light for free-space quantum network links.

Integrated photonics is widely regarded as a key enabler for scalable quantum key distribution (QKD), offering compactness, stability, and compatibility with semiconductor fabrication. Despite rapid advances in chip-based QKD, the implementation security of integrated photonic components remains insufficiently understood. Here we present the first systematic study of an implementation-level security vulnerability associated with p-n junction-based variable optical attenuators (VOAs), a ubiquitous component in integrated QKD transmitters. We theoretically and experimentally demonstrate that electrically biased p-n junction VOAs emit spontaneous luminescence. Using a single-photon-sensitive spectral measurement technique, we identify the emission wavelength to be centered around 1107 nm, well separated from the C-band quantum signals. This spectral separation gives rise to a previously unrecognized wavelength-resolved side channel, enabling potential wavelength-splitting attacks without directly disturbing the encoded quantum states. By incorporating the measured luminescence into a quantitative security analysis, we show that even extremely weak emission can lead to non-negligible information leakage. Our findings reveal a fundamental and previously overlooked security risk in photonic integrated QKD systems and highlight the necessity of security-aware device design for future integrated quantum communication technologies.

Quantum computing is a new approach to computation that utilizes superposition, entanglement, interference, and tunneling to solve problems too complex for classical computers. This paper discusses the basic concepts and development of quantum computing, exploring its potential applications in the built environment and urban microclimate research. In buildings, quantum computing may help optimize energy management, control HVAC systems, and plan electric vehicle charging networks more efficiently. For urban microclimates, it could accelerate renewable energy planning and support multi-objective design, making it easier to balance urban building performance with climate conditions. Since current quantum hardware is still in the Noisy Intermediate-Scale Quantum (NISQ) stage, we propose the "BITE" principle to guide researchers in choosing suitable problems for quantum acceleration: B (Big search), I (Input-light), T (Tiny computation), and E (Evaluation polish). Although quantum computing still faces challenges such as noise and hardware limits, it offers great potential for developing more climate-resilient, sustainable, and energy-efficient cities of the future.

We propose a broadband Purcell-protection scheme based on a single shared filter integrated directly into the feedline, enabling simultaneous protection of multiple qubits in a compact architecture with minimal hardware overhead. The filter consists of two open-ended stubs connected by an in-line transmission line, forming a $\Pi$ geometry, and operates via engineered passive microwave interference that suppresses the real part of the environmental admittance over a wide frequency window. Circuit simulations and finite-element modeling show that transmission is suppressed by several orders of magnitude within the target band (the qubits' frequencies) while preserving the readout mode of the multiplexed architecture. For realistic device parameters, the proposed design yields Purcell-limited relaxation times exceeding $1$ ms over a frequency span of approximately $1.5$ GHz. Our results establish the $\Pi$ filter as a compact and scalable solution for broadband impedance engineering in superconducting quantum circuits, compatible with standard dispersive readout protocols.

We experimentally demonstrate the detection of momentum transfers from individual collisions of Kr, Xe, and SF$_6$ with an optically levitated nanoparticle, finding good agreement with theoretical expectations. The observed event rates accurately measure the gas partial pressures, while the spectral shape provides a sensitive probe of the surface properties of the nanoparticle, including its temperature. The reconstruction of impulse signals as small as 200 keV/$c$ further establishes that levitated optomechanical sensors can reach the sensitivity required for precision measurements of fundamental particle interactions, and demonstrates a proof-of-principle for a primary pressure sensor based on the detection of individual gas particle collisions.

Variational Monte Carlo (VMC) combined with expressive neural network wavefunctions has become a powerful route to high-accuracy ground-state calculations, yet its practical success hinges on efficient and stable wavefunction optimization. While stochastic reconfiguration (SR) provides a geometry-aware preconditioner motivated by imaginary-time evolution, its Kaczmarz-inspired variant, subsampled projected-increment natural gradient descent (SPRING), achieves state-of-the-art empirical performance. However, the effectiveness of SPRING is highly sensitive to the choice of a momentum-like parameter $\mu$. The original sensitivity of $\mu$ and the instability observed at $\mu=1$, have remained unclear. In this work, we clarify the distinct mechanisms governing the regimes $\mu<1$ and $\mu=1$. We establish convergence guarantees for $0\le\mu<1$ under mild assumptions, and construct counterexamples showing that $\mu=1$ can induce divergence via uncontrolled growth along kernel-related directions when the step-size is not summable. Motivated by these theoretical insights and numerical observations, we further propose Principal Range Informed MomEntum SR (PRIME-SR), a tuning-free momentum-adaptive SR method based on effective spectral dimension and subspace overlap. PRIME-SR achieves performance comparable to optimally tuned SPRING while significantly improving robustness in VMC optimization.

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

In this article we present a comprehensive theoretical investigation of phonon lasing with mixed-species trapped ions, as demonstrated in [T. Behrle, Phys. Rev. Lett. 131 (2023)], employing both a semi-classical mean-field description and a full quantum theory. We derive an analytic expression for the second-order coherence function, confirming the experimental observation of the system's lasing behaviour above threshold. Building on the successful implementation of the two-ion lasing scheme, we propose a novel approach for achieving phonon lasing with a single trapped ion, offering significant experimental advantages and making the implementation of multiple phonon lasers within a single setup feasible. Furthermore, we explore lasing in a squeezed basis and in different regimes of the Lamb-Dicke approximation, highlighting the potential to produce non-classical states with promising applications in precision sensing. Our analysis of a sensing protocol based on squeezed states, using experimentally feasible parameters, shows a sensitivity enhancement of up to two orders of magnitude.

The limited number of qubits is a major bottleneck in Quantum Approximate Optimization Algorithm (QAOA) for large-scale combinatorial optimization in the Noisy Intermediate-Scale Quantum (NISQ) era. To make progress, existing techniques rely on qubit reduction at the cost of information loss, hence leading to degraded computational performance. As a remedy, we propose the Equivalence-preserving Qubit Efficient QAOA (EQE-QAOA), which significantly reduces the required number of qubits without degrading the performance of QAOA. By exploiting intrinsic symmetries and conserved quantities, we first demonstrate that the QAOA dynamics are strictly confined to an invariant subspace of the Hilbert space. We subsequently prove that the evolution within this subspace is exactly equivalent to that of the full-scale system, achieving the same optimal solution as the original QAOA. Moreover, to reduce the number of qubits, we propose an isometric mapping that re-encodes the subspace into a space relying on fewer qubits. Furthermore, we derive the applicability conditions of EQE-QAOA and show that it is broadly applicable to large-scale combinatorial optimization problems, excluding only unconstrained problems with completely independent variables. Numerical simulations based on Max-Cut instances validate that EQE-QAOA significantly reduces qubit requirements and computational resources, while preserving exact optimization performance.

Upper and lower quantum functionals, introduced by Christandl, Vrana and Zuiddam (STOC 2018, J. Amer. Math. Soc. 2023), are families of monotone functions of tensors indexed by a weighting on the set of subsets of the tensor legs. Inspired by quantum information theory, they were crafted as obstructions to asymptotic tensor transformations, relevant in algebraic complexity theory. For tensors of order three, and more generally for weightings on singletons for higher-order tensors, the upper and lower quantum functionals coincide and are spectral points in Strassen's asymptotic spectrum. Moreover, the singleton quantum functionals characterize the asymptotic slice rank, whereas general weightings provide upper bounds on asymptotic partition rank. It has been an open question whether the upper and lower quantum functionals also coincide for other cases, or more generally, how to construct further spectral points, especially for higher-order tensors. In this work, we show that upper and lower quantum functionals generally do not coincide, but that they anchor new spectral points. With this we mean that there exist new spectral points, which equal the quantum functionals on the set of tensors on which upper and lower coincide. The set is shown to include embedded three-tensors and W-like states and concerns all laminar weightings, significantly extending the singleton case. Moreover, it is shown that these spectral points provide obstructions to asymptotic restriction beyond the previously known spectral points.

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols like Quantum Singular Value Transformation (QSVT) and Quantum Signal Processing (QSP), the generation of compilable implementations of block-encodings poses a formidable challenge. This work presents the BlockEncoding interface within the Eclipse Qrisp framework, establishing block-encodings as a high-level programming abstraction accessible to a broad scientific audience. Serving as both a technical framework introduction and a hands-on tutorial, this paper explicitly details key underlying concepts abstracted away by the interface, such as block-encoding construction and qubitization, and their practical integration into methods like the Childs-Kothari-Somma (CKS) algorithm. We outline the interface's software architecture, encompassing constructors, core utilities, arithmetic composition, and algorithmic applications such as matrix inversion, polynomial filtering, and Hamiltonian simulation. Through code examples, we demonstrate how this interface simplifies both the practical realization of advanced quantum algorithms and their associated resource estimation.

Quantum many-body scars are rare exceptions to thermalization: they sustain non-thermal stationary states without the protection of any local conservation law, and are generally expected to be fragile. Here we construct an analytically tractable random unitary circuit hosting a single scar, and derive from first principles the thermalization mechanism governing perturbations thereof - described by a picture of fluctuating interfaces. Surprisingly, despite being thermodynamically irrelevant for local observables, the scar leaves a sharp fingerprint in the entanglement dynamics, driving a transition as a function of perturbation strength that is not probed by any local measurement.

Bell inequalities exclude a broad class of local hidden-variable explanations of quantum correlations. A recurring objection is that the usual Bell form is static, whereas real measuring devices may contain local memory, stochastic dynamics, and measurement-induced disturbances of their hidden variables. We formulate this objection as a general transition-kernel model for dynamical hidden variables. The only locality assumption is imposed at the ontic level: conditional on the pre-measurement ontic state, the transition kernel and response function in each wing depend on the local setting but not on the distant setting or on distant post-measurement variables. Under measurement independence, all such dynamics can be absorbed into effective local response functions. The resulting probabilities have exactly the static Bell-local form and therefore obey the CHSH inequality. The result identifies the available escape routes for reproducing quantum correlations: violating ontic dynamical locality, violating measurement independence, or abandoning a classical hidden-variable ontology. As a consequence, local classical dynamical complexity cannot by itself spoof Bell-nonlocal statistics in device-independent protocols.

Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum search technique. However, Grover-based approaches face a key limitation: they typically require prior knowledge of the number of satisfying assignments of the target Boolean formula. This information is unavailable in most practical settings. Quantum counting can be used to estimate this quantity, but it incurs a computational overhead that is several orders of magnitude higher than Grover search. In this paper, we propose a novel quantum SAT solver based on entanglement and equivalence checking. Our method does not assume prior knowledge of the number of solutions and is computationally more efficient than quantum counting. Although the worst case time complexity is inevitably exponential, we prove that the expected time complexity of our approach is only constant time O(1) over random Boolean functions. Experimental results also support our theoretical claim.

Dark and subradiant states have emerged as a promising resource for stabilizing open quantum batteries against dissipation, but existing studies are largely limited to qubit ensembles and symmetry-based constructions. Here we introduce a systematic, thermodynamically consistent framework for identifying long-lived energy storage states in interacting multilevel quantum batteries, combining the Davies master equation with a Morris-Shore (MS)-type decomposition of dissipative coupling blocks. Focusing on a minimal model of two interacting qutrits coupled to a common bath, we analytically construct dark, bright, and funnel states-excited states that decay exclusively into protected manifolds. We also derive quantitative robustness conditions governed by the ratio of interaction strength to anharmonicity. We show that multilevel ladder structure and exchange interactions enable energetic storage states beyond the qubit case. Numerical simulations confirm that these states exhibit long-lived energy storage under typical Markovian dissipation. Finally, we show that high-energy funnel states provide a natural design target for multilevel quantum batteries, as their decay pathways are highly structured and directed toward protected manifolds. The knowledge and understanding of these pathways offers a principled basis for developing future protection and control strategies in superconducting multilevel platforms.

Superconducting qubits, realized by incorporating Josephson junctions into superconducting circuits, behave as artificial atoms with anharmonic energy spectra and can be precisely controlled and measured using microwave cavities within the framework of circuit quantum electrodynamics (cQED). Since its emergence in the early 2000s, cQED has established superconducting qubits as leading candidates for scalable quantum devices and has enabled the exploration of hybrid quantum systems that integrate disparate physical platformsThis review surveys superconducting hybrid quantum electromechanical systems in which mechanical resonators are coupled to superconducting qubits, with a focus on two widely used qubit platforms: the transmon and the fluxonium. We provide an overview of the underlying coupling mechanisms arising from interactions through the phase and charge degrees of freedom of the qubit, and discuss how these mechanisms give rise to both longitudinal and transverse qubit-mechanical interactions. We further review extensions of electromechanical platforms to electro-optomechanical architectures, in which optical cavities are integrated to enable coherent interfacing between superconducting circuits and optical photons. This review aims to present a unified framework and perspective on qubit-mechanical and qubit-mechanical-optical hybrid systems in superconducting quantum technologies and applications related to sensors.

Large language models (LLMs) show strong capabilities in general reasoning but typically lack reliability in scientific domains like quantum mechanics, which demand strict adherence to physical constraints. This limitation arises from the scarcity of verifiable training resources and the inadequacy of coarse feedback signals in standard alignment paradigms. To address the data challenge, we introduce QuantumQA, a large-scale dataset constructed via a task-adaptive strategy and a hybrid verification protocol that combines deterministic solvers with semantic auditing to guarantee scientific rigor. Building on this foundation, we propose the verification-aware reward model (VRM) tailored for Reinforcement Learning with Verifiable Rewards (RLVR), which employs an adaptive reward fusion (ARF) mechanism to dynamically integrate deterministic signals from a scientific execution suite (SES) with multidimensional semantic evaluations for precise supervision. Experimental results demonstrate that our method consistently outperforms baselines and general-purpose preference models. Notably, our optimized 8B model achieves performance competitive with proprietary models, validating that incorporating verifiable, rule-based feedback into the reinforcement learning loop offers a parameter-efficient alternative to pure scaling.

Atmospheric turbulence makes free-space quantum polarization links intrinsically time varying, whereas receiver-side reduced interfaces are often treated as static. This paper develops a slow-time receiver interface by extending an aperture-conditioned static model to the temporal domain. The receiver-plane phase field, beam-centroid displacement, and scintillation are modeled as hidden slow-time stochastic processes, from which the reduced interface is generated at each instant. A leading-order closure maps coarse-grained phase roughness to an effective polarization-mixing variance while preserving the inherited local polarization-channel family. Aperture conditioning then yields time-dependent effective depolarization, coherence, and detection descriptors. In a representative weak-turbulence case, the polarization branch remains close to the near-ideal regime, with effective depolarization on the order of \(10^{-3}\) and effective coherence close to unity, whereas the detection branch exhibits visibly stronger fluctuations and a longer correlation time. These results show that a single static receiver-side parameterization is insufficient to characterize the temporal behavior of turbulent free-space quantum links. The resulting interface is intended for receiver-side characterization of time-varying quantum links, with MDI-QKD as one representative downstream application.