Papers

Quantum Neural Networks (QNNs) are a promising class of quantum machine learning models with potential quantum advantages when implemented on scalable, error-corrected quantum computers. However, as system sizes increase, deploying QNNs becomes challenging. Similar to their classical counterparts, a key obstacle to their practical applications is that large-scale QNNs may not be easily deployed on smaller systems that have limited resources. Here, we tackle this challenge by compressing QNNs via knowledge distillation. We demonstrate how well-trained QNNs on large systems can be distilled into smaller architectures with similar configurations. We numerically show that knowledge distillation helps reduce the training cost of QNNs in terms of the number of qubits and circuit depth. Additionally, we find that a self-knowledge-distillation approach can accelerate training convergence. We believe our results offer new strategies for the efficient compression and practical deployment of QNNs.

Non-equilibrium dynamics of strongly and rapidly driven quantum many-body systems is poorly understood beyond periodic driving, where heating is exponentially slow in the drive frequency (Floquet Prethermalization). In contrast, non-periodic drives were found to exhibit widely different heating scalings with no unifying principle. This work identifies a resonance-suppression principle governing slow heating up to a prethermal lifetime $\tau_*$: When the drive's spectral arithmetic structure restricts multiphoton resonances, $\tau_*$ is controlled by low-frequency spectral suppression. The principle distinguishes (i) Single-photon suppression, quantified by a low-frequency suppression law $f(\Omega)$ for the drive's Fourier Transform weight near $\Omega=0$, from (ii) Multi-photon suppression, where nested commutators remain controlled if exceptional arithmetic structure satisfies a subadditive property. Remarkably, if multi-photon suppression holds, $\tau_*$ scaling with drive speed $\lambda$ is governed by $f(\Omega)$. This law of $\tau_*$ is found through a small-divisor mechanism in this work's iterative rotating frame scheme. Multi-photon suppression breakdown separates $\lambda$-scaling of $\tau_*$ in linear response and non-perturbative theory, shown by a case study of Quasi-Floquet driving. The principle is applied to (i) Resolve inconsistencies in literature on non-periodic driving, and (ii) Provide design principles for engineering prethermal phases of matter in programmable quantum simulators, exemplified by new non-periodic `Factorial' drives with tunable $\tau_*$.

Fixed-frequency transmon qubits, characterized by simple architectures and long coherence times, are promising platforms for large-scale quantum computing. However, the rapidly increasing frequency collisions, which directly reduce the fabrication yield, hinder scaling, especially in cross-resonance (CR) gate-based architectures, wherein the restricted drive frequency severely limits the available design space. We investigate the Stark-induced ZZ by level excursions (siZZle) gate, which relaxes this limitation by allowing arbitrary drive-frequency choices. Extensive numerical analyses across a broad parameter range – including the far-detuned regime that has received negligible prior attention – reveal wide operating windows that support controlled-Z (CZ) fidelities >99.6%. Leveraging these windows, we design lattice architectures containing >1000 qubits, showing that even under 0.25% fabrication-induced frequency dispersion, the zero-collision yields in square and heavy-hexagonal lattices reach 80% and 100%, respectively. Thus, the siZZle-CZ gate is a scalable and collision-robust alternative to the CR gate, offering a viable route toward high-yield fixed-frequency transmon quantum processors.

Quantum error correcting codes (QECC) are essential for constructing large-scale quantum computers that deliver faithful results. As strong competitors to the conventional surface code, quantum low-density parity-check (qLDPC) codes are emerging rapidly: they offer high encoding rates while maintaining reasonable physical-qubit connectivity requirements. Despite the existence of numerous code constructions, a notable gap persists between these designs – some of which remain purely theoretical – and their circuit-level deployment. In this work, we propose Auto-Stabilizer-Check (ASC), a universal compilation framework that generates depth-optimal syndrome extraction circuits for arbitrary qLDPC codes. ASC leverages the sparsity of parity-check matrices and exploits the commutativity of X and Z stabilizer measurement subroutines to search for optimal compilation schemes. By iteratively invoking an SMT solver, ASC returns a depth-optimal solution if a satisfying assignment is found, and a near-optimal solution in cases of solver timeouts. Notably, ASC provides the first definitive answer to one of IBM's open problems: for all instances of bivariate bicycle (BB) code reported in their work, our compiler certifies that no depth-6 syndrome extraction circuit exists. Furthermore, by integrating ASC with an end-to-end evaluation framework – one that assesses different compilation settings under a circuit-level noise model – ASC reduces circuit depth by approximately 50% and achieves an average 7x-8x suppression of the logical error rate for general qLDPC codes, compared with as-soon-as-possible (ASAP) and coloration-based scheduling. ASC thus substantially reduces manual design overhead and demonstrates its strong potential to serve as a key component in accelerating hardware deployment of qLDPC codes.

Topological lasers and random lasers embody two contrasting strategies for disorder management in photonics: the former suppresses disorder via protected edge transport, while the latter exploits multiple scattering for feedback. Here, we theoretically demonstrate that these seemingly incompatible paradigms can be unified through a topological Anderson random laser (TARL), where disorder itself induces a topological phase that enables robust lasing. Starting from a trivial photonic lattice, we show that engineered disorder drives the system into a topological Anderson insulator regime, generating emergent chiral edge states that serve as boundary-selective lasing channels. Remarkably, the TARL exhibits rapid mode selection toward a single edge state, producing an ultranarrow emission spectrum and enhanced slope efficiency optimized near disorder strength with maximal topological mobility gap. Furthermore, they exhibit single-mode-like coherence properties, deviating from Kardar-Parisi-Zhang behavior in conventional chiral topological lasers, while remaining significantly more robust against local perturbations than conventional random lasers. Our findings establish a disorder-enabled flexible route to topologically protected single-mode lasing and introduce a fundamentally new design principle for robust, high-coherence photonic light sources.

In 2006 we proposed Quantum Fuzzy Sets, observing that states of a quantum register could serve as characteristic functions of fuzzy subsets, embedding Zadeh's unit interval into the Bloch sphere. That paper was deliberately preliminary. In the two decades since, the idea has been taken up by researchers working on quantum annealers, intuitionistic fuzzy connectives, and quantum machine learning, while parallel developments in categorical quantum mechanics have reshaped the theoretical landscape. The present paper revisits that programme and introduces two main extensions. First, we move from pure states to density matrices, so that truth values occupy the entire Bloch ball rather than its surface; this captures the phenomenon of semantic decoherence that pure-state semantics cannot express. Second, we introduce the Q-Matrix, a global density matrix from which individual quantum fuzzy sets emerge as local sections via partial trace. We define a category QFS of quantum fuzzy sets, establish basic structural properties (monoidal structure, fibration over Set), characterize the classical limit as simultaneous diagonalizability, and exhibit an obstruction to a fully internal Frobenius-algebra treatment.

We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard Kähler framework, we introduce an extension in which the symplectic structure is allowed to couple to a metric-affine background geometry, leading to a deformation of the Hamiltonian flow on the state space. We show that, under suitable conditions, the deformed structure remains symplectic and defines a well-posed Hamiltonian system. The formulation reduces to standard Schrödinger dynamics in the limit where the geometric deformation vanishes. Explicit analytical examples are constructed to illustrate the effect of the deformation. In particular, curvature-dependent deformations lead to a rescaling of Hamiltonian flows, while torsion-induced contributions produce direction-dependent corrections. In addition, geometric phases acquire corrections determined by the deformed symplectic structure. These results provide a mathematically consistent framework for exploring geometric modifications of quantum evolution induced by background curvature and affine structure.

Contextuality is widely regarded as a hallmark of quantum information, yet its structural origin is often obscured by probabilistic or operational formulations. In this work, we show that non-distributive orthomodular structure need not be postulated, but arises canonically as a left adjoint from classical Boolean contexts. We introduce a gluing functor that takes pairs of Boolean algebras and identifies only their minimal and maximal elements via a categorical pushout. The resulting lattice is orthomodular but generically non-distributive. We prove that this construction is left adjoint to a forgetful functor selecting Boolean subalgebras, thereby providing a free but constrained generation of quantum-logical structure from classical contexts. Furthermore, we demonstrate that the failure of this pushout to remain Boolean is equivalent to the absence of global sections in the sheaf-theoretic framework of Abramsky and Brandenburger. This establishes a precise correspondence between contextuality as a sheaf obstruction and non-distributivity as a colimit failure. Our results offer a categorical and lattice-theoretic reconstruction of contextuality that precedes probabilistic notions and clarifies the structural necessity of quantum logic in information-theoretic settings.

Boron nitride is a layered crystal whose properties depend on how its atomic sheets are stacked. Its negatively charged boron vacancy is a well-established magnetic defect that can be prepared and read out optically, but in the common hexagonal form it emits very little light, because the symmetry of the surrounding lattice forbids the relevant optical transition. Here we show, using first-principles calculations, that stacking the sheets in the rhombohedral sequence instead removes this restriction and increases the emitted intensity by one to two orders of magnitude, while the magnetic properties remain comparable or improve. We predict that the resulting emission is bright enough for a single defect to be addressed at room temperature, and that a sharp emission line, absent in the hexagonal form, should appear on cooling. Stacking order therefore acts as a design parameter for tailoring the quantum properties of defects embedded in layered materials.

We consider a non-relativistic quantum particle in $\mathbb{R}^d$, $d=2$ or $d = 3$, interacting with singular zero-range potentials concentrated on a large collection of points. We analyze the homogenization regime where the intensities of the singular potentials and the distances between the points simultaneously go to zero as their number grows, while the total interaction strength remains finite. Assuming that the singular potentials have negative scattering lengths and are uniformly distributed, we prove the strong resolvent convergence as $N \to \infty$ of the family of operators to a Schrödinger operator with a regular electrostatic potential. The result is obtained via $\Gamma$-converge of the associated quadratic forms. Moreover, in presence of an external trapping potential, the convergence is lifted to uniform resolvent sense.

We investigate the rotational response of a confined, two-dimensional quantum droplet, which emerges in an attractive binary Bose mixture that is stabilized against collapse by beyond-mean-field effects. We consider both a harmonic and an anharmonic form for the external confining potential. We go beyond the widely employed “phase-locked" single-order-parameter model, maintaining two separate order parameters for the two components, and calculating the lowest-energy state for various values of the angular momentum. For a population-balanced quantum droplet and sufficiently tight confinement, we find that near certain half-integer values of the angular momentum the droplet is excited in a “heterosymmetric" manner, with the two components carrying different vorticities. This mode is naturally missed by the single-order-parameter model. We additionally investigate the effects of a small population imbalance in the droplet. Apart from an energy increase associated with the population difference, the imbalance also lifts the double degeneracy of the heterosymmetric states, which characterizes the $\mathbb{Z}_2$-symmetric balanced droplet. The heterosymmetric mode is found to be favored by the energy term which captures the beyond-mean-field effects in the mixture.

Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient for scalable quantum technologies. Despite the importance of accurately characterizing these states, conventional tomography methods are often impractical because they require large sample sizes and can yield unphysical states. Here we present a reliable and efficient tomography method for multimode Gaussian states based on maximum-likelihood estimation. By directly operating on covariance matrices, the method avoids the exponential overhead associated with density-matrix reconstruction. We consider two commonly used detection schemes–single and joint homodyne detection–and systematically analyze the reconstruction performance. Our method outperforms conventional approaches by ensuring physical covariance matrices and achieving better agreement with the true states. To demonstrate the experimental applicability of the method, we experimentally generate various multipartite entangled states–six-mode graph states with different connectivity, a six-mode GHZ state, and a fully connected ten-mode graph state–and reconstruct their covariance matrices. Using the reconstructed covariance matrices, we quantify fidelities, detect entanglement, and reveal the multimode structure of squeezing and noise. Our technique offers a practical diagnostic tool for developing scalable quantum technologies.

Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated approaches-including memory restriction, weak measurements, operation near the edge of quantum chaos, and dissipative dynamics-are in fact governed by the same underlying principle, namely a tunable balance between memory retention and nonlinear response. Using the information processing capacity, a dynamical measure from nonlinear systems theory, we place these behaviors in a unified framework and identify the regimes in which quantum reservoirs surpass the standard protocol. Our results reveal a fundamental connection between memory and nonlinear response. This provides a general design principle for enhanced information processing and enables systematic analysis and optimization inspired by classical dynamical quantifiers.

A long-standing problem in the foundations of quantum mechanics is to identify a physical principle that explains why algebraically maximal violations of Bell inequalities can generally not be achieved in Nature. One recently proposed approach considers iterated Bell tests, where a Bell test is performed on a state that has undergone several rounds of entanglement swapping. Obtaining large violations in this scenario is more demanding, because it requires a theory to have both highly entangled states and highly entangled measurements. It has been conjectured that the maximal quantum mechanical Clauser-Horne-Shimony-Holt (CHSH)-value of $2\sqrt2$ might be optimal for any probabilistic theory which, like quantum mechanics, maintains its CHSH-value after an arbitrary number of rounds of entanglement swapping. However, in a previous paper, we have exhibited a first example of a probabilistic theory that can sustain a CHSH value of $4$ in this setting. In this work, further investigating this property, we give a classification of all general probabilistic theories (GPTs) whose CHSH value is stable in the above sense. The problem reduces to a representation-theoretic condition that allows for exactly seven solutions. The GPT from our previous work showed some counter-intuitive features, e.g. that the local state space had a higher dimension than seemed necessary to realize CHSH tests. The classification shows that this is necessarily so. Along the way, we generalize the concept of self-testing to GPTs.

Advances in the study of relativistic quantum phase space have established the set of Linear Canonical Transformations (LCTs) as a candidate for the fundamental symmetry group associated with relativistic quantum physics. In this framework, for a spacetime of signature $(N_+,N_-)$, the symmetry of the relativistic quantum phase space is described by the LCT group, isomorphic to the symplectic Lie group $Sp(2N_+,2N_-)$, which preserves the canonical commutation relations (CCRs) and treats spacetime coordinates and momenta operators on an equal footing. In this work, we investigate the contraction structure of the Lie algebra associated with the LCT group for signature $(1,4)$, clarifying how familiar spacetime symmetry groups emerge from this more fundamental quantum phase space symmetry. Using the Inönü-Wigner group contraction formalism, we examine each limit case corresponding to the possible combinations of asymptotic values of two fundamental length scale parameters associated with the theory, namely a minimum length $\ell$ and a maximum length $L$, which may be identified respectively with the Planck length and the de Sitter radius. We explicitly analyze how contractions of the LCT Lie algebra lead to the physically relevant de Sitter algebra $\mathfrak{so}(1,4)$ and, in the flat-curvature limit, to the Poincaré algebra $\mathfrak{iso}(1,3)$ of four-dimensional spacetime. This provides an explicit mechanism through which relativistic spacetime symmetry can emerge from a deeper symplectic structure of quantum phase space.

We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector generated by the Dunkl angular momentum tensor and the modified Laplace-Runge-Lenz vector. The equidistant analogue of the Hamiltonian, with a linear spectrum, is expressed in terms of the conformal subalgebra $so(1,2)$. In addition, the wave functions of the Calogero-Coulomb Hamiltonian are classified into infinite-dimensional lowest-weight $so(1,2)$ multiplets.

Variational Quantum Algorithms (VQAs) have been extensively researched for applications in Quantum Machine Learning (QML), Optimization, and Molecular simulations. Although designed for Noisy Intermediate-Scale Quantum (NISQ) devices, VQAs are predominantly evaluated classically due to uncertain results on noisy devices and limited resource availability. Raising concern over the reproducibility of simulated VQAs on noisy hardware. While prior studies indicate that VQAs may exhibit noise resilience in specific parameterized shallow quantum circuits, there are no definitive measures to establish what defines a shallow circuit or the optimal circuit depth for VQAs on a noisy platform. These challenges extend naturally to Variational Quantum Classification (VQC) algorithms, a subclass of VQAs for supervised learning. In this article, we propose a relative entropy-based metric to verify whether a VQC model would perform similarly on a noisy device as it does on simulations. We establish a strong correlation between the average relative entropy difference in classes, transpilation circuit depth, and their performance difference on a noisy quantum device. Our results further indicate that circuit depth alone is insufficient to characterize shallow circuits. We present empirical evidence to support these assertions across a diverse array of techniques for implementing VQC, datasets, and multiple noisy quantum devices.

We demonstrate precision laser spectroscopy of a trapped $^{173}$Yb$^+$ ion that is not directly laser cooled by coupling it to ultracold atoms. The atomic bath continuously cools the internal degrees of freedom of the ion to its hyperfine ground state via spin-exchange collisions. Successful laser excitation is detected via state-selective charge transfer and subsequent ion loss. We probe the $6^2S_{1/2}\rightarrow 6^2P_{3/2}$ transition at 329 nm and measure the magnetic and electric hyperfine interaction constants for the $6^2P_{3/2}$ state to be $A=-241(1)$ MHz and $B=1460(8)$ MHz, respectively. Our results are in agreement with a previous measurement obtained in a hollow-cathode discharge experiment but are a factor of 6-9 more precise. The techniques demonstrated in this work may be extended to perform precision spectroscopy on other ions with complex level structures.

For a traveling salesperson problem (TSP) of $n$ cities, we present a compact quantum encoding based on a time-register representation of tours. A candidate route is represented as a sequence of $n-1$ city labels over discrete time steps, with one fixed start city and the remaining cities encoded in binary registers. We describe three ingredients of the construction: uniform route generation over the route register, a reversible validity oracle, and a phase oracle that encodes the total tour cost. The validity oracle checks both that the non-start city labels form a permutation and, for incomplete graphs, that every directed edge used by the route exists. The cost oracle then accumulates the start-edge, intermediate-transition, and return-edge costs into a tour-dependent phase for valid routes. This yields a coherent superposition of candidate routes with feasibility and tour-length information embedded directly in the quantum state. The complete construction uses $\mathcal{O}(n\log n)$ qubits, while a naive implementation requires $\mathcal{O}(n^3\log_2 n)$ CX gates and $\mathcal{O}\!\left(n^3[\log_2 n+\log_2(1/\epsilon)]\right)$ $T$ gates, where $\epsilon$ denotes the target approximation precision. The encoding is compatible with amplitude amplification or spectral filtering techniques such as the quantum singular value transform (QSVT) or Grover's algorithm. However, due to the exponentially small fraction of valid tours, the overall complexity remains exponential even when combined with amplitude amplification.

The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework – a point of ongoing debate in the field. This work addresses this issue by proposing a consistent formulation that reconciles existing controversies and establishes a unified theoretical understanding. Our approach rests on two foundational premises: (i) the dynamics of both left and right-vectors of a non-Hermitian system must satisfy the Schrödinger equation; (ii) the theoretical framework must preserve gauge invariance, ensuring that physical quantities are independent of unobservable phase choices. Building on these physically motivated assumptions, we refine the biorthogonal framework, leading to a gauge-invariant non-Hermitian quantum theory. Our framework naturally encompasses the open-system effective non-Hermitian evolution as a special case, and can naturally reduce to standard quantum mechanics in the Hermitian limit. As a concrete application, we analyze the dynamical phase transition in a one-dimensional Su-Schrieffer-Heeger (SSH) model within this gauge-invariant non-Hermitian quantum theory. Notably, our formulation naturally generalizes the known condition for such transitions in Hermitian two-band systems, namely, $\mathbf{d}_{k}^i\cdot\mathbf{d}_{k}^f=0$, to the non-Hermitian case, where it takes the form $\mathrm{Re}\Bigl[\frac{\mathbf{d}_{k}^i}{d_{k}^i}\cdot\frac{\mathbf{d}_{k}^f}{d_{k}^f}\Bigr]=0$. Furthermore, we identify entirely new dynamical phase transitions that cannot be characterized by the winding number. We hope that this gauge-invariant non-Hermitian quantum theory will find broad applications in the study of non-Hermitian systems.

The non-uniform (or inhomogeneous) electron gas has received much attention in many-body quantum mechanics and quantum chemistry in the early days of density functional theory, mainly as a theoretical device to construct gradient approximations via linear response theory. In this article, motivated by the recent works of Lewin, Lieb and Seiringer, we propose a definition of the quantum (resp. classical) non-uniform electron gas through the use of the grand-canonical Levy-Lieb functional (resp. the grand-canonical strictly correlated electrons functional), establish these systems as rigorous thermodynamic limits and analyze their basic properties. The non-uniformity of the gas comes from an arbitrary lattice-periodic background density.

We develop a time-dependent, grid-based framework for simulating infrared spectra that is specifically designed for quantum computers. The proposed circuit employs a probabilistic strategy for applying the non-unitary dipole operator and an Split Operator-Quantum Fourier Transform time evolution scheme. Using a vibrational model of the water molecule as a test system, our classical emulation results demonstrate accurate determination of fundamental and overtone band positions and intensities via Fourier-transformed dipole-dipole autocorrelation functions. We also identify the optimal time parameters that minimise gate depths while maintaining high fidelity. For further resource reduction, we validate the feasibility of utilising harmonic oscillator approximations in state preparation and dipole operator truncations. With its scalability to higher-dimensional normal mode spaces, this wavefunction-based approach establishes a robust foundation for studying IR spectra on future quantum hardware.

Quantum federated learning (QFL) has recently emerged as a promising paradigm for privacy-preserving collaborative learning, yet most existing studies focus on horizontal federated learning and ignore the vertical federated learning (VFL), where parties hold complementary features of aligned samples. In this work, we propose Evidential Quantum Vertical Federated Learning (eviQVFL), a VFL-tailored QFL framework that employs a hybrid classical-quantum architecture for party-side feature processing, mapping local features into a quantum state. To preserve privacy and avoid information loss, party-side output states are directly transmitted to the server via quantum teleportation, and the server fuses the received quantum states with a non-parametric evidential fusion circuit grounded in evidence theory, followed by measurement-based inference. Extensive simulations on image classification and other real-world datasets demonstrate that eviQVFL consistently achieves higher classification accuracy than other classical and quantum baselines under comparable parameter budgets. Both empirical observations and theoretical analysis indicate that eviQVFL achieve less approximation error with limited quantum resources, while maintaining training stability and offering stronger feature privacy.

Practical performance of quantum sensors is often curtailed by uncontrolled environmental drift (bias-field instability, temperature fluctuations, mechanical vibration), background fields, and imperfect control pulses. This motivates developing physical mechanisms that intrinsically compensate for such perturbations while retaining high sensitivity to target fields. We introduce an interaction-protected magnetometry scheme where periodic driving steers the collective magnetization onto two long-lived, prethermal Floquet "orbit" axes well-separated on the Bloch sphere. Rapid toggling between these axes encodes target fields as a differential signal, whereas background fields appear as common-mode motion that is strongly rejected, achieving >1000-fold suppression while canceling prethermal transients. This enables accurate reconstruction of rapidly varying audio-band magnetic signals without predictive filtering or spectral tuning. We provide an experimental proof-of-principle using a dense ensemble of coupled nuclear spins, operated here as a broadband (0-1 kHz) magnetometer. The protocol is remarkably tolerant to imperfections, operating robustly across millions of pulses under pulse-angle (~10{\deg}) and pulse frequency (>1 kHz) errors, large bias-field drifts (>50 $\mathrm{\mu}$T), temperature variations over 150 K, and harsh mechanical vibrations. These results establish Floquet prethermalization as a resource for robust quantum sensors that combines broadband magnetic-field sensitivity with intrinsic immunity to diverse environmental and control perturbations, opening a path toward stable quantum metrology beyond controlled laboratory conditions.

Filtering a unitary coupled-cluster ansatz by molecular point-group symmetry has no settled variational cost for groups with degenerate irreducible representations. We prove that the symmetry-adapted subvariety of the amplitude space is a critical subvariety of the energy, for irreducible representations of any dimension. The gradient along every removed direction vanishes there, so a quasi-Newton optimisation with exact gradients started at the reference determinant cannot distinguish the filtered from the unfiltered ansatz. Every operator invariant under the full point group already lies in the span of the pool retained by an Abelian subgroup, so the filtered pool reaches at every geometry an energy no higher than the fully invariant one reaches. A Hamiltonian-informed pool lies inside the set the equivariant pool touches, and in a symmetry-adapted basis inside the symmetry-filtered pool, which makes a published pair of parameter counts a certificate for the orbital basis. Across six molecules and two basis sets, the full-group filter changes the classical coupled-cluster correlation energy by at most $3.4 \times 10^{-12}$ millihartree in the larger basis where the point group is finite. The parameter count of the unitary ansatz falls from 75 to 30 for ammonia and from 65 to 21 for methane, measured against the Abelian filter current practice uses. The freeness measured for the full-group filter holds near equilibrium and degrades into the static-correlation regime.

We propose an erasure conversion scheme on the $|e\rangle-|f\rangle$ and $|g\rangle-|f\rangle$ qubits in integer fluxonium qubits (IFQs), which are both first-order insensitive to $1/f$ flux noise. The $|e\rangle-|f\rangle$ transition is identical to that of a usual fluxonium qubit and hence is expected to have excellent coherence time, while the $|g\rangle-|f\rangle$ transition is additionally protected from the energy relaxation by the parity symmetry. The dominant error in both qubits arises due to the energy relaxation: from $|e\rangle$ to $|g\rangle$ in the $e\text{--}f$ qubit and from $|f\rangle$ to $|e\rangle$ in the $g\text{--}f$ qubit. Such errors can be treated as erasure events, and their efficient detection improves the performance of quantum error-correcting codes. We consider a protocol for such erasure conversion based on the dispersive readout. Our main finding is that, with proper circuit parameter choice, carefully designed gate sets, and the integration of erasure conversion, IFQs promise high effective coherence times.

Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating cascade probabilities when supplier dependencies are strongly correlated. At n=40 nodes, the full correlated failure distribution requires O(2^n) classical samples, a regime where exact simulation demands 17.6 TB of memory and over 369,000 hours of computation on a standard workstation. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a three-algorithm quantum pipeline implemented using the Qiskit framework with the Aer statevector_simulator backend. First, a 40-node, 4-tier retail supply network is encoded as a 40-qubit Ising Hamiltonian using OpenFermion QubitOperator, where ZZ coupling terms encode correlated cascade probabilities structurally absent from classical Monte Carlo. Second, a hardware-efficient VQE circuit finds the ground-state stress distribution with zero error, detecting entangled cascade failures in 14/40 nodes with max|{\Delta}P|=0.637 versus classical Monte Carlo. Third, we introduce the first application of ADAPT-VQE gradient screening to counterfactual macroeconomic policy evaluation: six crisis interventions are ranked in O(1) Qiskit operator evaluations per policy, a 287x speedup over sequential VQE re-optimisation. Fourth, Density-of-States QPE (DOS-QPE) reconstructs the full eigenspectrum via 32-step Trotter evolution and introduces a novel mapping of the Boltzmann catastrophe probability P_cat(T) to VIX-equivalent market volatility temperature, enabling direct integration into regulatory Value-at-Risk frameworks. Qiskit Aer scaling benchmarks confirm exponential classical intractability at 40 qubits.

We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy and the static structure of a bosons, fermions and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe in order to overcome the sign problem. Even if this recipe is exact for the non interacting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many body path configuration during the evolution of the computer experiment show that the “speed” of the single particle path near the poles slows down as a consequence of the “hairy ball theorem” of Poincaré. The influence of curvature on the thermodynamic and structural properties of the many body fluid is also studied.

Open quantum batteries (QBs) operate under unavoidable system–environment interactions, where both dissipation and coherent frequency renormalization can affect their dynamics. While dissipative effects have been extensively studied, the role of environment-induced frequency shifts, such as the Lamb shift, remains less explored. Here, we investigate a driven open QB consisting of two coherently coupled quantum harmonic oscillators representing the charger and the battery. By incorporating dissipation and Lamb-shift corrections within a Lindblad master equation, we show that the Lamb shift renormalizes the system eigenfrequencies and modifies the resonance condition with the external drive. We further demonstrate that the resulting frequency renormalization leads to a mode-selective energy-transfer process, producing a redistribution of energy between the charger and the battery. This behavior is characterized through a supermode decomposition of the coupled system, which reveals how the environment-induced frequency shift alters the dominant energy-transfer channel. Our results clarify the role of coherent environmental effects in open quantum batteries and provide a physical framework for understanding work-extraction dynamics beyond purely dissipative descriptions.

We establish an exact noise-model-derived characterization of quantum error correction under diagonal local phase noise. Under uniform locality, the maximal logical dimension under t-local phase errors equals Aq(n,2t+1), the classical q-ary packing function. Because no affine or stabilizer structure is imposed, nonlinear spectral supports achieve this bound and strictly exceed all affine constructions whenever Aq(n,2t+1)>Bq(n,2t+1). This follows from a harmonic translation principle: diagonal phase operators act as rigid translations in the Fourier domain, reducing the Knill-Laflamme conditions exactly to an additive non-collision constraint (S-S) cap Et={0}. For structured phase noise, exact correction is equivalent to independence in an additive Cayley graph, connecting biased quantum capacity to classical zero-error theory and the Lovasz theta function. Under mixed Pauli noise, simultaneous protection in conjugate domains incurs an intrinsic rate penalty R <= 1-(gamma_X+gamma_Z)/2, exposing a discrete harmonic uncertainty principle. In contrast with stabilizer- or graph-based frameworks, this classical correspondence is derived directly from the phase-noise model itself rather than from an auxiliary algebraic construction.