Papers

Context-sensitive behavior can be modeled by enriching an internal state, by allowing a response rule to access context directly, or by preserving a shared state while introducing an auxiliary criterion or control variable. This paper isolates an information-theoretic constraint on the third architecture. Let $C$ denote context, $S$ a candidate internal or latent state, $O$ an observable response, and $M$ an auxiliary variable such that $O\perp C\mid(S,M)$. Then \[ I(C;O\mid S)\le I(C;M\mid S)\le H(M\mid S). \] Once a shared state has been specified, residual context dependence in behavior therefore lower-bounds both the context information and the conditional entropy that an auxiliary context-mediating mechanism must carry. The bound is representation-relative rather than a measure of state-space size or a universal contextuality measure. A worked recognition-memory example shows how the quantity can be computed for payoff-induced criterion shifts and compared across alternative representational allocations. Ontological contextuality and quantum probability are treated as a separate specialization rather than as prerequisites for the cognitive interpretation. More broadly, the framework provides a basis for analyzing context-memory-control trade-offs in cognitive models and artificial agents that must maintain coherent behavior across changing contexts under bounded internal representations.

Quantum program generation demands a level of precision that may not be compatible with the statistical reasoning carried out in the inference of large language models (LLMs). Hallucinations are mathematically inevitable and not addressable by scaling, which leads to infeasible solutions. We argue that architectures prioritizing verification are necessary for quantum copilots and AI automation in domains governed by constraints. Our position rests on three key points: verified training data enables models to internalize precise constraints as learned structures rather than statistical approximations; verification must constrain generation rather than filter outputs, as valid designs occupy exponentially shrinking subspaces; and domains where physical laws impose correctness criteria require verification embedded as architectural primitives. Early experiments showed LLMs without data verification could only achieve a maximum accuracy of 79% in circuit optimization. Our positions are formulated as quantum computing and AI4Research community imperatives, calling for elevating verification from afterthought to architectural foundation in AI4Research.

Long-lived beatings in two-dimensional electronic spectroscopy (2DES) remain difficult to interpret within standard excitonic open-system models, which typically assume factorized initialization and predict rapid coherence decay. We show that persistent beatings can arise from a correlation-driven mechanism that requires both slow bath memory and ultrafast pulse sequences that propagate system-bath correlations across optical interactions. In this regime, the pulse sequence unitarily dresses the bath-memory contribution and activates nonsecular population-coherence transfer during field-free evolution, sustaining coherence signatures far beyond factorized or weak-memory descriptions. Rather than addressing what is oscillating (excitonic versus vibronic) or quantum-versus-classical semantics, this work reframes long-lived beatings as a protocol-level dynamical effect: correlation-mediated retrieval under ultrafast control.

The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and software. Tensor networks have become forefront mathematical tools for these tasks. Here we introduce a method to approximately simulate quantum circuits using sparsely-populated tensors. We describe a sparse tensor data structure that can represent quantum states with no underlying symmetry, and outline algorithms to efficiently contract and truncate these tensors. We show that the data structure and contraction algorithm are efficient, leading to expected runtime scalings versus qubit number and circuit depth. Our results motivate future research in optimization of sparse tensor networks for quantum simulation.

Mid-circuit measurements (MCMs) are critical components of the quantum error correction protocols expected to enable utility-scale quantum computing. MCMs can be modeled by quantum instruments (a type of quantum operation or process), which can be characterized self-consistently using gate set tomography. However, experimentally estimated quantum instruments are often hard to interpret or relate to device physics. We address this challenge by adapting the error generator formalism – previously used to interpret noisy quantum gates by decomposing their error processes into physically meaningful sums of "elementary errors" – to MCMs. We deploy our new analysis on a transmon qubit device to tease out and quantify error mechanisms including amplitude damping, readout error, and imperfect collapse. We examine in detail how the magnitudes of these errors vary with the readout pulse amplitude, recover the key features of dispersive readout predicted by theory, and show that these features can be modeled parsimoniously using a reduced model with just a few parameters.

We present a unified category-theoretic framework for quantum Hall hierarchy constructions and anyon superconductivity based on modular tensor categories over $\mathrm{Rep}(\mathrm{U}(1))$ and $\mathrm{sRep}(\mathrm{U}(1)^f)$. Our approach explicitly incorporates conserved $\mathrm{U}(1)$ charge and formulates doping via a generalized stack-and-condense procedure, in which an auxiliary topological order is stacked onto the parent phase, and the quasiparticles created by doping subsequently condense. Depending on whether this condensation preserves or breaks the $\mathrm{U}(1)$ symmetry, the system undergoes a transition to a quantum Hall hierarchy state or to an anyon superconductor. For anyon superconductors, the condensate charge is determined unambiguously by the charged local bosons contained in the condensable algebra. Our framework reproduces all known anyon superconductors obtained from field-theoretic analyses and further predicts novel phases, including a charge-$2e$ anyon superconductor derived from the Laughlin state and charge-$ke$ anyon superconductors arising from bosonic $\mathbb{Z}_k$ Read-Rezayi states. By placing hierarchy transitions and anyon superconductivity within a single mathematical formalism, our work provides a unified understanding of competing and proximate phases near experimentally realizable fractional quantum Hall states.

We present a variational quantum eigensolver (VQE) approach for solving the Anderson Impurity Model (AIM) arising in Dynamical Mean-Field Theory (DMFT). Recognizing that the minimal two-site approximation often fails to resolve essential spectral features, we investigate the efficacy of VQE for larger bath discretizations while adhering to near-term hardware constraints. We employ a symmetry-adapted ansatz enforcing conservation of particle number $(N)$, spin projection $(S_z=0)$, and total spin $(S^2=0)$ symmetry, benchmarking the performance against exact diagonalization across different interaction strengths using bath parameters extracted from the DMFT self-consistency loop. For a four-site model, the relative error in the ground state energy remains well below $0.01%$ with a compact parameter set $(N_p \le 30)$. Crucially, we demonstrate that the single-particle Green's function-the central quantity for DMFT-can be accurately extracted from VQE-prepared ground states via real-time evolution in the intermediate to strong interaction regimes. However, in the weak interaction regime, the Green's function exhibits noticeable deviations from the exact benchmark, particularly in resolving low-energy spectral features, despite the ground state energy showing excellent agreement. These findings demonstrate that VQE combined with real-time evolution can effectively extend quantum-classical hybrid DMFT beyond the two-site approximation, particularly for describing insulating phases. While this approach offers a viable pathway for simulating strongly correlated materials on near-term devices, the observation that accurate ground state energy does not guarantee accurate dynamical properties highlights a key challenge for applying such approaches to correlated metals.

The relaxation of a quantum field from a metastable state (false vacuum) to a stable one (true vacuum), also known as false vacuum decay, is a fundamental problem in quantum field theory and cosmology. We study this phenomenon using a two-dimensional interacting and coherently coupled Bose-Bose mixture, a platform that has already been employed experimentally to investigate false vacuum decay in one dimension. In such a mixture, it is possible to define an effective magnetization that acts as a quantum field variable. Using the Stochastic Gross-Pitaevskii equation (SGPE), we prepare thermal equilibrium states in the false vacuum and extract decay rates from the magnetization dynamics. The decay rates show an exponential dependence on temperature, in line with the thermal theory of instantons. Since the SGPE is based on complex scalar fields, it also allows us to explore the behavior of the phase, which turns out to become dynamic during decay. Our results confirm the SGPE as an effective tool for studying coupled magnetization and phase dynamics and the associated instanton physics in ultracold quantum gases.

By introducing spatially varying profiles of pairing interaction or spin polarization to quasi one-dimensional two-component atomic Fermi gases confined in box potentials, we analyze the ground state structures and properties when multiple phases coexist in real space by implementing the Bogoliubov–de~Gennes equation suitable for describing inhomogeneous fermion systems. While the BCS, Fulde–Ferrell–Larkin–Ovchinnikov (FFLO), and normal phases occupy different regions on the phase diagram when the parameters are uniform, a spatial change of pairing strength or spin polarization can drive the system from the FFLO phase to a normal gas or from a BCS superfluid to the FFLO phase in real space. The FFLO phase exhibits its signature modulating order parameter at the FFLO momentum due to population imbalance, and the pair correlation penetrates the polarized normal phase and exhibits proximity effects. Meanwhile, the BCS phase tends to repel population imbalance and maintain a plateau of pairing. Interestingly, a buffer FFLO phase emerges when the spatial change attempts to join the BCS and normal phase in the presence of spin polarization. By analyzing the pairing correlations, interfacial properties, and momentum-space spectra of the inhomogeneous structures, relevant length- and momentum- scales and their interplay are characterized. We also briefly discuss implications of inhomogeneous multi-phase atomic Fermi gases with population imbalance.

Passive qubit reset is a key primitive for quantum information processing, whereby qubits are initialized by allowing them to relax to their ground state through natural dissipation, without the need for active control or feedback. However, passive reset occurs on timescales that are much longer than those of gate operations and measurements, making it a significant bottleneck for algorithmic execution. Here, we show that this limitation can be overcome by exploiting the Mpemba effect, originally indicating the faster cooling of hot systems compared to cooler ones. Focusing on the regime where coherence times exceed energy relaxation times ($T_2 > T_1$), we propose a simple protocol based on a single entangling two-qubit gate that converts local single-qubit coherences into fast-decaying global two-qubit coherences. This removes their overlap with the slowest decaying Liouvillian mode and enables a substantially faster relaxation to the ground state. For realistic parameters, we find that our protocol can reduce reset times by up to $50\%$ compared to standard passive reset. We analyze the robustness of the protocol under non-Markovian noise, imperfect coherent control and finite temperature, finding that the accelerated reset persists across a broad range of realistic error sources. Finally, we present an experimental implementation of our protocol on an IQM superconducting quantum processor. Our results demonstrate how Mpemba-like accelerated relaxation can be harnessed as a practical tool for fast and accurate qubit initialization.

Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semi-classical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for non-equilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the non-stationary noise induced by the cavity field.

In the three-flavor neutrino oscillation framework, we investigate the transition probabilities of an initial muon neutrino flavor state in the presence of nonstandard interactions (NSIs) characterized by complex off-diagonal ($|\epsilon_{\alpha\beta}|e^{i\phi_{\alpha\beta}}$) and diagonal parameters ($|\epsilon_{\alpha\alpha}-\epsilon_{\beta\beta}|$), including a $CP$-violating phase and a constant matter potential, under both normal (NO) and inverted mass ordering (IO) scenarios. Within these scenarios and through the lens of mode entanglement, bipartite entanglement measures such as entanglement entropy and capacity of entanglement are quantified in terms of the transition probabilities, which can be measured in neutrino oscillation experiments. Using these two bipartite entanglement measures, we further explore the quantum speed limit (QSL) time, which describes how rapidly bipartite entanglement evolves during neutrino oscillations. We illustrate our results using the baseline lengths and energies corresponding to ongoing long-baseline accelerator neutrino experiments, such as T2K, NO$\nu$A, and the upcoming DUNE experiment. In the presence of a $CP$-violating phase and a constant matter potential, both with and without NSI effects, we compare the QSL time behavior for bipartite entanglement in neutrino oscillations for NO and IO. The most pronounced discrepancies in the QSL time for bipartite entanglement arise from the off-diagonal NSI parameter $\epsilon_{\mu\tau}$ across both the NO and IO scenarios. We emphasize that among all the experiments considered, NO$\nu$A and DUNE exhibit a rapid suppression of bipartite entanglement in neutrino oscillations in the standard oscillation scenario with NO at the end of their baseline lengths for the corresponding best-fit value of $CP$-violating phase. Our results hint at a possible imprint of new physics in neutrino oscillations.

We theoretically explore protocols for measuring the spin polarization of an ensemble of solid-state spins, with precision at or below the standard quantum limit. Such measurements in the solid-state are challenging, as standard approaches based on optical fluorescence are often limited by poor readout fidelity. Indirect microwave resonator-mediated measurements provide an attractive alternative, though a full analysis of relevant sources of measurement noise is lacking. In this work we study dispersive readout of an inhomogeneously broadened spin ensemble via coupling to a driven resonator measured via homodyne detection. We derive generic analytic conditions for when the homodyne measurement can be limited by the fundamental spin-projection noise, as opposed to microwave-drive shot noise or resonator phase noise. By studying fluctuations of the measurement record in detail, we also propose an experimental protocol for directly detecting spin squeezing, i.e. a reduction of the spin ensemble's intrinsic projection noise from entanglement. Our protocol provides a method for benchmarking entangled states for quantum-enhanced metrology.

Distributed quantum sensing leverages quantum correlations among multiple sensors to enhance the precision of parameter estimation beyond classical limits. Most existing approaches target phase estimation and rely on a shared phase reference between the signal and the probe, yet many relevant scenarios deal with regimes where such a reference is absent, making the estimation of force or field amplitudes the main task. We study this phase-insensitive regime for bosonic sensors that undergo identical displacements with common phases randomly varying between experimental runs. We derive analytical bounds on the achievable precision and show that it is determined by first-order normal correlations between modes in the probe state, constrained by their average excitations. These correlations yield a collective sensitivity enhancement over the standard quantum limit, with a gain that grows linearly in the total excitation number, revealing a distributed quantum advantage even without a global phase reference. We identify families of multimode states with definite joint parity that saturate this limit and can be probed efficiently via local parity measurements already demonstrated or emerging in several quantum platforms. We further demonstrate that experimentally relevant decoherence channels favor two distinct sensing strategies: splitting of a single-mode nonclassical state among the modes, which is robust to loss and heating, and separable probes, which are instead resilient to dephasing and phase jitter. Our results are relevant to multimode continuous platforms, including trapped-ion, solid-state mechanical, optomechanical, superconducting, and photonic systems.

This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides the state-of-the-art provable, asymptotic performance: polynomial in problem dimension and quadratic in inverse-precision. While quantum algorithms are known to offer quadratic speedups over classical Monte Carlo methods, end-to-end speedups have been proven only in the simplified setting over the Black-Scholes geometric Brownian motion (GBM) model. This paper extends existing frameworks to demonstrate novel quadratic speedups for more practical models, such as the Cox-Ingersoll-Ross (CIR) model and a variant of Heston's stochastic volatility model, utilizing a characteristic of the underlying SDEs which we term fast-forwardability. Additionally, for general models that do not possess the fast-forwardable property, we introduce a quantum Milstein sampler, based on a novel quantum algorithm for sampling Lévy areas, which enables quantum multi-level Monte Carlo to achieve quadratic speedups for multi-dimensional stochastic processes exhibiting certain correlation types. We also present an improved analysis of numerical integration for derivative pricing, leading to substantial reductions in the resource requirements for pricing GBM and CIR models. Furthermore, we investigate the potential for additional reductions using arithmetic-free quantum procedures. Finally, we critique quantum partial differential equation (PDE) solvers as a method for derivative pricing based on amplitude estimation, identifying theoretical barriers that obstruct achieving a quantum speedup through this approach. Our findings significantly advance the understanding of quantum algorithms in derivative pricing, addressing key challenges and open questions in the field.

We study the thermodynamics of the isotropic Heisenberg XXX spin chain with negative spin, focusing on the case $s=-1$. The model is equivalent to the quantum lattice nonlinear Schrödinger (NLS) model and appears as an effective theory in deep inelastic scattering in high-energy quantum chromodynamics. Owing to its integrability, it admits a consistent Bethe Ansatz description and a well-defined thermodynamic limit. Using the thermodynamic Bethe Ansatz, we analyze the ground state, elementary excitations, and finite-temperature properties. In contrast to the conventional positive spin XXX chain, the negative spin model exhibits a distinct vacuum structure and excitation spectrum, leading to modified TBA equations and unconventional low-temperature behavior. Although the integral equations resemble those of the Lieb-Liniger Bose gas, the thermodynamics and scaling properties are qualitatively different and cannot be continuously connected. We derive the free energy, entropy, and specific heat, and identify a quantum phase transition separating different thermodynamic regimes. At zero temperature, the excitation spectrum becomes linear in the continuum limit and can be described by a conformal field theory. The low-temperature regime realizes a Luttinger-liquid like phase with features unique to the negative spin XXX chain.

Electronic circular dichroism (ECD) spectroscopy captures the chiroptical response of molecules, enabling absolute configuration assignment that is vital for enantioselective synthesis and drug design. The practical use of ECD spectra in predictive modeling remains restricted, as existing approaches offer limited confidence for chiral discrimination. By contrast, theoretical ECD calculations demand substantial computational effort rooted in electronic structure theory, which constrains their scalability to larger chemically diverse molecules. These limitations underscore the need for computational approaches that retain first principles physical rigor while enabling efficient and scalable prediction. Motivated by recent advances in quantum algorithms for chemistry, we introduce a variational quantum framework combined with the quantum equation of motion formalism to compute molecular properties and predict ECD spectra, implemented within a multi GPU or QPU accelerated hybrid quantum/classical workflow. We demonstrate its efficient applicability on 12 clinically relevant chiral drug molecules accessing expanded active spaces. The proposed framework is assessed by comparison with established classical wavefunction based methods, employing Coupled Cluster Singles and Doubles (CCSD) for ground-state energy benchmarks and Complete Active Space Configuration Interaction (CASCI) as the reference method for excited state energies and chiroptical properties within the same active orbital space. Notably, the quantum computed ECD spectra, obtained from chemically relevant active spaces mapped onto quantum circuits of approximately 20 to 24 qubits, exhibit near quantitative agreement with classical reference calculations, accurately reproducing spectral line shapes, Cotton effect signs, and relative peak intensities.

Quantum measurements can inject energy into quantum systems, enabling engines whose operation is powered entirely by measurements. We develop a general theory of quantum vacuum measurement engines by introducing the quantum vacuum bending function (QVBF), a quantity that characterizes the lowering of the ground-state energy due to interactions. We show that all thermodynamic observables, including work and efficiency, are governed solely by the shape of the ground-state energy landscape encoded in the QVBF, regardless of microscopic details. We further demonstrate that work fluctuations are defined by the curvature of QVBF modulated by a model-dependent quantity, and are constrained by a generalized quantum fluctuation relation that involves the interplay between quantum Fisher information and the ground-state energy landscape. Exactly solvable models and numerical simulations of single and many-body systems confirm the theory and illustrate how the QVBF alone determines the performance of quantum vacuum measurement engines.

Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.

The effective Hamiltonian serves as the conceptual pivot of quantum engineering, transforming physical complexity into programmable logic; yet, its construction remains compromised by the mathematical non-uniqueness of block diagonalization, which introduces an intrinsic "gauge freedom" that standard methods fail to resolve. We address this by establishing the Least Action Unitary Transformation (LAUT) as the fundamental principle for effective models. By minimizing geometric action, LAUT guarantees dynamical fidelity and inherently enforces the preservation of symmetries–properties frequently violated by conventional Schrieffer-Wolff and Givens rotation techniques. We identify the Bloch-Brandow formalism as the natural perturbative counterpart to this principle, yielding analytic expansions that preserve symmetries to high order. We validate this framework against experimental data from superconducting quantum processors, demonstrating that LAUT quantitatively reproduces interaction rates in driven entangling gates where standard approximations diverge. Furthermore, in tunable coupler architectures, we demonstrate that the LAUT approach captures essential non-rotating-wave contributions that standard models neglect; this inclusion is critical for quantitatively reproducing interaction rates and revealing physical multi-body interactions such as $XZX+YZY$, which are verified to be physical rather than gauge artifacts. By reconciling variational optimality with analytical tractability, this work provides a systematic, experimentally validated route for high-precision system learning and Hamiltonian engineering.

A complex tensor with $n$ binary indices can be identified with a multilinear polynomial in $n$ complex variables. We say it is a Lee-Yang tensor with radius $r$ if the polynomial is nonzero whenever all variables lie in the open disk of radius $r$. In this work we study quantum states and observables which are Lee-Yang tensors when expressed in the computational basis. We first review their basic properties, including closure under tensor contraction and certain quantum operations. We show that quantum states with Lee-Yang radius $r > 1$ can be prepared by quasipolynomial-sized circuits. We also show that every Hermitian operator with Lee-Yang radius $r > 1$ has a unique principal eigenvector. These results suggest that $r = 1$ is a key threshold for quantum states and observables. Finally, we consider a family of two-local Hamiltonians where every interaction term energetically favors a deformed EPR state $|00\rangle + s|11\rangle$ for some $0 \leq s \leq 1$. We numerically investigate this model and find that on all graphs considered the Lee-Yang radius of the ground state is at least $r = 1/\sqrt{s}$ while the spectral gap between the two smallest eigenvalues is at least $1-s^2$. We conjecture that these lower bounds hold more generally; in particular, this would provide an efficient quantum adiabatic algorithm for the quantum Max-Cut problem on uniformly weighted bipartite graphs.

Magnons are the low-energy excitations of magnetically ordered materials. While the magnetic moment of a ferromagnet aligns with an applied magnetic field, it has been experimentally shown that the magnetic order can be inverted by injecting spin current into the magnet. This results in an energetically unstable but dynamically stabilized state where the magnetic moment aligns antiparallel to an applied magnetic field, called the inverted magnetic state. The excitations on top of such a state have negative energy and are called antimagnons. The inverted state is subject to fluctuations, in particular, as shot noise in the spin current, which are different from fluctuations in equilibrium, especially at low temperatures. Here, we theoretically study the fluctuations of the inverted magnetic state and their signatures in experimental setups. We find that the fluctuations from the injection of spin current play a large role. In the quantum regime, the inverted magnetic state exhibits larger fluctuations compared to the equilibrium position, which can be probed using a qubit. Our results advance the understanding of the fundamental properties of antimagnons and their experimental controllability, and they pave the way for applications in spintronics and magnonics, such as spin wave amplification and entanglement.

Quantum computers connected through classical and quantum communication channels can be combined to function as a single unit to run large quantum circuits that each device is unable to execute on their own. The distributed quantum computing paradigm is therefore often seen as a potential pathway to scaling quantum computing to capacities necessary for practical and large-scale applications. Whether connecting multiple quantum processing units (QPUs) in clusters or over networks, quantum communication requires entanglement to be generated and distributed over distances. Using entanglement, the remote CX protocol can be performed, which allows the application of the CX gate involving qubits located in different QPUs. In this work, we use a specialized simulation framework for a high-level evaluation of the impact of the protocol when executed under noise in various network configurations using different number of QPUs. We compare naive and graph partitioning qubit assignment strategies and how they affect the fidelity in experiments run on Grover, GHZ, VQC, and random circuits. The results provide insights on how QPU and network configurations or naive scheduling can degrade performance.

Open Quantum Brownian Motion (OQBM) was introduced as a scaling limit of discrete-time open quantum walks. This limit defines a new class of quantum Brownian motion, which incorporates both the external and internal degrees of freedom of the Brownian particle. We consider a weakly driven Brownian particle confined in a harmonic potential and dissipatively coupled to a thermal bath. Applying the rotating wave approximation (RWA) to the system-bath interaction Hamiltonian, we derive a completely positive Born-Markov master equation for the reduced dynamics. We express the resulting master equation in the coordinate representation and, utilizing the adiabatic elimination of fast variables, derive a completely positive hybrid quantum-classical master equation that defines OQBM. We illustrate the resulting dynamics using examples of initial Gaussian and non-Gaussian distributions of the OQBM walker. Both examples reveal the emergence of Gaussian distributions in the limiting behavior of the OQBM dynamics, which closely matches that of the standard OQBM. With the help of the obtained OQBM master equation, we derive the equations for the $n$-th moments and the cumulants of the position distribution of the open Brownian walker. We subsequently solve these equations numerically for Gaussian initial distributions across various parameter regimes. Notably, we find that the third-order cumulant is nonzero, indicating that the dynamics' intrinsic generator is non-Gaussian.

Quantum Reservoir Computing (QRC) has emerged as a strong pa- radigm for Noisy Intermediate-Scale Quantum (NISQ) machine learning, ena- bling the processing of temporal data with minimal training overhead by exploi- ting the high-dimensional dynamics of quantum states. This paper introduces QRC-Lab, an open-source, modular Python framework designed to bridge the gap between theoretical quantum dynamics and applied machine learning work- flows. We provide a rigorous definition of QRC, contrast physical and gate- based approaches, and formalize the reservoir mapping used in the toolbox. QRC-Lab instantiates a configurable gate-based laboratory for studying in- put encoding, reservoir connectivity, and measurement strategies, and validates these concepts through three educational case studies: short-term memory re- construction, temporal parity (XOR), and NARMA10 forecasting as a deliberate stress test. In addition, we include a learning-theory motivated generalization- gap scan to build intuition about capacity control in quantum feature maps. The full source code, experiment scripts, and reproducibility assets are publicly available at: https://doi.org/10.5281/zenodo.18469026.

Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these techniques called quantum circuit cutting. With circuit cutting, a quantum circuit is decomposed into smaller sub-circuits, each of which can be run on smaller quantum hardware. We compare the performance of quantum circuit cutting with different cutting strategies, and then apply circuit cutting to a QAOA algorithm. Using simulations, we first show that Randomized Clifford measurements outperform both Pauli and random unitary measurements. Second, we show that circuit cutting has trouble providing correct answers in noisy settings, especially as the number of circuits increases.

Deploying large language models (LLMs) as optimizers for black-box scientific design problems requires efficient test-time refinement under expensive evaluations and without training data. We propose a memory-augmented test-time optimization framework that combines episodic memory of high-scoring candidates, score-difference feedback, and restart-from-best sampling to improve iterative search. We evaluate the approach on quantum circuit synthesis, where the objective is to maximize the Meyer–Wallach (MW) global entanglement measure under an exponentially expensive black-box oracle. On 20-qubit circuits, the framework achieves $Q(\psi)=0.99$ without feedback. On the more challenging 25-qubit task, feedback and restart mechanisms enable multiple runs to reach $Q(\psi)=1.0$ within 45 oracle calls, while a budget-matched random hill-climbing baseline stalls below $Q(\psi)\approx0.29$. These results demonstrate that memory and evaluator feedback substantially improve the sample efficiency of LLM-based black-box optimization and establish quantum circuit synthesis as a challenging benchmark for test-time optimization.

Stationary entanglement between the motion of macroscopic objects and light is a long-standing goal of quantum optomechanics, with implications for both fundamental tests of quantum physics and emerging quantum technologies. We report the generation of quantum entanglement between the center-of-mass motion of a nanosphere levitated in an optical tweezer inside an optical cavity and the electromagnetic field. By heterodyne detection, we reconstruct the full set of optomechanical correlations and observe a violation of separability bounds between the mechanical motion and the quadratures of a propagating optical mode. This demonstrates the distribution of nonclassical correlations beyond the interaction region. The entanglement is generated at room temperature and remains robust over a broad range of parameters. Our results establish levitated optomechanical systems as a promising platform for continuous-variable quantum communication and for tests of macroscopic quantum physics.

Quantum generative models offer a novel approach to exploring high-dimensional Hilbert spaces but face significant challenges in scalability and expressibility when applied to multi-modal distributions. In this study, we explore a Hybrid Quantum-Classical U-Net architecture integrated with Adaptive Non-Local Observables (ANO) as a potential solution to these hurdles. By compressing classical data into a dense quantum latent space and utilizing trainable observables, our model aims to extract non-local features that complement classical processing. We also investigate the role of Skip Connections in preserving semantic information during the reverse diffusion process. Experimental results on the full MNIST dataset (digits 0-9) demonstrate that the proposed architecture is capable of generating structurally coherent and recognizable images for all digit classes. While hardware constraints still impose limitations on resolution, our findings suggest that hybrid architectures with adaptive measurements provide a feasible pathway for mitigating mode collapse and enhancing generative capabilities in the NISQ era.

We investigate the topological properties of a generalized Dirac–Kronig–Penney model, a continuum one-dimensional model for a relativistic quantum chain. By tuning the coupling parameters this model can accommodate five Altland–Zirnbauer–Cartan symmetry classes, three of which (AIII, BDI and D) support non-trivial topological phases in dimension one. We characterize analytically the spectral properties of the Hamiltonian in terms of a spectral function, and numerically compute the Zak phase to probe the bulk topological content of the insulating phases. Our findings reveal that, while the Zak phase is quantized in classes AIII and BDI, it exhibits non-quantized values in class D, challenging its traditional role as a topological marker in continuum settings. We also discuss the bulk-boundary correspondence for a truncated version of the chain, analyzing how the emergence of edge states depends on both the truncation position and the boundary conditions. In classes AIII and BDI, we find that the Zak phase effectively detects edge states as a relative boundary topological index, although the correspondence is highly sensitive to the parameters characterizing the truncation.