Papers

Valley splitting in strained Si/SiGe quantum wells is a central parameter for silicon spin qubits and is commonly described with envelope-function and effective-mass theories. These models provide a computationally efficient continuum description and have been shown to agree well with atomistic approaches when the confinement potential is slowly varying on the lattice scale. In modern Si/SiGe heterostructures with atomically sharp interfaces and engineered Ge concentration profiles, however, the slowly varying potential approximation underlying conventional (local) envelope-function theory is challenged. We formulate an exact multi-valley envelope-function model by combining Burt-Foreman-type envelope-function theory, which does not rely on the assumption of a slowly varying potential, with a valley-sector decomposition of the Brillouin zone. This construction enforces band-limited envelopes, which satisfy a set of coupled integro-differential equations with a non-local potential energy operator. Using degenerate perturbation theory, we derive the intervalley coupling matrix element within this non-local model and prove that it is strictly invariant under global shifts of the confinement potential (choice of reference energy). We then show that the conventional local envelope model generically violates this invariance due to spectral leakage between valley sectors, leading to an unphysical energy-reference dependence of the intervalley coupling. The resulting ambiguity is quantified by numerical simulations of various engineered Si/SiGe heterostructures. Finally, we propose a simple spectrally filtered local approximation that restores the energy-reference invariance exactly and provides a good approximation to the exact non-local theory.

We revisit the localization tensor (LT) from geometric and probabilistic perspectives and construct extensions that are naturally compatible with periodic boundary conditions (PBC), without redefining the position operator. In open boundary conditions, we show that the LT can be written exactly as the covariance of a bivariate probability distribution built from density-density correlations. This leads to two conceptually distinct extensions to PBC: (i) a geometric one based on the Riemannian center (Frechet mean) on the circle, and (ii) a metric-free one based on the mutual information I, which treats the configuration space purely as a probability space. We then relate the LT to the static structure factor by identifying the diagonal part, Cpp, as a "localization function" C(p), whose small-momentum behavior determines the LT in the thermodynamic limit. This clarifies why the LT is sensitive to transitions out of the extended phase but by itself cannot distinguish Anderson-type localization from dimerization: both share the same low-momentum asymptotics. We show that the finite-momentum behavior of C(p), together with an inverse participation ratio (IPR)-based upper bound valid in localized phases, provides a sharp criterion that discriminates localization from dimerization. These results are illustrated on the Su-Schrieffer-Heeger and Aubry-Andre models, with and without interactions, and suggest that structure factor-based probes offer robust and experimentally accessible diagnostics of localized and dimerized phases under PBC.

Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent space excitation ansatz for quantum circuits. We show that, both topological ground state degeneracy and the chiral edge mode can be faithfully captured by this approach. We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.

We introduce a geometric framework for efficient few-parameter pulse optimization in multi-level quantum systems, enabling high-fidelity state transfer beyond the adiabatic limit. Our method interpolates smoothly between adiabatic and diabatic dynamics to minimize unwanted excitations and maximize desired transitions even within a multi-level structure. Crucially, for single-parameter pulse control, the optimization reduces to solving a first-order ordinary differential equation. We showcase the flexibility of our diabatic-adiabatic protocols through two examples in spin-based quantum information processing: state initialization and qubit state transfer.

Quantum states with sub-Planck features exhibit sensitivity to phase-space displacements beyond the standard quantum limit, making them useful for quantum metrology. In the context of the SU(1,1) group, sub-Planck features have been constructed through the superposition of four Perelomov coherent states on the hyperbolic plane (the SU(1,1) compass state). However, these structures differ in scale along different phase-space directions (anisotropic features), resulting in nonuniform sensitivity enhancement to phase-space displacements. Here, we construct $N$-component compass states, which are obtained by superposing $N \geq 6$ SU(1,1) coherent states with an even total number, evenly arranged along a circular path on the hyperbolic plane; that is, all components lie at the same distance from the origin and have equal angular spacing of $\frac{2\pi}{N}$. We observe that these generalized SU(1,1) compass states exhibit isotropic sub-Planck structures, leading to an isotropic enhancement in sensitivity to phase-space displacements that progressively increases with larger $N$. These states are directly relevant to quantum platforms supporting Kerr-type interactions between two bosonic modes, where the underlying SU(1,1) dynamical symmetry enables the generation of multicomponent SU(1,1) compass states. Specifically, the compact evolution of SU(1,1) coherent states under the considered dynamics enables the generation of multicomponent SU(1,1) compass states at specific times. We also investigate the effects of thermal decoherence on these multicomponent compass states within a frequency-resolved Lindblad framework, demonstrating the evolution and degradation of their nonclassical signatures.

We study quantum repeater chains in which entangled links between neighbouring nodes are created through heralded entanglement generation and adjacent links are swapped as soon as possible. Since heralded entanglement generation attempts succeed only probabilistically, some links will have to be stored in quantum memories at the nodes of the chain while waiting for adjacent links to be generated. The fidelity of these stored links decreases with time due to decoherence, and if they are stored for too long then this can lead to low end-to-end fidelity. Previous work has shown that the end-to-end fidelity can be improved by deterministically discarding links when their ages exceed some cutoff value. Such deterministic cutoff policies provide strict control of the fidelity of all links, but they come at the expense of having to track link ages. In this work, we introduce a probabilistic cutoff policy that does not require tracking link ages, at the cost of abandoning strict control of the fidelity. We benchmark this new probabilistic cutoff policy against a deterministic cutoff policy. We compare the policies in terms of the end-to-end rate and fidelity, and the secret-key rate. We find that even though the probabilistic cutoff policy keeps track of less state, it can provide secret-key rates of the same order of magnitude as the deterministic cutoff policy in chains with few nodes or high elementary link generation probabilities. Moreover, we identify a scenario in which the probabilistic cutoff policy can deliver end-to-end links that are required to have some minimum threshold fidelity at a higher rate than the deterministic cutoff policy.

Photonic quantum memristors provide a measurement-induced route to nonlinear and history-dependent quantum dynamics. Experimental demonstrations have so far focused on isolated devices or simple cascaded devices configurations. Here, we experimentally realize and characterize a network of two coupled photonic quantum memristors with crossed feedback, implemented on a silicon nitride photonic integrated circuit and fed by a room-temperature single-photon source based on a silicon-vacancy color center SiV$^-$ in a nanodiamond. Each memristor consists of an integrated Mach-Zehnder interferometer whose transfer function is adaptively updated by photon detection events on another memristor, thus generating novel non-Markovian input-output dynamics with an enhanced memristive behaviour compared to single devices. In particular, we report inter-memristor input-output hysteresis curves exhibiting larger form factors and displaying self-intersecting loops, respectively revealing marked bistability and self-intersecting hysteresis geometry. Furthermore, numerical simulations show how these features emerge from the interplay between memory depth and relative input phase, for both intra- and inter-memristor input-output relations. We experimentally test the performance of our system in the NARMA task. Our results establish coupled integrated photonic quantum memristors as scalable nonlinear building blocks and highlight their potential for implementing compact quantum neuromorphic and reservoir computing architectures.

The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most $k$ subsystems. For $n$-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the $k$-local Pauli-accessible amplitude $A_{k}(p)$, which lower bounds the optimal $k$-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where $k$-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.

We derive simple and unified closed-form expressions for projections with respect to fidelity (equivalently, the Bures and purified distances) onto several sets of interest. These include projections of bipartite positive semidefinite (PSD) matrices onto the set of PSD matrices with a given marginal, and projections of ensembles of PSD matrices onto the set of PSD decompositions of a given matrix, with important special cases corresponding to projections onto the set of quantum channels (via the Choi isomorphism) and onto the set of measurements. We introduce prior-channel decompositions of completely positive (CP) maps, which uniquely decompose any CP map into a prior PSD matrix and a quantum channel. This decomposition generalizes the Choi-Jamiolkowski isomorphism by establishing a bijective correspondence between arbitrary bipartite PSD matrices and channel-state pairs, and we show that it arises naturally from the fidelity projections developed here. As applications, we show that the pretty good measurement - associated with a weighted ensemble - is the fidelity projection of the ensemble onto the set of measurements, and that the Petz recovery map - associated with a reference state and forward channel - is the projection of a CP map (constructed from the channel-state pair) onto the set of reverse quantum channels, thereby recasting the well-known identification of the Petz map with quantum Bayes' rule in information-geometric terms. Our results also provide an information-geometric underpinning of the Leifer-Spekkens quantum state over time formalism [Leifer and Spekkens, Phys. Rev. A 88, 052130 (2013)].

In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting the structural properties of the underlying graph states. Although distinct error patterns may yield the same syndrome, we demonstrate that the post-measurement state follows a well-defined structure determined by the projective syndrome measurement. Building on this idea, we introduce a hierarchical decoder in which each level can be solved in polynomial time. Additionally, this decoder achieves optimal decoding performance at the lower levels of the hierarchy. This strategy avoids the need for full maximum-likelihood decoding of graph codes. Numerical results illustrate the efficiency and effectiveness of the proposed approach.

Non-Hermitian systems with globally reciprocal couplings – such as the Hatano-Nelson model with stochastic imaginary gauge fields – avoid the conventional non-Hermitian skin effect, displaying erratic bulk localization while retaining ballistic transport. An open question is whether similar behavior arises when non-reciprocity originates at the Liouvillian level rather than from an effective non-Hermitian Hamiltonian obtained via post-selection. Here, a lattice model with globally reciprocal Liouvillian dynamics and locally asymmetric incoherent hopping is investigated, a disordered setting in which Liouvillian-specific effects have remained largely unexplored. While the steady state again shows disorder-dependent, erratic localization without boundary accumulation, {\color{black}excitations in the incoherent-hopping regime spread via Sinai-type subdiffusion, dramatically slower than ordinary diffusion in symmetric stochastic lattices.} {\color{black}This highlights that the genuinely distinct Liouvillian signature is the coexistence of global reciprocity with ultra-slow, disorder-induced subdiffusive transport, rather than the erratic localization itself.} {\color{black}These results reveal a fundamental distinction between globally reciprocal Hamiltonian and Liouvillian systems: in both cases the skin effect is suppressed, but only in Liouvillian dynamics erratic skin localization can coexist with subdiffusive transport

Spurious couplings and decoherence degrade the performance of solid-state quantum processors, demanding careful design, calibration, and mitigation protocols. These strategies often rely on characterization of the idling processor, but tomographic recovery of (time-independent) Lindblad dynamics scales exponentially with qubit count. Here, we experimentally benchmark and demonstrate that randomized ("shadow") measurements accelerate Lindblad tomography on a superconducting transmon processor. We first implement extensible Lindblad tomography, which estimates Lindblad parameters using a complete tomographic dataset, and use it as a baseline to benchmark a shadow tomography approach, shadow Lindblad tomography. The shadow approach recycles randomized configurations to estimate the same Lindblad parameters using far fewer resources under physically motivated locality assumptions. We experimentally verify these assumptions in our processor by implementing the protocols on one- and three-qubit subsystems; here, shadow Lindblad tomography reproduces extensible Lindblad tomography within uncertainties while using exponentially fewer configurations. Leveraging this efficiency, we apply shadow Lindblad tomography to the full five-qubit processor and recover all single qubit dissipation and two-qubit coupling parameters in 9 hours of acquisition time compared to an estimated 58 hours for extensible Lindblad tomography. Additionally, our shadow implementation is compatible with conventional Gaussian error propagation, avoiding the use of median-of-means estimators. Together, these results demonstrate how randomized shadow tomography protocols can be practically implemented to learn quantum processor dynamics at an increasing qubit count.

Multiparameter quantum metrology plays a fundamental role in uncovering and exploiting the distinctive features of quantum systems. In this work, we propose an effective and experimentally feasible scheme to significantly enhance the simultaneous quantum estimation of the photon magnon and magnon mechanical coupling strengths in a hybrid cavity magnon mechanical platform. Our approach relies on the assistance of a coherent feedback loop combined with the injection of a coherent driving field. We show that an appropriate tuning of the system and feedback parameters leads to a substantial reduction of the estimation errors associated with both coupling strengths. To quantify the metrological performance of the proposed scheme, we employ the quantum Cramer Rao bound (QCRB) as a fundamental benchmark for multiparameter estimation. We explicitly compute and compare the QCRBs derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD) formalisms. Our results demonstrate that the RLD based QCRB is systematically lower than the SLD based bound, indicating superior estimation precision in the considered noncommutative estimation scenario. We further analyze the performance of heterodyne detection and show that, in suitable parameter regimes, the corresponding classical estimation precision closely approaches the ultimate quantum limit predicted by our scheme. Finally, we discuss the experimental feasibility of the proposed setup within currently available cavity magnon mechanical platforms. Owing to its general character, the framework developed here can be readily extended to the high precision estimation of other physical parameters in hybrid quantum systems.

Compatibility with noisy intermediate-scale quantum (NISQ) devices is crucial for the realistic implementation of quantum cryptographic protocols. We investigate a cryptographic scheme based on discrete-time quantum walks (DTQWs) on cyclic graphs that exploits Parrondo dynamics, wherein periodic evolution emerges from a deterministic sequence of individually chaotic coin operators. We construct an explicit quantum circuit realization tailored to NISQ architectures and analyze its performance through numerical simulations in Qiskit under both ideal and noisy conditions. Protocol performance is quantified using probability distributions, Hellinger fidelity, and total variation distance. To assess security at the circuit level, we model intercept-resend and man-in-the- middle attacks and evaluate the resulting quantum bit error rate. In the absence of adversarial intervention, the protocol enables reliable message recovery, whereas eavesdropping induces characteristic disturbances that disrupt the periodic reconstruction mechanism. We further examine hardware feasibility on contemporary NISQ processors, specifically ibm_torino, incorporating qubit connectivity and state-transfer constraints into the circuit design. Our analysis demonstrates that communication between spatially separated logical modules increases circuit depth via SWAP operations, leading to cumulative noise effects. By exploring hybrid state-transfer strategies, we show that qubit selection and connectivity play a decisive role in determining fidelity and overall protocol performance, highlighting hardware-dependent trade-offs in NISQ implementations.

Finding optimal measurement operators is crucial for the performance of quantum reservoir computers (QRCs), since they employ a fixed quantum feature map. We formulate the training of both stateless (quantum extreme learning machines, QELMs) and stateful (memory dependent) QRCs in the framework of kernel ridge regression. We thus extend the kernel viewpoint of supervised quantum models to recurrent QRCs by deriving an exact Hilbert–Schmidt kernel representation of the optimal readout observable on history space. This approach renders an optimal measurement operator that minimizes prediction error for a given reservoir and training dataset. For large qubit numbers, this method is more efficient than the conventional training of QRCs. We discuss efficiency and practical implementation strategies, including Pauli basis decomposition and operator diagonalization, to adapt the optimal observable to hardware constraints. To demonstrate the effectiveness of this approach, we present numerical experiments on image classification and time series prediction tasks, including chaotic and strongly non-Markovian systems. The developed method can also be applied to other quantum machine learning models.

This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated properties of the most commonly used geometric representation, the Bloch sphere visualization of qubit states, we show how concepts, algorithms, and spatial relations viewable on this geometric representation can be extended to representations of qudit states of any finite quantum dimension $d$ and on to the infinite-dimensional limit. A primary goal of the work is helping the reader develop a visual intuition of these spaces, which can complement the understanding of the algebraic formalism of quantum mechanics for learners, teachers, and researchers at any level. Particular emphasis is given both to understanding states in a basis-independent way and to understanding how probability amplitudes and density matrix elements used to algebraically represent states in a particular basis correspond to line segments and angles in the geometric representations. In addition to providing visualizations for such concepts as superpositions, mixtures, decoherence, and measurement, we demonstrate how the representations can be used to substitute simple geometrical calculations for more cumbersome linear algebra ones, which may be of particular use in introducing mixed states and density matrices to beginning quantum students at an early stage. The work concludes with the geometrical interpretation of some commonly used metrics such as the purity of states and their relation to real, Euclidean vectors in the infinite-dimensional limit of the space, which contains all lower-dimensional qudit spaces as subspaces.

We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schrödinger equation. On one hand, we show that a closed quantum system is defined by local boundary conditions. On the other hand, we argue that, because of the uncertainty principle, no local boundary condition can be defined for open quantum systems. For this reason plane waves or wave packet trains cannot be simulated on a finite numerical lattice with the usual procedures. We suggest a method that avoids these difficulties by using only a small numerical lattice and maintains the correspondence with the physical picture, in which the incident and scattered waves may be infinitely extended.

A major challenge in open quantum dynamics is the inclusion of Matsubara-decay terms in the memory kernel, which arise from the quantum-Boltzmann delocalisation of the bath modes. This delocalisation can be quantified by the radius of gyration squared ${\mathcal R}^2(\omega)$ of the imaginary-time Feynman paths of the bath modes as a function of the frequency $\omega$. In a Hierarchical Equations of Motion (HEOM) calculation with a Debye–Drude spectral density, ${\mathcal R}^2(\omega)$ is the only quantity that is treated approximately (assuming convergence with respect to hierarchy depth). Here, we show that the well-known Ishizaki–Tanimura correction is equivalent to separating smooth from `Brownian' contributions to ${\mathcal R}^2(\omega)$, and that modifying the correction leads to a more efficient HEOM in the case of fast baths. We also develop a simple `A4' adaptation of the `AAA' (Adaptive Antoulas–Anderson) algorithm in order to fit ${\mathcal R}^2(\omega)$ to a sum over poles, which results in an extremely efficient implementation of the standard HEOM method at low temperatures.

Biomarker-based prediction of clinical outcomes is challenging due to nonlinear relationships, correlated features, and the limited size of many medical datasets. Classical machine-learning methods can struggle under these conditions, motivating the search for alternatives. In this work, we investigate quantum reservoir computing (QRC), using both noiseless emulation and hardware execution on the neutral-atom Rydberg processor Aquila. We evaluate performance with six classical machine-learning models and use SHAP to generate feature subsets. We find that models trained on emulated quantum features achieve mean test accuracies comparable to those trained on classical features, but have higher training accuracies and greater variability over data splits, consistent with overfitting. When comparing hardware execution of QRC to noiseless emulation, the models are more robust over different data splits and often exhibit statistically significant improvements in mean test accuracy. This combination of improved accuracy and increased stability is suggestive of a regularising effect induced by hardware execution. To investigate the origin of this behaviour, we examine the statistical differences between hardware and emulated quantum feature distributions. We find that hardware execution applies a structured, time-dependent transformation characterised by compression toward the mean and a progressive reduction in mutual information relative to emulation.

The study of spin decoherence is often performed by assuming that spin-phonon interactions lead to relaxation at high temperatures, and spin-spin dipolar interactions instead contribute to pure dephasing at low temperatures. This has resulted in the neglect of spin relaxation due to spin-spin dipolar interactions and its influence on decoherence at low temperatures. For a complete understanding of low temperature spin dynamics, it is then imperative to focus also on the latter mechanism. One such method which has shown great promise in the efficient calculation of central spin dynamics due to spin-spin dipolar interactions with a surrounding spin bath is the Cluster-Correlation Expansion (CCE). An extension of this method through the explicit inclusion of the central spin degrees of freedom, known as the generalized Cluster-Correlation Expansion (gCCE) is capable of simulating the transfer of energy from the central spin into the bath, and thus could have the potential to investigate spin relaxation in this setting. In this work, we show that gCCE, in its standard form, is insufficient for providing even a qualitatively accurate description of spin-spin relaxation. A full mathematical deconstruction of the underlying theory of gCCE clearly points to the origin of such a breakdown and provides a starting point for its potential future resolution.

We explain the achievements that were awarded 2022 Nobel Prize in Physics, as well as the preceding and the later developments. The main notions and historic cornerstones of Bell inequalities, the related researches on quantum entanglement are reviewed, and the key physical ideas are emphasized. Among the early work, C. S. Wu's contributions using polarization-entangled photons from electron-positron annihilation are introduced.

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity while remaining compatible with near-term quantum hardware. In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs, using one- and two-dimensional heat equations as canonical benchmarks. We introduce two quantum-assisted architectures that differ in their embedding components. In the first approach, a classical feed-forward neural network generates trainable feature maps for quantum data encoding (FNN-TE-QPINN). In the second, the embedding stage is realized entirely by a parameterized quantum circuit (QNN-TE-QPINN), yielding a fully quantum feature map. Our findings emphasize the critical role of embedding design and support hybrid quantum-classical approaches for parabolic PDE modeling in the NISQ era.

Zernike phase-contrast imaging is unique among imaging techniques in that it enables the upper limit of Fisher information allowed by quantum mechanics. Here we show that, in a departure from an ideal setting, using an incident beam of finite width, and a $\pi/2$ phase plate having a finite cutoff, the technique can still deliver $>95\%$ of the quantum limit. We point out that the Zernike method is, in principle, applicable to any incident beam. As an example, we sketch an approximate implementation of the method for an incident speckle beam, and show that it too can deliver $>95\%$ of the quantum limit.

We introduce dissipative spectroscopy as a framework for extracting spectral information from quantum systems via controlled dissipation. By establishing a general dissipative response theory applicable to both Markovian and non-Markovian environments, we develop a protocol to access the dissipative spectrum (DS) through driven oscillation-dissipation resonance. We show that the DS can identify two-particle soft modes near quantum critical points and, on the normal-phase side, predict the emergence of macroscopic order exhibiting power-law growth following a dissipation quench. These distinctive signatures appear in quasiparticle-dominant regimes, previously considered trivial. Furthermore, we introduce extended dissipative susceptibilities that capture leading memory effects and demonstrate their utility in a dissipative fermionic model. Our results indicate that the DS is readily accessible and offers a versatile tool for probing equilibrium properties as well as predicting nonequilibrium dissipative dynamics.

Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a predefined set of basis functions, and the corresponding coefficients are sparsely estimated from observed time-series data. In this study, we propose sparse identification of quantum Hamiltonian dynamics (SIQHDy), a SINDy-inspired quantum circuit learning framework for estimating quantum Hamiltonian dynamics from time-series data of quantum measurement outcomes. In SIQHDy, the unitary evolution of a quantum Hamiltonian system is expressed as a product of basis quantum circuits, and the corresponding circuit parameters are estimated through sparsity-promoting optimization. We numerically demonstrate that SIQHDy accurately reconstructs the dynamics of single-, three-, and five-spin systems, and exhibits robustness to measurement noise in the three-spin case. Furthermore, we propose an extension of SIQHDy for scenarios with limited accessible observables and evaluate its performance in identifying two-spin systems and in network-structure identification for five-spin systems.

We study relativistic twisted (orbital-angular-momentum) states of a massive charged particle propagating through an axially symmetric, longitudinally inhomogeneous solenoid field and a co-directed accelerating or decelerating electric field. Starting from the Dirac equation and using controlled spinless and paraxial approximations, we show that the transverse envelope obeys an effective nonstationary Schrödinger equation governed by a Caldirola–Kanai Hamiltonian. The longitudinal energy gain or loss encoded in $f(z)=[E_0-V(z)]^2-m^2$ generates an effective gain or damping rate $\widetilde{\gamma}(z)=\partial_z f(z)/[2f(z)]$ and a $z$-dependent oscillator frequency $\widetilde{\omega}(z)=p_0\Omega(z)/\sqrt{f(z)}$. Exploiting the Ermakov mapping (unitary equivalence of Caldirola–Kanai systems), we obtain a closed-form propagated twisted wave function by transforming the stationary Landau basis. The transverse evolution is controlled by a single scaling function $b(z)$ that satisfies a generalized Ermakov–Pinney equation with coefficients determined by $E_z(z)$ and $B_z(z)$. In the limiting cases of uniform acceleration with $B_z=0$ and of solenoid focusing with negligible acceleration, our solution reduces to previously known analytic results, providing a direct bridge to established models.

Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the multi-objective optimization conflicts and local optima traps inherent in coupled problems. To address the first issue, we propose a Forked PINN (FPINN) framework designed for coupled systems of DEs. FPINN employs a shared base network with independent branches, isolating gradient pathways to stabilize training. We demonstrate the effectiveness of FPINN in simulating non-Markovian open quantum dynamics governed by coupled DEs, where multi-objective conflicts and local optima traps often cause evolutionary stagnation. To overcome this second challenge, we incorporate an evolution regularization loss that guides the model away from trivial solutions and ensures physically meaningful evolution. We demonstrate the effectiveness of FPINN in simulating non-Markovian open quantum dynamics governed by coupled DEs, where multi-objective conflicts and local optima traps often cause evolutionary stagnation. For the spin-boson and XXZ models, FPINN accurately captures hallmark non-Markovian features, such as quantum coherence revival and information backflow, significantly outperforming standard PINNs. The proposed FPINN architecture offers a general and effective framework for solving coupled systems of equations, which arise across a broad spectrum from classical physics to modern artificial intelligence, including applications in multi-body rotational dynamics, multi-asset portfolio optimization, chemical reaction kinetics, and deep representation learning.

Classical polarization optics is naturally described by a two-dimensional complex Hilbert space (Jones vectors), so the tensor-product kinematics underlying bipartite nonseparability is already available classically. For statistical (stochastic) optical fields, and under an operational stance where outcomes are not assumed pre-assigned prior to detection, suitably prepared two-beam polarization states can exhibit Bell–CHSH correlations of quantum strength. The same platform offers a tunable, low-cost testbed for stress-testing Bell/CHSH and contextuality witnesses under realistic imperfections (noise, coarse binning, selective sampling). We also outline an alternative preparation based on external conical refraction (ECR), where engineered intersecting conical-refraction rings mimic the intersecting emission cones of SPDC. We give a self-contained categorical formulation: the preparation-and-conditioning pipeline (Hadamard-like splitting, CNOT-like coupling, and routing/conditioning that removes unwanted contributions) is treated as a single morphism in an operational process theory (e.g. $\mathbf{CPM}(\mathbf{FHilb})$). From it we functorially extract an empirical model, i.e. a compatible family of context-indexed probability distributions. The Abramsky–Brandenburger sheaf criterion then applies: noncontextuality is the existence of a global section, and CHSH violation is a precise failure-to-glue. This separates kinematic nonseparability from operational contextuality and clarifies why neither, by itself, entails nonlocal causation; contextuality can arise in a classically implementable stochastic-optics regime.

Transversal Pauli Z rotations provide a natural route to fault-tolerant logical diagonal gates in quantum Calderbank-Shor-Steane (CSS) codes, but their capability is inherently constrained. We develop a homological framework that organizes transversal diagonal gates in terms of their logical action and physical implementation, revealing two layers of structure that govern their behavior. At a fixed level, we establish that their logical action admits a classification in terms of homological data of the underlying chain complex, extending the standard description of logical operators. We then formulate the refinement to finer angles as a lifting problem and derive two Bockstein-type obstruction maps, whose vanishing is a necessary and sufficient condition for the existence of a transversal logical diagonal gate at the next level. Within this framework, known algebraic conditions such as divisibility and triorthogonality are reinterpreted as necessary conditions for the existence of transversal logical diagonal gates with uniform rotation angles. Our results identify homological obstructions governing transversal implementability and provide a conceptual foundation for a formal theory of transversal structures in quantum error correction.

The establishment of extremely strong bounds on the magnitude of the electric dipole moment of the neutron, a quantity that is of great importance for determining the level of time reversal symmetry respected by the strong interactions, offers an important lesson regarding the manner in which quantum uncertainties are interpreted in the inflationary cosmological account of the generation of the primordial inhomogeneities that give rise to the universe's structure. The identification of quantum uncertainties with actual stochastic fluctuations, a standard aspect of the current physical account for the emergence of the cosmic structure, is called into question. This opens the door for novel aspects of physics that are needed in order to provide a satisfactory account that is both conceptually clear and does not conflict with the use of quantum theory in other settings.