Quantum Physics Paper Analysis

Non-Abelian gauge fields play a key role in describing the behavior of particles whose motion is coupled to internal degrees of freedom, such as their spin. Here, we experimentally realize a tuneable non-Abelian gauge field in an active mechanical lattice by using pairs of oscillators to encode a local pseudo-spin for each site, with inter-site spin-dependent couplings engineered via real-time measurement and feedback. We experimentally extract Wilson-loop observables in our set-up and hence demonstrate that we can create a genuinely non-Abelian gauge field. We then exploit the controllability of our mechanical lattice to engineer non-reciprocal hoppings to explore non-Hermitian non-Abelian gauge potentials. For a two-dimensional (2D) lattice, we demonstrate that the non-Hermiticity can manifest in direction-dependent Wilson loops for a single plaquette, while for a one-dimensional (1D) system, we show that a non-Abelian gauge potential can switch the localization of non-Hermitian skin modes between opposite ends of a chain. Our work establishes active mechanical lattices as a flexible and programmable platform for probing non-Abelian gauge fields and exploring their interplay with non-Hermitian dynamics.

Real-time decoding is a critical bottleneck for large-scale fault-tolerant quantum computing. AI-based neural pre-decoders locally correct most physical errors before passing residual syndromes to a global decoder, enabling sub-microsecond latencies. However, existing architectures carry significant overhead from dense 3D convolutions. We present QuantiSpect, a lightweight 3D convolutional neural network (CNN) pre-decoder for the rotated surface code, built on the decoding pipeline of Chamberland et al. The key idea is to replace the dense 3D convolutions with three parallel branches in each residual block: a depthwise spatial branch, a depthwise temporal branch, and a grouped spatio-temporal branch, followed by a squeeze-and-excitation channel gate. This reflects the structure of surface code errors, where spatial and temporal syndrome correlations are partially separable. On a unified 4xA100 GPU benchmark, QuantiSpect matches the receptive field of the Accurate baseline at R=13 while using ~2.71x fewer parameters (0.663M vs 1.80M) and ~2.84x fewer per-voxel convolutional MACs. It matches Accurate's circuit-level threshold and accuracy at moderate and large code distances, reduces the logical error rate by up to ~1.85x relative to uncorrelated PyMatching at d=13, p=0.5%, and speeds up the PyMatching decode by up to 3.11x at d=23. We also explored enlarging the receptive field by adding blocks. Even at R=21, the model uses only 1.18M parameters, fewer than both the R=13 Accurate baseline (1.80M) and the R=17 dense model (4.22M), despite its larger receptive field. This expanded variant significantly outperforms the Accurate model, raising the circuit-level threshold to ~0.80% and further reducing the logical error rate. Together, both variants show that a structure-aware factorized design is an effective, parameter-efficient alternative to a dense one for decoding the surface code.

Sample-based Quantum Diagonalization (SQD) is a hybrid quantum-classical method that replaces variational optimization with a self-consistent recovery loop over QPU samples. Although SQD is considered robust to noisy samples and imperfect classical inputs, its robustness across practical deployment choices has not been systematically analyzed. As a result, shot budgets, qubit layouts, noise mitigation strategies, and the coupled-cluster singles and doubles (CCSD) amplitudes that initialize the ansatz are often chosen without clear empirical guidance. We analyze SQD robustness on IBM Heron hardware across these dimensions. Structured CCSD-amplitude perturbations, including complete zeroing, produce only modest energy shifts from the clean baseline. Differences across layouts and noise-mitigation settings are large in the first recovery iteration but narrow within a few iterations. Accuracy saturates at moderate shot budgets, while very large budgets slightly worsen recovered energies, likely because working-set selection limits the value of additional samples. These results identify where SQD provides genuine deployment robustness and where its limits remain.

We study a quantum particle hopping on an infinite Cayley tree with nearest-neighbor hopping amplitudes drawn from a distribution singular as $|t|^{-a}$ near weak links and no on-site disorder. Because the graph is bipartite, the model has chiral symmetry, which strongly affects the statistics of eigenstates at the center of the spectrum. Using population dynamics to solve the cavity equations for the propagator, we analyze the distribution of the local density of states and show that it develops broad power-law tails. These tails imply an unusual form of wave-function statistics, which we call semi-fractality: the eigenstates occupy an extensive fraction of the system, but their higher moments behave as in a multifractal state. We find that the symmetry properties of the local-density-of-states distribution are not fixed only by the symmetry class, but vary continuously with the exponent controlling the power-law hopping distribution. As this exponent is changed, the system crosses from a semi-fractal regime to a localized one. At the transition, the wave functions realize an extreme intermediate form that we call semi-localized, simultaneously extended in their support but localized according to higher moments.

We construct and experimentally implement compact gate-native circuits that simulate the state-transfer interference underlying three- and four-level chiral-resolution protocols. Both models are encoded in a two-qubit register, with the enantiomer-dependent sign of one of the couplings simulated by a conditional-phase operation in the four-level circuit and by the sign of a final rotation in the three-level circuit. On an IBM quantum processor, the two circuits produce the expected enantiomer-dependent output states with probabilities of nearly $98\%$. We then use these circuits as physically motivated, phase-sensitive benchmarks for composite quantum gates. We introduce rotation-angle error to the single-qubit operations and replace them by several composite gates, including B5, SK1, BB1, H5s, and X5. The comparison demonstrates that single-gate robustness does not translate to equivalent whole-circuit robustness. In particular, variable-rotation sequences do not preserve the required relative phases, making them unsuitable for error correction in circuits. By contrast, the H5s/X5 sequences maintain high target-state populations for relative errors as large as $50\%$, whereas elementary rotations reach the same threshold only for approximately $8\%$. The three-level circuit exhibits a similar enhancement and additionally reveals an error-cancellation symmetry whose protection under composite replacement is exact only when the relevant full propagators satisfy an inverse relation.

Variational Quantum Algorithms (VQAs) are a leading paradigm for near-term quantum computing, combining parameterized quantum circuits with classical optimization across quantum chemistry, combinatorial optimization, and quantum machine learning. Since real-world VQA deployments routinely require circuits that exceed available hardware capacity, quantum circuit cutting has become an indispensable execution strategy, and pre-trained parameters are increasingly distributed through public repositories, introducing supply-chain security risks that have received little attention. Prior quantum backdoor attacks either introduce detectable circuit modifications or depend on device-specific noise, and none consider circuit cutting as an attack surface. We present CutBackdoor, the first parameter-supply-chain backdoor that uses cut circuit execution from CutQC as the deployment-time trigger against VQAs. Under noisy finite-shot circuit-cut execution, poisoned parameters preserve full-circuit validation performance while substantially increasing cut-path reconstruction error, without any circuit modification. The trigger activates when a resource-limited victim responds to a qubit-capacity mismatch by invoking the cutting workflow, requiring no attacker presence at deployment. We provide a theoretical analysis and empirically validate it across varying shot budgets. Evaluation across multiple VQA benchmarks on IBM quantum backends demonstrates cut-path energy amplification of $1.3\times$ to $2.9\times$ \revA{over clean baselines on the VQE and VQD benchmarks while maintaining small stealthiness error on the full-circuit path. The cut-path gap persists across the evaluated backends and cut placements under matched compilation; Zero-Noise Extrapolation provides only partial mitigation, and the diagonal-cost QAOA benchmark delineates the attack's structural boundary

Can a quantum PDE algorithm avoid the polynomial cost of resolving a fine spatial mesh? For standard fixed-order discretizations, direct classical methods require work polynomial in $h^{-1}$, or equivalently in the number of spatial degrees of freedom $N_h=Θ(h^{-d})$. Direct quantum implementations of a parabolic semigroup still have coherent complexity $\widetilde{\mathcal O}(\sqrt{T}/h)$, and gradient-dependent observables such as heat flux and dissipation introduce additional mesh dependence. Decay of the solution norm will further suppress the postselection probability for preparing a normalized final state. We develop a multilevel quantum algorithm that estimates linear and quadratic observables $directly$ and places the fine--coarse cancellation inside the circuit before measurement. A contour-based LCU reconstructs each target-time correction from a coherent family of shifted resolvent differences. Rather than block encoding the fine and coarse inverses separately, we encode their difference through a shifted Ritz--Schur factorization, exposing its $\mathcal O(h_\ell^2)$ two-grid normalization. For Fourier hierarchies, the corresponding SELECT oracle consists of a quantum Fourier or sine transform, a spectral-band selector, and reversible diagonal arithmetic. We also give a non-Fourier realization based on energy-orthogonal dyadic midpoint details in one dimension, together with structured tensor-product extensions under fixed-rank coefficient and access assumptions. For readouts with derivative order $0\leχ\le2$, optimized amplitude estimation removes $all$ polynomial dependence on the finest mesh size. Under the stated access assumptions, both linear and quadratic observables can be estimated with complexity $\widetilde{\mathcal O}(1+(Tε)^{-1})$, with only polylogarithmic dependence on $h^{-1}$.

We investigate the topology of the set $\mathsf E$ of entangled bipartite density operators acting on $\mathbb{C}^{n_1}\otimes\mathbb{C}^{n_2}$. We start by showing that $\mathsf E$ is path-connected, and even simply connected except in the two-qubit case. In this exceptional case $\mathsf E$ turns out to be homotopy equivalent to the set of maximally entangled states, which itself is homeomorphic to $\mathbb{RP}^3$. Here we also compute the complete homology of the closure and interior of $\mathsf E$. In all larger dimensions, we show that the homology and homotopy groups of $\mathsf E$ vanish in degrees $1\leq k\leq 2(n_1-1)(n_2-1)-2$, and all homology groups of degree $k\geq (n_1n_2)^2-3$ also vanish. This range is controlled by the space $\mathsf W$ of entanglement witnesses, which we show is highly connected beyond two qubits and homotopy equivalent to $\mathsf E$. By computing the Euler characteristic, using a torus-action fixed point argument together with Alexander duality, we show that $\mathsf E$ nevertheless has non-trivial reduced homology over every field for all $n_1, n_2 \geq 2$.

Quantum materials experiments increasingly rely on microwave, electrical, thermal, optical, and structural probes, but these capabilities are typically assembled from custom hardware that limits reproducibility and scalability. Here we show that a commercial 65-nm CMOS process can be repurposed as a passive, foundry-manufacturable characterization platform by functionally partitioning its metal stack into microwave, thermal, and electrical subsystems within a 1 mm2 footprint. The integrated RF architecture enables cryogenic magnetic susceptibility measurements of Fe3GeTe2 heterostructures at 1.75 K without sample-specific fabrication. We further demonstrate NV-center optically detected magnetic resonance (ODMR) with >20% contrast at 4-9 dBm microwave power, reducing power requirements by 20-25 dB relative to conventional antenna-based approaches while maintaining sensitivities of 2-3 uT/sqrt(Hz). We additionally confirm compatibility with in-situ electron-beam imaging, showing no measurable degradation in image quality upon device operation. These results establish a scalable, foundry-manufacturable platform for multimodal quantum sensing and materials characterization.

In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers $S_{1},S_{2}\geq1$ of generalized quantum measurements at two sites. In the present article, we find analytically a new general condition sufficient for a nonseparable Werner state with a dimension $d\leq\min\{S_{1},S_{2}\}$ to satisfy all Bell inequalities under every $S_{1}\times S_{2}$-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous $-$ that is, to be $S_{1}\times S_{2}$-setting Bell local, for short. For a variety of $S_{1},S_{2}\geq1$ values, this new general locality condition is beyond Werner's and Barrett's locality conditions for a nonseparable Werner state. We also prove explicitly in the operator terms the optimization result by Terhal et. el. [Phys. Rev. Lett. \textbf{90,} 157903 (2003)] via semi-programming that every nonseparable Werner state with a dimension $d>\min\{S_{1},S_{2}\}$ is $S_{1}\times S_{2}$ -setting Bell local. The new results of the present article are important both for Bell nonlocality theory and for quantum applications based on Bell nonlocality.

We revisit the problem of \textit{real-time} quantum dynamics of the paradigmatic two dimensional transverse-field Ising model using the recently developed fuzzy sphere regularization scheme. By linearly ramping the transverse field from the paramagnetic phase to criticality, we study the finite-time scaling behavior of the squared order parameter $\langle m_z^2 \rangle$, the excitation energy density $Q$, and the two-point correlation function of $m_z$. We establish numerically that, at intermediate quench rate, $\langle m_z^2 \rangle$ follows the conventional Kibble-Zurek prediction set by the critical exponents of the $3$D Ising universality class, and the correlation function exhibits the expected exponential decay whose correlation length can be used to estimate the non-universal scaling coefficient in the freeze-out time/length. In contrast, the excitation energy density $Q$ does not reach the same scaling regime at available system sizes due to large effective finite-size gap from symmetry-enforced level sparsity in the energy spectrum. At slow quench rates the universal quasi-adiabatic scaling for both $\langle m_z^2 \rangle$ and $Q$ is recovered. Since the fuzzy sphere construction can realize not only the Ising conformal field theory (CFT), but a broad family of $(2+1)d$ CFTs, our results establish a route to the real-time critical dynamics of strongly coupled CFTs that are otherwise computationally challenging to study.

Can a many-body state relax faster because it is blind to the slowest decay channel? We show that this mechanism gives rise to a robust strong quantum Mpemba effect in locally dephased constrained Rydberg chains. The key observation is that, for constrained single-spin-flip Hamiltonians, local dephasing turns the Hamiltonian itself into an exact left Liouvillian slow mode, $\mathcal L^\dagger(H)=-γH$. A thermal state generically retains this slow channel, whereas translationally invariant states with vanishing energy expectation remove it and are forced to relax through faster visible modes. This exact selection rule produces a strong quantum Mpemba effect in the locally dephased PXP chain, including for a zero-energy scar eigenstate, the $|0\cdots0\rangle$ product state, and a translation-invariant $Z_2$ cat state. We further show that the same mechanism persists in the $(2,3)$ model and in the longer-range blockade family. Our results identify exact slow-mode selection, rather than special scar wave functions, as a general organizing principle for anomalously fast relaxation in constrained open quantum systems.

Fourier-transform infrared (FTIR) spectroscopy is a well-established technique for qualitative and quantitative chemical analysis. Classical FTIR systems rely, however, on direct mid-infrared (mid-IR) scan-based time-domain measurements of coherence functions; thus, the signal-to-noise ratio and measurement speed are constrained by design. In this paper, we demonstrate a scanless quantum FTIR (sQFTIR) technique that exploits principles of metrology with entangled photons to circumvent the limitations inherent to classical FTIR systems. The approach exploits the interferometric nature of the sensing paradigm and relies on frequency-domain measurements performed with a static, low-gain nonlinear interferometer. A robust reconstruction algorithm is used to retrieve time-domain signals and reconstruct respective mid-infrared (mid-IR) spectra (3000$~$cm$^{-1}$ to 2380$~$cm$^{-1}$) from near-IR measurements (approx. 780$~$nm to 820$~$nm). The suggested sQFTIR protocol eliminates the need for optical delay scanning and leverages inherent mapping between the related domains. In the theoretical section, we evaluate the intrinsic signal-to-noise advantage of the proposed method over conventional scan-based time-domain measurements; a difference of 26.8 dB (factor of 21.8) is demonstrated. Building on the enhanced sensitivity of the scheme, we demonstrate rapid sQFTIR-based hyperspectral imaging with a spatial resolution of 12.3$~μ$m and a spectral resolution down to 8$~$cm$^{-1}$. Hyperspectral mapping of human colon tissue, microplastics, and multilayer polymer samples composed of polypropylene and ethylene vinyl alcohol yield high-quality single-pixel spectra with acquisition times down to 10$~$ms.

High-speed LDPC decoding is a major bottleneck in CV-QKD and motivates hardware acceleration with fixed-point arithmetic. This work compares SPA, MSA, and NMS under a unified low-SNR fixed-point framework using common graph, matrix, and quantization settings. Multiple formats are evaluated through FER, and average iterations. The results show that performance depends strongly on the interaction between decoder rule and numerical precision. SPA achieved the best overall performance. For reduced-complexity decoders, Q16.8 was the lowest consistent precision, with NMS outperforming MSA. Practically, SPA with Q8.4 offered the best balance between reliability and hardware efficiency for large-scale implementations.

We analyze fixed-depth Trotter simulation as a method for structuring hardware noise in digital many-body dynamics. The number of layers is chosen using the largest endpoint time and is then kept fixed throughout the time scan, making the total noise dose approximately independent of the endpoint time. For local stochastic faults, we show that, once propagated faults lose memory of their insertion layer, the noisy circuit factorizes into ideal evolution followed by a stationary finite-depth binomial channel. In the dilute-layer limit, this channel reduces to a Poissonian exponential. The memory time of a single fault is related to a Loschmidt echo. An important consequence is observable-level depolarization: for selected macroscopic observables at low to moderate noise levels, the stationary channel can act as an almost time-independent affine contrast correction, even though the full channel need not be depolarizing, which is crusial for error mitigation purposes. At short times, the same protocol produces a digital Zeno-like transient, in which a fixed number of noise opportunities competes with a vanishing coherent angle per layer. Our results also reveal limitations of naive zero-noise extrapolatin strategies based on oversimplified functions.

We apply a hybrid variational framework to interacting spin-boson Hamiltonians, targeting regimes where simulations are limited by the unbounded bosonic Hilbert space and strong many-body correlations. The bosonic sector and spin-boson correlations are captured within a compact non-Gaussian variational manifold, while the minimized spin sector is obtained as the solution to an effective spin Hamiltonian. Minimization is carried out inside a self-consistent energy-minimization loop, where variational parameters are minimized and the effective Hamiltonian is solved via DMRG. The results are obtained without eliminating or truncating the photonic field. We benchmark the method on the Dicke and Dicke-Ising models by comparison to converged spin-boson DMRG, finding accurate ground-state solutions with reduced bond dimension.

We develop a framework for minimally perturbing local measurements in relativistic quantum field theory, with the aim to sense local properties of the field in a non-destructive manner. The field properties are sensed by weakly coupled pointers and encapsulated in conditional expectation values dependent on a postselection of the field state. Our operational protocol uses causally admissible Kraus updates for the field, in line with recent relativistic measurement theories, keeping in mind restrictions related to ``impossible measurements''. We illustrate our approach with three applications: a spacelikeness detector for causal-structure sensing, counting particle-creation densities in a supercritical potential and non-destructive discrimination between entangled states of the field and mixtures.

Bell proved that no theory of pre-existing local values can reproduce the predictions of quantum mechanics, but his proof leaves the culprit ambiguous: one may reject either of two independence conditions, Outcome Independence or Parameter Independence, and most commentators have found Outcome Independence the safer sacrifice. The first part of this paper presents, in a form adapted to spin-1/2 particles in the singlet state, an argument (Forster 2014) that removes the ambiguity: using a chained family of experiments in which quantum mechanics predicts an extreme pattern of correlations -- the quantum Sorites phenomenon -- a contradiction is derived without ever assuming Outcome Independence. Under the resulting theorem, anyone who holds that hidden variables could improve on the quantum probabilities must give up Parameter Independence itself. That looks like a heavy price, because Parameter Independence appears to be protected twice over: rejecting it seems to put superluminal influences into spacetime, and its statistical shadow -- the No-Signaling condition -- is experimentally beyond reproach The second part of the paper shows that the price is payable. In the random-matrix collapse dynamics proposed by Kryukov, measurement is a random walk of the quantum state, and the hidden variable is not a stock of values fixed at the source but the random stream that drives the walk -- like the stored random numbers of a computer simulation, with the measurement settings playing the role of seeds. In that framework Parameter Independence is false while Outcome Independence and No-Signaling are both true, and one can say exactly how the Sorites argument is blocked, why the violation involves no process propagating in spacetime, and why the influence of one wing's setting on the other wing's outcome -- demonstrated here in a simulation -- can never be used to send a message.

Charge-learnability transitions in monitored symmetric quantum circuits reveal how local measurement records acquire sufficient information to infer a conserved charge. Here we extend charge learnability to probabilistic weak measurements, for which the measurement probability and measurement strength are independently tunable. We find that the learnability phase boundary is organized by the informational power of local measurement. We further introduce cross entropy as a label-sensitive diagnostic that distinguishes unbiased, biased, and antibiased decoder variants. Finally, the exact record--label mutual information provides a decoder-independent benchmark for the information fundamentally available for charge inference. Our results establish informational power of local measurement as a unifying principle for charge learnability under general monitoring protocols.

Circuit cutting promises to scale quantum computations beyond current hardware, but variational quantum advantage also requires low cutting overhead, classical hardness, and trainability. We show that these properties are strongly constrained by entanglement geometry. Matrix product state (MPS) and tree tensor network (TTN) circuits with constant seam bond dimension can be cut with \(O(1/\varepsilon^2)\) sampling overhead, but remain efficiently classically simulable, ruling out asymptotic quantum advantage within these families. By independently controlling seam and intra-block entanglement, we construct a two-block circuit family that remains cheaply cuttable while requiring a super-polynomial global MPS bond dimension, as supported numerically up to \(n=100\). However, MPS hardness and trainability require incompatible depth regimes, \(d=ω(\log n)\) and \(d=O(\log n)\), respectively. Using magic rather than entanglement as the hardness resource avoids this conflict: shallow Clifford+\(T\) circuits remain cuttable and trainable while their stabiliser-simulation cost grows exponentially with the \(T\)-count.

We show that the Belopol'skaya-Daletskii formulation of stochastic differential equations on a Riemann manifold offers an elementary way to construct equivariant representations of finite-dimensional approximations to the path measure of a diffusion. The key ingredient is the use of the exponential map to describe increments of the diffusion.

Here we propose a general protocol for dual-channel lock-in detection of high-frequency ac signals. We find that the effect of a high-frequency target signal can be modulated through the application of rapidly oscillating driving fields. Based on this mechanism, we develop a quantum dual-channel lock-in detection protocol for high-frequency signals, which not only extends the accessible frequency range of quantum sensing but also enables the simultaneous estimation of the signal amplitude and initial phase. Furthermore, we present a feasible implementation scheme of the protocol based on nitrogen-vacancy centers in diamond. Numerical simulations demonstrate that the proposed protocol can effectively filter out background noise and significantly improve the signal-to-noise ratio. Our results provide a promising approach for realizing noise-resistant detection of weak signals in the high-frequency regime.

Pauli-based simulators offer a promising route to large-scale classical simulation of quantum circuits in the low-magic regime. Yet their applicability remains largely limited to forward simulation, making them inadequate for optimization-driven quantum tasks such as variational state preparation and parameter initialization. Existing approaches either lack native support for gradient-based optimization or suffer from severe gradient bias. Here we propose the stochastic Pauli-path simulator (SPPS), a computational framework for large-scale quantum optimization that enables unbiased stochastic gradient estimation via Pauli-path sampling across optimization iterations. Our theoretical analysis shows that the proposed simulator yields unbiased gradient estimates and admits provable convergence guarantees. We systematically evaluate our proposal, including quantum eigensolver benchmarks with up to 100 qubits and quantum neural network benchmarks with up to 40 qubits. Across these tasks, SPPS faithfully tracks optimization dynamics, converges within minutes, and broadens the role of Pauli-based simulation from forward estimation to large-scale quantum optimization.

Common-mode metrics of a high-$Q$ helical resonator do not determine the residual ion-side field in a dual-electrode drive. We combine a two-node differential RF model with single-electrode finite-element bases to obtain a computation-only, geometry-resolved projection for a same-phase blade trap. For a 3.5 pF external load per branch, the model gives a total effective branch capacitance of 7.640 pF and an HWHM-equivalent full branch-difference scale of 12.7 fF at $Q_{\mathrm{loaded}}=600$. The seven-segment geometry gives center and axial-RMS differential field coefficients of 640 V m$^{-1}$ and 635 V m$^{-1}$ per differential peak volt. A representative 10 fF mismatch with an effective 0.1 pF balance scale projects to 44.5/44.1 nm center/RMS $^{171}\mathrm{Yb}^{+}$ micromotion at 100 V common peak voltage. Supplementary thermal, bypass-admittance, and tested numerical cases characterize model sensitivity. All reported displacements are projections; no RF-bench or ion-side validation is claimed.

Randomized measurements provide an efficient way to extract physical properties of an unknown quantum state from limited data. On near-term hardware, gate and readout errors bias the reconstructed observables. Here we develop a microscopic description of this bias for locally scrambled shallow circuits. Independent local twirling reduces local implementation noise to stochastic Pauli damping, and a noise event contributes only when it overlaps the Heisenberg evolution of the measured Pauli operator. This gives an activated path-average formula for the noisy Pauli coefficient. In one-dimensional shallow circuits, the activated noise volume grows linearly with the size of a contiguous observable, leading to an exponential damping ratio. We verify this scaling for two-qubit random Clifford and locally scrambled iSWAP circuits with two-qubit Pauli noise, including spatial fluctuations and temporal drift. The scaling supports a small-string calibration protocol that predicts larger string observables without learning the full noisy measurement channel. Our result relates the noise bias of shallow-shadow protocols directly to operator-evolving dynamics.

Quantitative quantum sensing with shallow electron spins, such as those hosted by nitrogen-vacancy (NV) centers in diamond, requires accurate knowledge of the spin's depth below the host material's surface. A widely used approach infers this depth from the 1H nuclear magnetic resonance (NMR) signal of immersion oil on the diamond surface that can be detected using dynamical decoupling sequences such as XY8. However, finite-width pulses make XY8 sensitive to subharmonic responses, including unwanted contributions from nearby 13C spins, and its instrument-limited spectral resolution provides only sparse sampling of the narrow 1H NMR lineshape. Here, we introduce Spin-Lock NMR as an alternative approach to single-NV depth determination. By tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, the NV probes the 1H NMR signal through the Hartmann-Hahn resonance without the harmonic ambiguities of pulsed decoupling sequences and with substantially higher instrument-limited spectral resolution. We derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination. To demonstrate its applicability, we employ our method to investigate the 1H nuclear spin signal that is regularly reported to be present on diamond, even in the absence of immersion oil.

We provide a formal framework for Continuous-Variable Quantum Computing (CQC). While CQC is supported by photonic quantum hardware, we are not aware of a formal semantics for continuous-variable quantum programs nor of a unary Hoare logic for their verification. There are several technical obstacles to extending to CQC any of the formal frameworks available for Discrete-Variable Quantum Computing (DQC). Most importantly, continuous-variable quantum programs act on {\em infinite-dimensional} Hilbert spaces; their measurement outcomes are often {\em unbounded} and have expected values that are defined by an improper integral (or an infinite series), which may not converge. We overcome these challenges to give a formal semantics to a universal programming language for CQC and to provide the first Hoare logic for CQC. The assertions of our logic are built from polynomials over canonical observables. Besides proving relative completeness, we implement a symbolic weakest-precondition calculator for CQC based on our logic. Our tool has successfully verified CQC algorithms from textbooks and calculated their approximation errors for physically realizable implementations, proved the correctness (i.e., equivalence) of gate decompositions for CQC hardware, and computed the resource requirements (i.e., number of photon-number states) for achieving a desired accuracy in the classical simulation of continuous-variable quantum programs.

Quantum machine learning on real noisy intermediate-scale quantum (NISQ) hardware has remained largely confined to binary or few-class tasks, limited by the cost of on-hardware training and the underuse of large devices at inference. We present a unified framework that classifies ten-class MNIST end-to-end on a $127$-qubit IBM Eagle processor, with three central contributions. First, a two-phase protocol decouples a gradient-based classical optimization of the encoder and readout from a gradient-free optimization of the quantum parameters, removing the parameter-shift gradient cost that makes on-hardware training impractical. Second, we introduce Quantum Multi-Programming to a trained quantum classifier for the first time, packing multiple circuit copies onto one device to deliver parallel inference at no mean-accuracy cost while cutting quantum-processor job submissions proportionally. Third, a controlled comparison shows that on-hardware fine-tuning yields no measurable accuracy gain, motivating a practical NISQ workflow: train on a classical simulator and reserve the hardware for inference only. Benchmarked against a matched-capacity classical network, the quantum module shows no per-parameter accuracy advantage at this scale; we therefore frame the work as a feasibility-and-workflow demonstration for multi-class quantum image classification on current hardware.

Quantum key distribution (QKD) over non-stationary channels, such as satellite links, is characterized by short, high-loss, and strongly fluctuating transmission windows that produce sparse detection events. In many QKD protocols, these data must be analyzed using non-IID statistical inequalities, yet existing methods either become loose for small sample sizes or heavily rely on fine-tuning, yielding poor estimates when the optical channel is mis-modeled. Using mixture martingale techniques, we introduce tight concentration inequalities that retain sharpness when the channel model is accurate, while remaining robust to model mismatch. In realistic simulations of satellite QKD with fluctuating loss, the resulting bounds can reduce the minimum required number of transmitted signals by more than $70\%$.

Monte-Carlo trajectory (quantum-jump) methods are the practical route to simulating noisy quantum circuits once the exact density-matrix method is precluded by its $4^n$ memory cost. Their bottleneck is estimator variance: resolving one expectation value can demand thousands of trajectories. Recent tensor-network work shows that \emph{variance-reduced unravelings} -- projector and analog sampling -- sharply cut this variance, but only on CPU matrix-product-state backends, with no path into production tooling. We implement both unravelings on a \emph{GPU dense-statevector} trajectory engine and validate them against the exact density matrix (ideal-circuit fidelity $1-2.2\times10^{-16}$; $1/\sqrt{N}$ convergence; all unravelings unbiased to trace distance $<0.01$). On a single consumer GPU, projector unraveling reaches a target standard error with $20.8\times$ fewer trajectories than Qiskit-Aer's \texttt{batched\_shots\_gpu} at $n=10$, a factor that holds at $19$--$26\times$ across $n=8$--$20$. A regime map places analog sampling optimal at weak noise and projector at strong noise, crossing near $γt\approx0.35$. We further report a systems finding: Qiskit-Aer applies noise at the \emph{channel} level and reconstructs a canonical Kraus decomposition at apply time, discarding any user-supplied unraveling, so variance-reduced unravelings cannot be delivered through its public API. Because Aer's Born-rule collapse machinery already exists, we specify a minimal change that would unlock the technique in production.

Superradiant emission from long-lived excited states of an atomic ensemble confined in an optical cavity constitutes a practical source of light with narrow linewidth. In the pulsed regime, however, superradiance implies rapid emission and a broadening of the spectrum. Recent experiments have demonstrated constructive and destructive interference of superradiant emission by different strontium atomic transitions. In this article, we show that by modulating the atomic transition frequencies with a magnetic field, it is possible to control the release of the atomic excitation energy as a prolonged pulse or a train of superradiant pulses. By simulations, we show that heterodyne detection of the prolonged superradiance shows extremely sharp spectral features, which leads to significantly reduced frequency uncertainty and fluctuation.

We investigate a fully-connected three-mode squeezed vacuum (FC-C3MSV) state, where all three modes are pairwise coupled through nonlinear interactions in a triangle ($K_3$) topology. Using the integration-within-ordered-product technique, we derive the normal product form of the squeezing operator and obtain the covariance matrix directly from the Bogoliubov transformation. Under symmetric coupling, the physical state is genuinely tripartite entangled for any nonzero squeezing, while the three Armstrong-type witnesses provide a finite-window sufficient experimental test; in the chain-type C3MSV only one of these witnesses is violated. We find that, despite two-mode entanglement, the fully-connected topology admits \emph{no} two-mode Gaussian steering ($\mathcal{G}^{i\to j}=0$) between any pair of physical modes; the steering resource is instead collective one-mode-versus-two steering $\mathcal{G}^{i\to jk}$, which is $θ$-independent and grows with $r$. We analyze independent vacuum losses and obtain critical transmittances for steering survival: under full symmetric loss at $r=0.5$, one-to-two collective steering disappears at $η\approx0.58$, whereas reverse two-to-one collective steering survives down to $η\approx0.502$ and the underlying two-mode entanglement persists for all $η>0$. Finally, we revisit photon subtraction using a normalized phase-space derivation. A photon subtraction on a single physical mode does not generate Wigner negativity on another single mode, consistent with the absence of two-mode steering. Wigner negativity can instead be generated when Bob subtracts from the collective mode $(b+c)/\sqrt{2}$, with a loss threshold $η_c\approx0.667$ at $r=0.5$. These results distinguish pairwise and collective nonclassical resources in the FC-C3MSV and clarify the operational role of the complete-graph topology.

Bell nonlocality is both a defining signature of entanglement and a key quantum information resource. However, visualizing and certifying nonlocal correlations across a spatially multimode photonic field remains challenging due to the rapidly growing measurement cost of spatially resolved projective tests. To address this issue, we build a spatial nonlocality imaging scheme that directly reveals the spatial distribution of quantum nonlocality by integrating a metasurface that performs parallel polarization projections with a quantum-adaptive neural network. Spatially resolved Clauser--Horne--Shimony--Holt (CHSH) tests are realized over a 400-pixel biphoton field using an average of only 1.7 detected coincidence pairs per pixel per basis. This approach yields a nonlocality image that maps the two-dimensional spatial distribution of Bell violations across the optical field and reveals the target-state-dependent spatial evolution of Bell violations. It provides a highly resource-efficient route to large-scale Bell certification and opens new possibilities for exploiting spatially multimode entanglement in quantum imaging, quantum networking, and scalable photonic quantum technologies.

Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz to 300 kHz is crucial for advancing both fundamental science and practical applications, owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint that efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor acted by an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.

Parametric frequency modulation is a standard tool in superconducting circuits for activating tunable interactions and implementing quantum gates. Here, we engineer dissipation in a flux-tunable transmon qubit by using sideband modulation to bring it into resonance with a lossy resonator, opening an on-demand Purcell decay channel. We find that pulsing this channel on and off does not simply lower the time-averaged decay rate; instead, it reorganizes the dissipation spectrum into a structured interference pattern. A Chebyshev-propagator model for the repeated on/off block reproduces the measured spectra and reveals a close structural correspondence to N-slit Fraunhofer diffraction, with each on-window acting as a temporal aperture. By varying the pulse duration and duty cycle, we demonstrate control over the spacing, contrast, and envelope of the dissipation spectrum. These results establish pulsed parametric modulation as a direct method for shaping engineered dissipation in superconducting circuits and provide a new control knob for open quantum system dynamics.

Mode connectivity has been widely studied in classical machine learning as a geometric property of low-loss regions in parameter space. In quantum machine learning (QML), however, the physically relevant object is not the parameter vector itself but the unitary transformation implemented by a parameterized quantum circuit. In this study, we formulate mode connectivity on the reachable unitary Lie group generated by the dynamical Lie algebra of the generators. We show that, under a near-minimum connectedness assumption and the absence of critical values in a low-loss band, the corresponding low-loss sublevel set on the reachable Lie group is path-connected. This provides a geometric interpretation of mode connectivity in QML that is independent of a particular parameterization. We further discuss how overparameterization can enable the lifting of Lie-group paths to parameter space, thereby making Lie-group connectivity observable in parameter-space experiments. Finally, we present toy numerical experiments in which geodesic interpolations between trained unitaries exhibit nearly zero loss barriers, consistent with the proposed interpretation.

Simulating the nonequilibrium dynamics of interacting open quantum systems remains challenging beyond small system sizes. Quantum phase-space representations provide a scalable approach, but their useful simulation time can be limited by broad distribution tails and the associated boundary terms. We introduce the neural gauge-$P$ representation for open bosonic systems, in which stochastic gauges are parameterized by neural networks and optimized using exact moment equation residuals. For the driven-dissipative Bose--Hubbard model in both single-site and square-lattice settings, the neural gauge-$P$ representation remains accurate during long-time evolution toward the steady state, whereas the corresponding ungauged representation becomes unreliable at substantially earlier times. These results demonstrate the potential of the neural gauge-$P$ representation for accurate simulations of nonequilibrium open quantum many-body dynamics.

Quantum optimal control (QOC) underpins adiabatic quantum computation, quantum annealing, and quantum state engineering, yet practical deployment is fundamentally bottlenecked by strict hardware constraints and substantial expert effort required to design protocols for each problem instance. To overcome this, we introduce QOC-Workbench, an auditable, large language model (LLM)-driven workflow that acts as an automated quantum co-scientist for cross-paradigm protocol design. Going beyond traditional numerical optimizers that merely tune parameters within a fixed formula, the LLM autonomously parses physics literature, proposes structural hypotheses, and writes code to validate them by direct simulation. This workflow supports cross-paradigm design by accumulating control motifs across tasks. We demonstrate this approach across three distinct settings: Case 1, Rydberg-atom maximum-independent-set arrays; Case 2, interacting XXZ spin chains; and Case 3, random transverse-field Ising models. In Cases 1 and 2, the workflow autonomously discovers hardware-compliant auxiliary controls, target catalysts, and schedule deformations that outperform literature baselines. In Case 3, it addresses the computational bottleneck of variational counterdiabatic driving by escalating from per-instance optimization to an amortized graph-neural-network generator, successfully transferring learned coefficient paths to larger unseen systems. By actively bridging the gap between theoretical algorithms and experimental restrictions across distinct control paradigms and Hamiltonian families, QOC-Workbench establishes a continuously evolving, cross-paradigm methodology for autonomous quantum control.

By applying the framework of entropic uncertainty relation (EUR) and the Quantum Leftover Hash Lemma (QLHL), we introduce a security-proof method for variable-length side-channel-secure (SCS) quantum key distribution (QKD) against coherent attacks. This method reframes composable security as a statistical fluctuation problem of phase errors, enabling direct proofs against coherent attacks through observables and virtual observables. It yields tight key rates for the SCS protocol and reduces pulse requirements by over two orders of magnitude compared to prior works that employ the post-selection technique. We prove that the secure key length for the SCS protocol can be determined after error correction by exploiting the fact that untagged bits are free from bit-flip errors, using the actual information leakage during error correction and the post-error-correction statistics of each state to calculate the final key rate. We further identify sufficient conditions under which the final key length may be determined after error correction in a broader class of QKD protocols. Under the framework of EUR and QLHL, we clarify the applicability of several commonly used concentration bounds to variable-length QKD and the appropriate manner of their implementation. This work enhances the practical value of the SCS protocol and clarifies the security justification of key-rate formulas used in practical variable-length QKD implementations.

We develop a sparse operator-centric realization of $n$-qubit variational quantum algorithms in the complex Clifford algebra $\mathrm{Cl}(2n,\mathbb{C}) \cong M(2^n,\mathbb{C})$. Density operators, gates, observables, channels, fermionic modes, and adaptive-selection observables are represented in one Pauli-word algebra, with the Jordan--Wigner map providing the exact bridge to anticommuting Clifford generators. We distinguish general Pauli-word rotations from Spin-group rotors and derive an exact transpose-parity rule: for real Hamiltonians and real states, every candidate Pauli word containing an even number of $Y$ factors has zero ADAPT gradient, while odd-$Y$ rotations preserve the real sector. For the critical open transverse-field Ising chain, a depth-three Hamiltonian variational ansatz gives relative energy errors $4.84\times10^{-5}$, $2.19\times10^{-3}$, and $3.67\times10^{-3}$ for $n=4,5,6$. A compact local ADAPT pool is exact at $n=4$ but leaves residual errors at larger sizes; a systematic contiguous three-local odd-$Y$ pool reaches relative errors below $1.3\times10^{-12}$ for $n\leq6$. In 100-seed finite-shot tests at $n=4$, fixed-shot selection succeeds in $0/100$ runs, whereas uniform escalation and confidence-bound racing each succeed in $84/100$ runs; racing lowers median shots by $34\%$. We claim no asymptotic speedup over matrix methods. The contribution is a corrected algebraic formulation, an exact pool-pruning rule, and a reproducible study of measurement-limited adaptive selection.

Large language models confabulate chemical objects (molecular formulas, space groups, formation energies) in fluent reasoning traces, concentrated on long-tail entities where confidence is least trustworthy. Deterministic, database-grounded verification can catch and repair such errors without the coverage cost of blanket retrieval; the binding constraint, we find, is detection, not repair. Our tiered verifier extracts each checkable claim, checks it against authoritative databases and physics, and feeds the reference into a gated correction loop. Across four models and 528 condition-pinned prompts, gated correction cuts committed-formula error from 22% to 4% at $3.2\times$ fewer retrievals than blanket augmentation, beating a conversational oracle. Repair succeeds wherever a flag fires (80--97%); the bottleneck is in-loop detection recall. Grounding improves the final answer only when the verifier's scope reaches the deliverable (83% to 90%), and the lift appears only where extractable long-tail error exists: absent on near-ceiling physical constants, large on isotope half-lives (11% to 0%).

Hilbert-space techniques are widely used not only for quantum theory, but also for classical physics. Two important examples are the Koopman-von Neumann (KvN) formulation and the method of ``classical'' wave functions. As this paper explains, these two approaches are conceptually distinct. In particular, the method of classical wave functions was not due to Bernard Koopman and John von Neumann, but was developed independently by a number of later researchers, perhaps first by Mario Schönberg, with key contributions from Angelo Loinger, Giacomo Della Riccia, Norbert Wiener, and E. C. George Sudarshan. The primary goals of this paper are to explain these two approaches, describe the relevant history in detail, and give credit where credit is due.

Polarization-encoded quantum communication requires compensation of polarization transformations induced by the optical links. If the compensator is embedded between two channel segments, the transformations before and after the compensator must be treated separately. Moreover, standard three-wave-plate polarization controllers can become non-universal when their retardances deviate from their ideal values. To address these two challenges, we introduce a four-wave plate compensator that synthesizes arbitrary SO(3) polarization transformations over a broad wavelength range, and an eight-Stokes vector protocol that reconstructs the two link-segment Mueller matrices on either side of the compensator. Our experiment reveals that the four-plate sequence suppresses polarization-induced excess quantum bit error rate (QBER) to the sub-percent level at an operating wavelength more than 100 nm from the design wavelength without further optimization. Combined with two auxiliary wavelengths, our scheme tracks the temperature-driven drift of a strongly wavelength-sensitive fiber spool while keeping the excess QBER below 1%. These results support flexible compensator placement and wavelength channel selection, as well as non-interruptive polarization control in wavelength-division-multiplexed quantum optical links.

We investigate colored $Δ_T$ noise, i.e., finite-frequency $Δ_T$ noise, as a probe of edge-mode (EM) transport in quantum Hall and quantum spin Hall systems. Colored $Δ_T$ noise probes finite-frequency nonequilibrium current fluctuations and dynamical transport properties that are often obscured in DC measurements of conductance and noise. Since $Δ_T$ noise is driven solely by a temperature and voltage bias under zero average charge current conditions, it eliminates current-induced Joule heating and directly probes intrinsic thermal fluctuations. We show that chiral, spin-conserving helical, and spin-flip helical (trivial) EMs exhibit distinct colored $Δ_T$-noise signatures under appropriate bias protocols. Incorporating energy-dependent scattering through a quantum point contact, we demonstrate that electron-hole asymmetry significantly modifies the finite-frequency spectrum while preserving these distinguishing features. Notably, colored $Δ_T$ noise exhibits a frequency-dependent sign reversal absent in the corresponding white ($ω=0$) $Δ_T$ noise. We further investigate zero-temperature colored quantum shot noise and find that it vanishes identically for chiral EMs, whereas the spin-conserving helical response changes sign with frequency. By contrast, spin-flip helical (trivial) EMs exhibit a positive colored shot-noise spectrum. However, the corresponding colored $Δ_T$ noise retains its characteristic sign reversal, providing a robust distinction between spin-conserving helical and spin-flip helical (trivial) EM transport. These results establish colored $Δ_T$ noise as a robust, experimentally accessible, complementary probe for identifying chiral, spin-conserving helical, and spin-flip helical (trivial) EM transport in mesoscopic topological systems.

Designing effective Lean proof agents is a central challenge in formal mathematical reasoning. Beyond building stronger provers, recent work emphasizes the workflow around Lean: how an agent decomposes proof obligations, uses tools and compiler feedback, diagnoses failures, repairs proofs, and maintains structured proof context. Motivated by code-level self-evolving agents, we study whether such workflows can be evolved rather than hand-designed. We present a self-evolving Lean proof agent in which a small fixed, trusted runtime wraps a fully mutable workspace: the proof workflow, prompts, and tools. Unlike most self-evolving systems, which optimize against a fixed external benchmark, our system coevolves the agent and its benchmark. Between generations, the highest-scoring agent (the champion) revises the active task distribution through a mastery-throttled curriculum update that introduces harder proof obligations only after the current level is mastered, and a single-anchor recalibration re-runs the champion on the updated benchmark to keep scores comparable as difficulty rises. All evolution stays inside a Lean-grounded verification loop: however the agent rewrites itself, a success counts only when its behavior yields Lean-verified proofs under a trusted snapshot, and each attempt must emit a machine-readable, Lean-grounded proof context whose representation may evolve but whose groundedness is enforced. We run the coevolving trajectory and a fixed-benchmark baseline for 15 active generations and compare them on a held-out miniF2F test split. The best coevolving agent reaches a 45.1% held-out solve rate, versus 12.7% for the seed and 32.0% for the best fixed-benchmark agent, showing that verifier-grounded self-evolution can improve Lean proof workflows under a coevolving benchmark.

We employ machine learning to quantify the information carried by three Krylov-space observables: the spread complexity $\mathcal{C}(t)$, the discrete Wigner negativity $N(t)$, and the normalized negativity $χ(t)=N(t)/|S(t)|$, with $S(t)$ the survival amplitude, recently proposed as a second-moment infall probe (arXiv:2607.04065). Small residual networks (16-32 neurons) and boosted trees are trained on half of $\sim 57{,}000$ labeled evolutions spanning the GUE, GOE and Poisson ensembles, the integrable $SL(2,\mathbb{R})$/CFT sector, and the chaos interpolation $H(\varepsilon)=H_{SL(2,\mathbb{R})}+\varepsilon R_0 W_{GUE}$. Either moment determines the thermofield temperature at $R^2\simeq 0.999$. Neither reconstructs the fine spectral form factor ($R^2\simeq 0.18$ in every ensemble); smoothing the target does not repair this, and windows wide enough to help erase the dip-ramp physics itself: the SFF strictly refines both moments. The coarse $e^S$ plateau is nevertheless recovered at $R^2=0.861$, mostly from the first 20% of $\mathcal{C}(t)$. A single curve identifies the symmetry class at up to 98% accuracy. In the integrable sector the observables are informationally equivalent, as exact negative-binomial slaving demands, while the negativity best resolves the $(h,α)$ degeneracy ($N\to h$: 0.999). Along the interpolation the asymmetry gap of $χ$ over $\mathcal{C}$ switches on with chaos, growing from +0.33 to +0.77 as the level statistics cross to GUE, while the raw-$N$ gap decays to zero. The second-moment informational surplus is therefore a signature of chaos, carried specifically by the normalized negativity, and we derive an analytical mechanism and a quantitative bound for it.

Quasicrystals exhibit long-range positional order without periodicity, arising from multiple incommensurate wave vectors. In self-assembled quasicrystals, the spontaneous breaking of translational invariance gives rise to two Goldstone modes-phonons and phasons-associated with two competing wave vectors. Here, we demonstrate a unique scenario exclusive to quasicrystals: a mechanism that gaps out only one Goldstone mode (associated with one wave vector), while the other remains gapless. In one dimension, this leads to the coexistence of long-range order at the gapped wave vector and quasi-long-range order at the gapless one, due to sustained fluctuations. We show that this phenomenon can be realized using ultracold bosonic atoms in optical cavities.

Quantum machine learning models define probabilistic input--output maps through coherent quantum evolution and measurement. While such models can exhibit computational advantages, their internal functioning and decision making generally resists interpretation in terms of stochastic trajectories through intermediate configurations. In contrast to classical (Markovian) stochastic processes, quantum dynamics generically violates the Chapman--Kolmogorov divisibility condition, preventing a decomposition into probabilistically meaningful intermediate transitions. We develop a probabilistic framework for representing quantum learning models as stochastic processes over configuration spaces where the dynamics are modeled as linear maps on probability distributions. Starting from a fixed POVM, arbitrary quantum channels induce transition kernels on the associated probability representation. For informationally complete POVMs, and in particular SIC-POVMs, these kernels are Markovian but generally quasi-stochastic, with non-classicality appearing as negativity. By contrast, projective spaces admit positive stochastic kernels but generally require non-Markovian dynamics due to the failure of Chapman--Kolmogorov divisibility. This yields a trade-off between negativity and dependence on past configurations, i.e. quantum dynamics can be represented either by Markovian quasi-stochastic maps or by positive stochastic processes with higher Markov order. We discuss how such representations of quantum dynamics can be interpreted as stochastic walks through a memory space in the spirit of Projective Simulation, a model of learning and agency in which decisions arise from random walks over an episodic memory network. We further outline how finite-order stochastic kernels can approximate such quantum deliberation processes and show in what regimes the classical machine learning model is recovered.

We formulate a loss-tolerant extension of entanglement-assisted long-baseline optical interferometry in which the astronomical optical coherence is first mapped coherently to distributed quantum memories and is subsequently protected by local scrambling encoders. The proposal must be distinguished from existing memory-assisted Gottesman--Jennewein--Croke (GJC) interferometers, in which quantum memories store an ancillary single-photon-entangled reference rather than the astronomical state itself. We derive the weak-thermal-light model, its two-parameter quantum Fisher information (QFI) matrix, the GJC measurement probabilities, and the associated classical Fisher information (CFI). We then prove that exact local correction of flagged erasures restores the complete complex visibility, its QFI matrix, and the operational GJC CFI. The relevant protection criterion is reference--environment decoupling, not volume-law entanglement alone. We state, as conjectures, quantitative decoupling bounds for local random encoders and finite-depth scramblers, and derive the expected threshold of fewer than one half of the physical memories erased per node. Finally, we formulate the phase-covariance and superselection-rule constraints required for a physically meaningful distributed protocol.

Driven-dissipative quantum emitters provide a powerful platform for controllable excitation storage and release, with promising applications in quantum batteries and quantum storage. Yet, transient excitation transfer in collective many-body systems is often obscured by the intricate interplay among coherent driving, dissipation, and correlation dynamics. Here, we uncover a scalable excitation-storage mechanism in two emitter ensembles coupled to a semi-infinite waveguide. A coherently driven ensemble acts as an effective excitation reservoir, while a second ensemble positioned near a dissipative node serves as a subradiant storage medium. Surprisingly, when the driven ensemble largely exceeds the storage ensemble in size, the transfer dynamics enters a nearly correlation-free regime, allowing the driven ensemble to behave effectively as a classical excitation source. This reveals a simple scaling law for optimal excitation transfer, under which the storage ensemble approaches near-complete population inversion as the driven ensemble size increases. Building on this mechanism, we propose a three-stage storage-and-release protocol enabling fast excitation storage and controllable photon emission. Our results demonstrate how coherent and dissipative collective interactions can be jointly harnessed for quantum energy storage and programmable nonequilibrium dynamics in waveguide QED platforms.