Papers

We establish the exact exponent for smoothing the max-relative entropy on arbitrary von Neumann algebras. The proof first develops the required large-deviation and smoothing estimates in the semifinite setting and then passes to general von Neumann algebras through Haagerup-Junge-Xu reduction. We next study catalytic quantum information decoupling when the reference system is described by an arbitrary von Neumann algebra. A key ingredient is an operator layer-cake formula valid on arbitrary von Neumann algebras. This formula leads to a convex-split estimate for normal states with a general von Neumann algebraic reference system. Combining this estimate with the smoothing exponent result, we obtain lower and upper bounds on the catalytic-decoupling reliability function. These bounds coincide below the corresponding critical rate, yielding the exact decoupling reliability function in that regime.

On finite system sizes, monitored one-dimensional free-fermion chains display a broad crossover in entanglement scaling as the measurement rate increases, from sub-extensive behavior at weak monitoring toward an area law at strong monitoring. Analytical field theory and recent large-scale simulations indicate that this apparent change is not a finite-rate transition in the thermodynamic limit. I test, using trajectory-resolved correlation-matrix simulations (chains up to $L=96$ and up to 128 Born-rule trajectories per parameter point), whether two quantities built from the single-particle entanglement spectrum are useful finite-size diagnostics: the bipartite particle-number fluctuation $F_A=\sum_k\nu_k(1-\nu_k)$ and a participation-style effective number of entangling modes, $\mathcal{M}_A=\exp[-\sum_k w_k\ln w_k]$, with $w_k\propto\nu_k(1-\nu_k)$. Both quantities track the crossover. However, for trajectory- and time-averaged steady-state values, $\mathcal{M}$ is nearly a deterministic function of $F$: a pooled curve explains 99.7% of its variance across all rates, so $\mathcal{M}$ carries little independent information. Its main advantage is statistical: its trajectory-to-trajectory coefficient of variation is up to a factor of $\sim2$ smaller than that of the entropy or $F$ under strong monitoring. Subsystem-scaling comparisons at $L=48$–$96$ also show that a pure logarithmic law is not statistically preferred under weak monitoring; a small residual quasi-extensive component and a drifting logarithmic coefficient are instead consistent with a crossover rather than a critical phase. Thus, $F$ remains the natural experimentally motivated companion to the entropy, whereas $\mathcal{M}$ is best viewed as a variance-reduced numerical summary of essentially the same information.

The Maximal Covering Location Problem (MCLP) is an NP-hard Combinatorial Optimization Problem (COP) that aims to determine the optimal facility placements that maximize total coverage. It is characterized by both equality and inequality constraints, which ensure correct coverage but significantly increase the complexity of exploring the solution space as instance size grows. Hybrid quantum-classical approaches might offer a promising alternative to classical optimization methods by enabling the exploration of complex energy landscapes through quantum superposition and probabilistic sampling. In this work, the MCLP is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model, where constraint embedding plays a critical role in solution quality. In particular, Unbalanced Penalization (UP) is employed as an alternative to the Slack Variables (SV) for handling inequality constraints without increasing the number of variables. This study focuses on QAOA and one of its variants, the WS-QAOA, which leverages a biased initial state derived from a continuous relaxation of the problem. Additionally, a linear ramp (LR) parameter schedule is incorporated to reduce optimization complexity. The performance of these techniques is evaluated both individually and in combination, as a function of circuit depth $p$ and problem size. Results show that the combined approach of UP, LR, and WS-QAOA consistently improves solution quality and feasibility metrics, while maintaining robust performance as the problem size increases, highlighting its potential within hybrid quantum-classical optimization frameworks.

Quantum-repeater networks require adaptive control policies that balance entanglement generation rate, end-to-end fidelity, purification overhead, and memory-induced latency. This tradeoff becomes more complex when the classical control plane is degraded by cyber anomalies or denial-of-service traffic. We develop a CUDA-Q/SeQUeNCe co-simulation workflow for studying adaptive entanglement purification in heterogeneous linear repeater chains. CUDA-Q noisy quantum kernels are used to estimate primitive entanglement purification and swapping behavior, while SeQUeNCe provides an event-layer model for stochastic link generation, waiting-time-dependent memory decay, purification failure, and end-to-end swapping. Under stationary conditions, we compare no purification, local threshold purification, mean-field predictive purification, fixed purification, and a resource-penalized risk-aware predictive policy. In an 8-node chain, the resource-penalized risk-aware controller increases above-target delivery probability relative to fixed purification while reducing latency and purification overhead. We then couple the quantum-network controller to anomaly scores derived from the CSE-CIC-IDS2018 benign-to-SSDP intrusion-detection trace. During the attack period, the attack-unaware controller maintains high raw delivery, but its above-target entanglement delivery falls to 0.098+/-0.007; the IDS-aware resource-adaptive controller switches to more purification-heavy masks and increases above-target delivery to 0.344+/-0.011, closely matching the oracle-aware value of approximately 0.335. These results demonstrate that cyber-state awareness can improve useful quantum-network outcomes by trading raw throughput for fidelity-qualified entanglement delivery.

Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating correlated cascade failures across multi-tier supplier networks. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a quantum-native framework for retail supply chain risk analysis implemented on the Qiskit ecosystem using OpenFermion-based Ising Hamiltonian encoding. A 40-node, four-tier supply network is mapped to a 40-qubit Hamiltonian with ZZ coupling terms representing correlated supplier dependencies. A hardware-efficient Variational Quantum Eigensolver (VQE) computes the stress ground state, revealing entangled cascade failures that differ substantially from classical Monte Carlo predictions. We further introduce the application of ADAPT-VQE gradient screening for counterfactual policy evaluation, enabling real-time ranking of six crisis interventions without repeated variational optimization. Finally, Density-of-States Quantum Phase Estimation (DOS-QPE) reconstructs the eigenspectrum through Trotter evolution and estimates Boltzmann-weighted catastrophe probabilities as a function of market-volatility temperature, providing a quantum-native tail-risk metric compatible with Value-at-Risk analysis. The framework demonstrates scalable quantum algorithms for correlated supply chain stress propagation, policy optimization, and systemic risk quantification while highlighting the exponential computational barriers faced by classical simulation at industrial-scale problem sizes.

Quantum convolutional neural networks, due to the involvement of quantum measurements and discrete quantum state evolution, face inherent training challenges associated with non-differentiable operations and discrete optimization dynamics, which make conventional gradient-based learning difficult to apply effectively. In this context, energy-based learning provides a promising alternative by reformulating network training as an energy minimization process without explicit gradient backpropagation.In this framework, input data are processed through convolutional operations, followed by quantum sampling to generate intermediate binary representations, while the output layer also relies on quantum sampling to produce final predictions. The overall network energy is composed of convolutional feature matching terms, linear coupling terms at the output layer, and global output constraint terms, enabling both parameter updates and feature evolution to be described through physically interpretable energy dynamics. Furthermore, under the equilibrium propagation mechanism, the energy difference between the free phase and the weakly clamped phase is exploited to drive parameter updates without explicit gradient computation, thereby enabling stable and consistent learning in non-differentiable and discrete spaces. While remaining consistent with classical convolutional learning theory, the proposed framework enhances interpretability and observability through quantum energy modeling, offering a unified physical perspective for efficient QCNN training and the integration of quantum computing with artificial intelligence.

What is the most expensive part of quantum device characterization? Clearly, the answer is quantum process tomography. However, especially for noisy intermediate-scale quantum (NISQ) computers, a comprehensive understanding of the noisy quantum dynamics is essential in interpreting the computational output. In this work, we introduce an efficient method – Procrustes tomography – that outperforms established methods in a number of aspects. After a pedagogical and constructive introduction, we demonstrate the utility of the method for representative examples of noisy quantum channels.

In this work, we have investigated the evolution of satellite intensity near the ionization threshold for Cu K-shell transitions through theoretical methods. Employing standard state-of-the-art ab initio methods, we have calculated all Cu K-shell transitions and simulated the full K$\alpha_1$ and K$\alpha_2$ spectrum where all transition parameters, as well as shake probabilities were determined theoretically. Through these calculations we show that standard state-of-the-art ab initio methods achieve good agreement with experiment and enable us to simulate the intensity evolution near ionization thresholds within a good margin of error. Below-threshold satellite intensity was found to originate from resonant 1s$\rightarrow$3d and 1s$\rightarrow$4p excitations in Cu(I) and Cu(II) oxide phases respectively, which were included in our simulations.

Quantum reservoir computing uses a fixed quantum circuit as a feature generator and trains only a simple linear readout on top of it. This makes it cheap to train and free of the optimisation problems that affect many quantum machine-learning models. A natural worry is that the very large feature space the circuit produces might inflate apparent performance without adding anything real. This paper provides two things. First, it gives a complete, reproducible recipe for one such reservoir applied to forecasting chaotic systems, including how data is fed in, how the circuit is built, and how the readout is trained. Second, it gives a way to tell whether the reservoir's high dimension is actually doing useful work. We grow the size of the prediction problem and the size of the quantum reservoir together, so that extra capacity cannot be the explanation for any improvement, and we track a single stability number that measures how well behaved the readout fit is. On two chaotic test systems, a spatiotemporal chain and a shallow-water fluid model, the quantum reservoir keeps a flat, stable error as both sizes grow, while a matched classical reservoir does not. We report where the classical baseline is in fact stronger, so the comparison is honest. The result is a clean specification plus a diagnostic that other groups can apply to any reservoir whose features have a known scale.

Quantum mechanics abandoned the classical notion of a particle trajectory, yet trajectories remain conceptually appealing for resolving foundational issues in quantum mechanics. Bohmian mechanics offers one route to associating trajectories with quantum processes, but it requires explicit non-locality to remain consistent with EPR-type experiments, placing it in tension with special relativity. We propose an alternative approach: rather than deriving trajectories from a quantum guidance equation, we search for classical trajectories whose radiated frequency spectra match those of quantum processes such as atomic transitions. Using the Liénard-Wiechert potentials, we compute the electric and magnetic fields generated by a point charge along a given trajectory, numerically solving the retarded-time and from these fields obtain the power spectrum of emitted radiation. By fitting the parameters of a chosen family of trajectories, we identify "equivalent spectrum" trajectories that reproduce a target frequency distribution, including ones of quantum mechanical origin. We discuss the implications of this method and propose future work to determine whether equivalent spectrum trajectories belong to a family governed by a differential equation, which would constitute a quantum-equivalent equation of motion.

Variational quantum algorithms depend on the geometry of their parametrised circuits: metric-aware optimisation and time evolution require the Fubini-Study metric, which has hitherto demanded costly auxiliary measurements and ill-conditioned inversions. This work introduces a hardware-efficient $n$-qubit ansatz, which parametrises states by a binary tree and whose Fubini-Study pullback metric is diagonal in closed form. Quantum natural gradient on the tree parameters, variational imaginary- and real-time evolution, and exact unitary-invariant (Haar) sampling on a symmetry sector run with no auxiliary metric circuits or matrix inversion. When the target state is supported on a subspace of $k$ computational-basis states, the redundant tree parameters carry a gauge freedom a pruning compiler converts into circuits whose two-qubit count provably grows linearly in $k$; a variant reaches near-optimal $O(nk/\log n)$ scaling with the closed-form metric intact. On electronic-structure calculations for small molecules and half-filled Hubbard quench dynamics, the method reaches reference-level accuracy with one to three orders of magnitude fewer two-qubit gates than leading alternatives. Interchangeable constructions (a Schur-transform dressing or internal reparameterisations) make the ansatz exactly spin-adapted, with fixed total spin at every parameter and no penalty terms. The bare ansatz is an exactly controllable, well-conditioned and barren-plateau-free primitive for preparing and sampling sector states: on its own, it is classically simulable in $k$ (a boundary proved for a general class of sector-sparse ansätze); composed with a classically hard dressing, it yields molecular ground states, sector-Haar benchmarking, thermal correlators, and exact effective Hamiltonians trained from energy measurements alone, with the composed circuit carrying the potential for quantum advantage.

We show the effect of gate-induced strain on the valence band of a silicon (Si) metal oxide semiconductor (MOS) confined two-dimensional hole gas (2DHG). Increasing aluminum gate thickness, and thereby the strain in the channel, results in the onset of a second subband contributing to Shubnikov-de Haas oscillations. Temperature-dependent magnetotransport measurements reveal distinct cyclotron masses of $m_c^*=(0.36\pm0.04)m_0$ and $m_c^*=(0.49\pm0.02)m_0$. The measured cyclotron masses differ from those expected for an idealized heavy-hole (HH)/light-hole (LH) picture, reflecting the combined influence of quantum confinement, strain, and HH-LH mixing on the valence band.

We report precision measurements of the ratio of Landé $g$ factors between the $3^2D_{5/2}$ and $4^2S_{1/2}$ states of a single trapped $^{40}\text{Ca}^+$ ion. The measurements are performed in two distinct ion trap apparatus: a cryogenic surface electrode radiofrequency Paul trap and a room-temperature permanent magnet Penning trap. The Penning trap measurements rely on resonant microwave excitation of magnetic sublevels and yield a ratio of $0.599~488~813~3(2)$, which is a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurements utilize optical electric quadrupole transitions and yield a concurring value of $0.599~488~813(6)$. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.

Machine-learning models often replace vectors by normalized directions, projectors, covariances, subspaces, ordered flags, quantum states, or density operators before any classifier is fitted. This replacement is an invariance decision: it determines which distinctions are kept and which are quotiented out. We develop a self-contained real-to-Hermitian taxonomy for auditing such representations in quantum machine learning. On the real side, we formalize Grassmann and flag projector kernels, prove positive semidefiniteness and block-gauge invariance of a weighted flag kernel, and give a same-span block-swap witness showing when whole-span Grassmann geometry must fail while ordered flags succeed. On the quantum side, we prove that a noiseless fidelity kernel is exactly the Hilbert–Schmidt inner product between the associated rank-one Hermitian projectors, and that a QVR-style return probability is exactly an overlap score between the input projector and a learned anchor operator. Rank-constrained returns correspond to complex Grassmann anchors, while mixed or multimodal class models are naturally represented by density or positive-semidefinite anchors. Controlled vector, subspace, statevector, anomaly, finite-shot, and quotient-witness experiments support the same conclusion: quantum and geometric lifts are useful when their invariances match the task, and fail correctly when discarded information is label-bearing. The paper makes no hardware-speedup or quantum-advantage claim.

We use linear programming to prove a separable version of Ky Fan's majorization relation for a sum of two operators that are each a tensor product of $n$ positive semidefinite operators. We give an example showing that such a relation does not hold in general for sums of three or more tensor products of three or more positive semidefinite operators.

Hyperon–antihyperon pairs produced in $e^{+}e^{-}\rightarrow J/\psi\rightarrow Y\bar{Y}$ ($Y=\Lambda,\Sigma^{+},\Xi^{-},\Xi^{0}$) constitute a unique high-energy platform for probing quantum correlations through experimentally accessible spin observables. We investigate the impact of correlated dephasing environments on the stationary and dynamical properties of logarithmic negativity, geometric quantum discord, and $l_{1}$-norm quantum coherence under both longitudinal and transverse beam polarizations. Our analysis reveals that environmental memory plays a crucial role in preserving quantum resources. In the non-Markovian regime, information backflow generates recurrent revivals of quantum correlations and significantly delays decoherence, whereas Markovian evolution drives the system toward asymptotic stationary states through an irreversible loss of quantum information. The influence of beam polarization is found to be strongly channel dependent and can substantially enhance the amount of accessible quantum correlations. A comparative investigation of different quantifiers uncovers a clear hierarchy of quantum resources. Quantum coherence remains robust over the widest parameter range, geometric quantum discord survives even in regions where entanglement is strongly reduced, while logarithmic negativity is the most sensitive to environmental degradation. This hierarchy persists for all considered hyperon channels and under both polarization configurations. The dependence of quantum resources on the production angle, azimuthal angle, polarization degree, and memory parameter is examined using experimental inputs from BESIII. The predicted effects are found to be compatible with the precision expected at BESIII and future high-luminosity facilities such as STCF and CEPC.

Integrated photonics provides a scalable platform for quantum information processing. In this context, measurement-based quantum computing (MBQC) offers an attractive approach in which quantum computation is realised by adaptive measurements on highly entangled graph states, circumventing the need for deterministic photon-photon interactions. Here, we demonstrate MBQC on an integrated silicon photonic chip capable of generating photonic graph states with up to four qubits. We achieve fidelities of $F_{Star} = (83.5 \pm 1.8)\,\%$ and $F_{Lin} = (75.6 \pm 1.1)\,\%$ for four-photon star and linear graph states, respectively. We use these resource states to implement MBQC-based single- and two-qubit gates and to demonstrate Grover's search algorithm and the Deutsch-Jozsa algorithm. These results establish the feasibility of reconfigurable four-photon MBQC on an integrated photonic platform and provide a foundation for future larger-scale implementations.

We study the complex eigenvalue statistics of the asymmetric quantum baker map with partial projective openings. The classical asymmetric baker map, with its discontinuity at $q=2/3$, is fully chaotic, has no reflection symmetry, and provides a clean setting with tunable escape rate and fractal repeller dimension. We consider three distinct opening geometries in position space: localized (contiguous channels), random, and uniform (equispaced channels), all controlled by a tunable amplitude reflectivity parameter $\rho$ that interpolates between the fully open ($\rho=0$) and the closed ($\rho=1$) limits. We use the partially truncated circular unitary ensemble (PTCUE) as the random matrix theory benchmark. The main focus is on the joint distribution of the complex spacing ratio $z$, defined as the ratio of the distances from an eigenvalue to its nearest and next-nearest neighbors in the complex plane. We find a smooth crossover from a quasi-1D spectral regime, where eigenvalues cluster near the unit circle and the phase distribution of $z$ is peaked, to a two-dimensional Ginibre-like regime, where the distribution becomes nearly uniform and level repulsion is fully developed. Both the number of open channels $M$ and the reflectivity $\rho$ modulate this crossover, and $\rho$ provides an additional continuous control even at fixed opening size. All three opening models converge to PTCUE statistics at large $M$, while differences are most pronounced for the localized model at small $M$. No evidence of an abrupt transition is found. This crossover which suggests a universal behavior, has deep consequences for open quantum and wave-chaotic experiments.

Physics-informed neural networks and neural quantum states have consolidated a new paradigm to analyze and discover physical phenomena through constrained neural parametrizations. In this context, we investigate whether the semiclassical structure of the eigenfunctions of a quantum chaotic system can be unveiled through unsupervised learning. To this end, we train a "quantum dictionary", formulated as an overcomplete autoencoder, that sparsely represents the eigenstates of the system, using as an illustration the quantum baker map. The only explicit physical information imposed on the dictionary atoms is their localization in phase space, without providing any kind of information about the periodic orbits of the corresponding classical system. The model achieves high fidelity in reconstructing eigenstates not used during training. By comparing the learned atoms with an independently constructed "semiclassical dictionary", we find that they spontaneously localize on the periodic orbits and develop scar-like structures. This result is interesting in two ways: a localization constraint is sufficient to recover nontrivial semiclassical organization from spectral data and at the same time periodic orbits confirm their fundamental role in the structure of quantum chaotic eigenfunctions. More generally, our proposed architecture opens a new route to learning representations whose atoms optimize other chosen physical properties.

Twisted atomically thin layers have attracted much attention for Moiré potential and correlated quantum phenomena. However, existing Moiré superlattices have largely been limited to extensive wavefunction without lateral confinement. Here we introduce a new platform where 1D nanoribbons of 2D MoS2 grown by vapor deposition can be easily superposed at various angles from stacking and transferring, to form Moiré quantum dots at their intersections with unique exciton physics. Angle-dependent Moiré intersections show enhanced exciton emission at commensurate angle 22 deg, which demonstrates faster relaxation at the cryogenic temperature. A size-dependent study further exhibits a reduced exciton energy and soften out-of-plane interlayer coupling for smaller Moiré areas. Our results reveal exciton physics turnability via precise overlapping of 1D nanoribbons.

We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration. The agents, coordinated through a structured mathematical blueprint and periodic human review, orchestrated and executed the full formalization autonomously. For some statements, the agents were able to explore new proof routes that are not part of the standard literature. Along the way the agents produced extensive tensor-network and quantum-information libraries not previously available in Mathlib, Lean's mathematical library. As a physical application, the formalization also extends towards symmetry-protected topological phases in one dimension. We find that the main bottleneck in large-scale autoformalization is enforcing mathematical intent and we provide a detailed study of the full process and various subtleties involved. We release the codebase as the library \href{https://github.com/LionSR/TNLean}{TNLean}, together with a \nChapters{}-chapter \href{https://lionsr.github.io/TNLean/blueprint/}{blueprint} of the formalization effort.

The advancement of chemistry and materials science relies on transformative analytical tools which can overcome the sensitivity, spatial resolution, and throughput limitations of conventional techniques. This review explores the application of quantum sensors - specifically optically pumped magnetometers (OPMs) and nitrogen-vacancy (NV) centers in diamond - as robust platforms for molecular and materials analysis. We contrast the extreme magnetic sensitivity of macroscopic OPM ensembles with the atomic-scale resolution and multimodal capabilities of solid-state NV centers. We highlight their deployment in zero- to ultralow-field and nanoscale NMR spectroscopy, real-time reaction monitoring, and transient radical and pH detection. Furthermore, we discuss their integration into high-throughput chemical assays and non-destructive materials diagnostics, such as operando battery monitoring. With the ongoing commercialization of these technologies and advances in quantum-enhanced sensitivities, quantum sensors are poised to routinely address complex real-world analytical challenges.

We study the entanglement dynamics of a one-dimensional spinful $s$-wave superconductor subjected to local continuous measurements. In the rare-measurement regime, we derive a replicated Keldysh non-linear sigma model (NLSM) to describe the steady-state entanglement. Within this field-theoretic framework, the interplay between measurement dephasing and superconducting pairing constrains the low-energy, long-wavelength fluctuations to an $\mathrm{SO(R)}$ target manifold. A one-loop renormalization-group analysis shows that the theory develops a weak-anti-localization flow, stabilizing a critical phase with super-logarithmic scaling of the steady-state entanglement. Our field-theoretic results explain the numerical evidence reported in the companion Letter [arXiv:2604.04375] and demonstrate that such a critical phase can emerge in a one-dimensional topologically trivial superconductor without relying on topological protection.

Gate teleportation, together with magic state distillation, is a promising route towards fault-tolerant, universal computation. In the context of bosonic quantum computation, Baragiola et al. PRL 123(20).200502 (2019) showed that within the framework of Gottesman–Kitaev–Preskill codes, encoded magic states suitable for distillation can be produced by error correcting Gaussian states, such as the vacuum. Here, we show that applying the same framework to simple non-Gaussian input states can significantly improve the quality of the magic states obtained, reducing the overall resources for the complete distillation procedure. We focus on superpositions of coherent states or Fock states, showing that many can lead to improvements in the generation of high-quality encoded magic states, which in some cases reduces the resources required for magic state distillation by about a factor $3$. We also investigate the primary source of these improvements and find that, unlike what was previously conjectured, the suitability of input states is not fully explained by symmetry arguments. Instead, the best states seem to avoid projection near stabilizer states as a result of the error correction procedure.

Silicon spin qubits have emerged as a promising qubit technology due to their favorable scaling and fabrication properties. However, efficiently compiling quantum circuits onto spin qubit platforms remains challenging, particularly when accounting for hardware constraints and the high sensitivity to static defects. Existing compilation approaches for spin qubits either largely ignore error correction, despite its critical role for large-scale quantum computation, or focus on low-level schedule constructions, missing a high-level compilation and routing for logical, error-corrected algorithms. To address this gap, we introduce a compilation framework for spin qubits based on the recent snakes on a plane model, which utilizes a 2D surface code and qubit teleportation to mitigate errors. Building on this model, we propose shortest-path and rotation-based algorithms as two novel classes of qubit-routing techniques, along with additional defect-handling and initial-mapping strategies. We evaluate both algorithms across diverse architectural settings and problem sizes, demonstrating that shortest-path methods excel in sparse, low-defect scenarios, while rotation-based approaches perform better in high-density environments. An open-source implementation of our framework is publicly available on GitHub as part of the Munich Quantum Toolkit (MQT) at https://github.com/munich-quantum-toolkit/spin-qubit-routing.

In a class of quantum circuits known as peaked circuits, the goal is to predict the most probable bit string at the output of the circuit. Since these circuits are designed to have a sharp peak in their output distribution, in principle it should be possible to simulate them using a truncated state vector with a limited number of terms, or a fraction of the total probability mass. This approximate simulation can be carried out on a classical computer with a sparse representation that stores only the nonzero amplitudes of the state vector, in contrast to the dense representations that are common in most quantum simulators. For efficiency, all operations on the state vector should be vectorized to the furthest possible extent and, if available, hardware acceleration can also be used. This work describes how these requirements were met in an open-source implementation, and discusses its performance and limitations.

Non-local magic has recently emerged as a fundamental resource for characterizing genuinely non-local non-stabilizer correlations. However, its direct calculation is an intractable numerical problem, except for small systems, and its understanding remains limited. We derive a representation of non-local magic in terms of the Walsh–Hadamard autocorrelations of the entanglement spectrum. Our representation makes the underlying harmonic structure explicit and enables a systematic analysis of its behaviors for various scenarios. We prove that non-local magic can be upper-bounded by an entanglement entropy and we derive exact analytical results for broad classes of quantum states, characterizing the scaling of non-local magic for volume-law states, as well as ground states of one-dimensional gapped and critical systems. Our results identify the spectral organization of the entanglement spectrum as the key ingredient governing non-local magic and provide a framework for further systematic analytical investigation.

Time-bin photonic qubits are well-suited for quantum network applications due to their robustness to polarization instability in fiber links and potential for heterogeneous networks. In this work, we implement the first entanglement-preserving polarization-to-time-bin conversion of a photon qubit in an entangled state with a matter qubit, together with the independent work of Haen et al. \cite{haen2026telecom}. Photons initially generated with polarization encoding are converted to the time-bin basis through a polarization-discriminating asymmetric Mach–Zehnder interferometer. The photonic qubits are generated via the $1092$~nm transition of a $^{88}$Sr$^{+}$ ion. We measure state fidelity bounds of $0.906 \pm 0.011 \le \mathcal{F} \le 0.934\pm 0.011$, with conversion error $< 0.028$, and find this fidelity shows no statistically significant reduction under depolarizing noise, even at full depolarization strength.

Shortcuts to adiabaticity (STA) reproduce adiabatic dynamics in finite time, but their counterdiabatic implementation relies on the adiabatic gauge potential (AGP), which is difficult to compute and implement in many-body systems and whose extension to open and non-Hermitian settings has remained largely model-specific. Here, we develop a general, diagonalization-free framework for engineering STA in non-Hermitian systems by representing the AGP in Krylov space. Starting from an integral representation of the counterdiabatic control, we recast the AGP as a nested-commutator series with controlled locality and generate the associated Krylov basis using the bi-Lanczos and Arnoldi algorithms. This reduces the exact or truncated AGP to a sparse tridiagonal or upper-Hessenberg matrix equation that generalizes the Hermitian construction. We demonstrate the method on a decaying two-level atom, where it recovers the exact drive and signals the exceptional point; on the interacting Hatano-Nelson model, where truncated controls rapidly suppress nonadiabatic excitations; and on a PT-symmetric Heisenberg chain, whose AGP norm detects the PT-symmetry-breaking transition. Throughout, the expansion converges with only a small fraction of the full Krylov space, offering a practical route to fast, accurate control of many-body non-Hermitian systems.

Decoherence is conventionally regarded as an obstacle to realizing topological quantum phases. This has motivated extensive efforts to suppress noise in candidate topological materials and devices. Here, we show that decoherence can instead induce topological phenomena. We demonstrate this in a lattice system subject to environment-induced dephasing. The noise-averaged dynamics, governed by an interacting quantum master equation, realize a topological phase characterized by a winding number and the non-Hermitian skin effect. The dynamical consequence is striking: the correlated nature of the stochastic noise yields asymmetric diffusion, whose direction is fixed by the winding number and is reversible only through a topological phase transition. This effect is induced purely by interactions, distinguishing it from previous studies of free, effectively single-particle systems. It also disappears upon postselecting measurement outcomes, confirming that it is a genuinely open-system phenomenon with no effective Hamiltonian description. Remarkably, the model remains analytically tractable. Our results establish correlated quantum noise as a route to topology in open many-body systems, beyond free-particle and non-Hermitian Hamiltonian paradigms.