Papers

Strong atom-photon interactions on scalable photonic platforms hold significant potential for both atomic and photonic quantum information platforms. In particular, trapping of a single atom on a planar photonic integrated resonator at the subwavelength distances required for strong coupling to the guided modes has remained an outstanding challenge. Here we demonstrate efficient trapping of a single ultracold rubidium atom within the evanescent field of an integrated silicon-nitride microring resonator, at distances of 150-200 nm from the chip surface. Efficient, single-stroke loading process is achieved using an evanescent-field mechanism related to Sisyphus cooling, in which a single scattering event dissipates the atom's kinetic energy and transfers it into a near-surface trap. We observe logarithmic scaling of trapping durations spanning from sub-millisecond timescales up to 1 second, without continuous cooling. The trapped atom couples efficiently to the resonator, enabling on-chip photon collection, photon antibunching, and Purcell-enhanced spontaneous emission with single-atom cooperativity exceeding unity. Our results establish the potential of CMOS-compatible chip-based atom-photon interfaces for scalable quantum photonic circuits.

Quantum batteries have recently emerged as promising candidates for microscopic energy-storage technologies exploiting uniquely quantum mechanical effects. In this work, we introduce the concept of a quantum capacitor, a coherence-based quantum energy-storage device exhibiting reversible and ultrafast charging-discharging dynamics. Unlike conventional quantum batteries, which primarily focus on extractable work, the proposed quantum capacitor operates through reactive energy accumulation mediated by coherent quantum polarization. We formulate a theoretical framework based on a driven two-level system and define a dynamical quantum capacitance associated with the response of stored energy to coherent external driving. The charging power, reversible energy exchange, and the effects of environmental decoherence are investigated analytically within the Lindblad formalism. We extend the proposal to interacting many-body systems and show that collective coherence and interactions can enhance the effective quantum capacitance and charging power, potentially leading to cooperative energy-storage advantages beyond the single-qubit regime.

Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In this paper, we propose CTQWformer, a hybrid graph learning framework that integrates continuous-time quantum walks (CTQW) with GNN. CTQWformer employs a trainable Hamiltonian that fuses graph topology and node features, enabling physically grounded modeling of quantum walk dynamics that captures rich and intricate graph structure information. The extracted CTQW-based representations are incorporated into two complementary modules:(i) a Graph Transformer module that embeds final-time propagation probabilities as structural biases in the self-attention mechanism, and (ii) a Graph Recurrent Module that captures temporal evolution patterns with bidirectional recurrent networks. Extensive experiments on benchmark graph classification datasets demonstrate that CTQWformer outperforms graph kernel and GNN-based methods, demonstrating the potential of integrating quantum dynamics into trainable deep learning frameworks for graph representation learning. To the best of our knowledge, CTQWformer is the first hybrid CTQW-based Transformer, integrating CTQW-derived structural bias with temporal evolution modeling to advance graph learning.

We consider the Clauser-Horn (CH) inequality for a qubit-qutrit system. We derive the necessary and sufficient conditions for the violation of the inequality as well as some sufficient conditions. Remarkably, we demonstrate the importance of local parameters in violation of the inequality. In other words, there are some families of mixed states violating the inequality for which the correlation part alone is useless in the Bell-CH test.

Loopy tensor networks exhibit internal correlations that often render their compression inefficient. We show that even local bond optimization can more effectively exploit locally available information about relevant loop correlations. By cutting a bond, we define a set of states whose linear dependence can be identified through a zero mode of the states' metric tensor and used to truncate the bond dimension. In the absence of an exact zero mode, a linear combination of a small number of the lowest modes can instead be optimized to provide the optimal approximation to a zero mode. The truncation does not require prior gauge fixing. The method is applied to the two-dimensional finite-temperature $Z_2$ lattice gauge theory, whose thermal-state purification is represented by an infinite projected entangled-pair state (iPEPS).

Fusion-based quantum computing (FBQC) relies on a set of small, typically photonic, resource states that are fused together through Bell state measurements. The main bottleneck of FBQC is the low rate of generating the resource states, which stems from the probabilistic nature of photonic fusion gates. Previous work introduced a general algorithm for constructing circuits that deterministically generate photonic resource states from a minimal number of quantum emitters for a specified photon emission ordering. However, finding the minimal number of emitters and CNOT gates across all possible orderings is an NP-hard problem. Here, we exploit the symmetries present in FBQC resource states to dramatically simplify this optimization problem. We find that logically encoded 24-photon FBQC resource states can be produced using as few as 3 emitters and 11 CNOTs.

Noise is a significant challenge in imaging. Conventional intensity-based techniques mitigate noise through various filtering methods, but they often require prior knowledge of noise characteristics and struggle, especially under low-light conditions and with spatially structured noise. Quantum distillation provides enhanced noise rejection; however, its applicability is limited as it requires specialised illumination and substantial modifications to existing imaging setups. In this article, we introduce a coherence-based image distillation approach that separates object from noise by leveraging the difference in their temporal coherence properties. We implement this through our interferometric protocol, which enables imaging based on spatial coherence while simultaneously filtering out noise via temporal coherence. This overcomes the limitations of both intensity-based and quantum distillation methods. We experimentally demonstrate noise resilience by successfully recovering feature-rich objects, such as QR codes and grayscale wheels, obscured by spatially uniform and structured noise 20 times as intense as the object. We further show that our method remains effective for fields with substantial spectral overlap, outperforming spectral filtering in regimes where the latter provides little noise suppression. This approach provides a robust framework for noise-resilient imaging with applications in optical communication, fluorescence microscopy, and biological imaging at both high and low light levels.

How can a learned representation remain useful when the question it must answer is chosen only after encoding? Preserving information is essential, but does not by itself ensure access to the requested target. We address this problem by deriving "neural information causality (Neural-IC)," a representation law that connects causal access to the physically specified interface capacity. For a fresh database of independent bits, the aggregate information recoverable across later queries cannot exceed that capacity, even with pre-established quantum resources. A decomposition separates capacity slack, information organized jointly across targets, and losses in producing answers. Exhaustive evaluation of trained binary codes reveals why nearly full use of a memory's information budget can coexist with limited retrieval. In a nested Bell-correlation construction, quantum assistance improves average retrieval over the optimal classical one-bit benchmark within the same communicated budget. These results give representation learning a design principle that connects information capacity to the organization and extraction of target information. By locating the constraints on later answers, the framework can inform memory allocation, encoding objectives, and decoder outputs, providing a basis for seeking better retrieval within a fixed budget.

We develop a microscopic theory for how slow Liouvillian sectors are selected in an open correlated lattice. The starting point is not a postulated non-Hermitian band, but a local interacting resonance between an on-site doublon and a branch-resolved nearest-neighbor bond. This resonance defines a composite shell orbital whose doublon weight controls reservoir visibility and whose mixed doublon-bond character controls shell mobility. Projecting the microscopic hopping onto the selected shell yields a branch-selective dimerized channel. In the dilute regime, a boundary doublon-loss channel yields an exponentially slow edge-memory pole through a Zeno-type return. At the shell-critical point, the edge pole is replaced by a near-zero standing-wave doublet with an algebraic coherent spacing. At finite shell filling, the same local shell becomes density dressed. A number-conserving phase-locking jump removes a bright mismatch sector, leaving defects as the asymptotic slow variables and producing a diffusive finite-size gap. We derive the local shell, the projected branch topology, the edge-memory law, the shell-critical doublet, the density-dressed shell Hamiltonian, and the defect generator within one Schur-projection framework. The resulting mechanism identifies the reservoir-engineered fast block as the selector of the observable slow sector, while the microscopic parent shell remains fixed.

We investigate a Dirac-type equation in $(2+1)$ dimensions modified by Lifshitz spatial derivatives with dynamical exponent $z=2$, focusing on the spectral properties of bound-states under radial confinement. Analytical solutions are obtained for constant backgrounds, hard-wall confinement, and harmonic potentials, while logarithmic confinement is treated numerically via the Numerov method and complemented by a semiclassical WKB analysis. The resulting spectra exhibit characteristic scaling laws governed by the Lifshitz parameter $b$, including $E - M \propto b/R_0^2$ for hard-wall confinement, $E - M \propto \sqrt{2b}\,\omega$ for harmonic trapping, and $E - M \sim \alpha \ln\sqrt{b}$ in the semiclassical regime of logarithmic confinement, where $M$ is a mass scale. These results provide a consistent characterization of how higher-order spatial derivatives modify the energy spectra in two-dimensional Dirac systems and may be relevant for effective descriptions of materials with quadratic low-energy dispersion, such as bilayer graphene and related anisotropic 2D systems.

Scalable qubit mapping and routing remain major bottlenecks in quantum compilation, especially for Trapped-Ion Quantum Charge-Coupled device (TI-QCCD) architectures, where qubit interactions require physically shuttling ions under strict movement, congestion, and trap-capacity constraints. We present a compilation framework built around the position graph abstraction, a unified representation of executable locations, movement paths, and routing constraints that enables heuristic mappers to operate directly on shuttling-based hardware. Using this abstraction, we accelerate the SWAP-based BidiREctional heuristic search (SABRE) by implementing relative move scoring, which caches repeated heuristic move evaluations that arise during search, and memoized congestion resolution, which speeds up the resolution of repeated congestion. This optimization removes redundant computation without changing routing/shuttling decisions, improving the scalability of SABRE-based methods on TI-QCCD systems. Our results show that combining an architecture-aware abstraction with memoized heuristic evaluation yields a practical and effective path toward scalable qubit mapping and routing across heterogeneous quantum architectures.

{\Psi}-epistemic models of quantum mechanics imply that the quantum state does not correspond to physical reality, but instead reflects the observer's knowledge of the underlying quantum system. The epistemic view of the quantum state has the potential to shed light on several foundational problems of quantum theory and has attracted considerable attention in the literature. On the other hand, the Pusey-Barrett-Rudolph theorem demonstrated that broad classes of {\psi}-epistemic models must lead to predictions that deviate from those of quantum mechanics. Although the original theorem involved entangled joint measurements on composite systems, alternative no-go theorems involving measurements on single quantum systems were developed shortly thereafter. Experimental investigations of the deviations predicted by {\psi}-epistemic models from quantum mechanics are still ongoing. So far, such tests have been performed within the framework of non-relativistic quantum mechanics and predominantly rely on quantum information based measurement procedures. In this work, we show that {\psi}-epistemic models can give rise to deviations from standard quantum field-theoretic predictions through modifications of polarized scattering cross sections and decay widths. Our results do not require a relativistic formulation of ontological models or of the Harrigan-Spekkens criterion; the essential assumption is merely that measurements implemented through relativistic processes can still be represented within the ontological framework by well-defined response functions and probabilities. The present work constitutes a proof-of-principle study demonstrating that particle physics tests of the ontological status of the quantum state are possible and that {\psi}-epistemic models may exhibit experimentally distinguishable signatures in particle phenomenology.

Deep Equilibrium Models (DEQs) replace a stack of explicit layers with a single operator whose fixed point defines the output, giving the expressive power of an arbitrarily deep network at the memory cost of a single layer. Quantum Deep Equilibrium Models (QDEQs) bring this idea to quantum machine learning, offering an alternative to Parameterized Quantum Circuits (PQCs), whose depth is limited by hardware coherence and trainability. Here, we introduce, formulate, and compare three ways of coupling a quantum signal to graph DEQs, differing in where the signal enters the fixed-point operator. Independent injection computes the quantum signal once per graph and forward fixed-point solve, and holds it fixed throughout the solve. State-dependent injection instead recomputes the signal at every solver step and applies it to the current iterate. Backbone-dependent injection likewise recomputes at every iteration but applies the signal to the classical backbone's output evaluated at the current iterate. We establish contraction guarantees for each variant under explicit assumptions on the Lipschitz constants of the classical backbone and the quantum signal. On the TU Dortmund graph-classification benchmarks NCI1, PROTEINS, and MUTAG, independent injection achieves the best test accuracy while using fewer forward-solver iterations than both the classical equilibrium baseline and the two dependent variants.

We present a method to quantize free fermions which eliminates the doublers when implemented on the lattice in any number of dimensions and in the $m=0$ limit. The elimination of doublers is achieved by combining a second-order description of fermions, with the tools associated with non-Hermitian Hamiltonians. We identify a new Pseudo-Hermitian symmetry of the second-order fermion equation, and we identify the associated $U(1)$ symmetry which will become charge when shifted to a local gauge theory. We validated the methods numerically.

We introduce a battery-explicit thermodynamic witness of post-quantum Bell correlations. In each round, a single supplied excitation is routed into an explicit two-level battery if and only if a Bell-game condition is satisfied. The routing operation is implemented by an energy-preserving controlled SWAP, with all logical control registers taken to be degenerate. Thus the correlation resource does not create energy; it only determines the probability that the supplied excitation reaches the battery. The construction is first formulated for finite two-player XOR games. For any such game, the mean battery charge is exactly the game success probability multiplied by the battery gap. Optimizing over local, quantum, or nonsignalling behaviours therefore turns the corresponding game values into local, quantum, or nonsignalling battery-charge ceilings. For the CHSH game, Tsirelson's bound becomes a strict quantum ceiling on the mean battery charge, while a PR-box behaviour reaches the single-excitation cap. The witness is trusted-module rather than device-independent: it assumes calibrated Hamiltonians, correct classical wiring, and a trusted energy-preserving battery module. We also discuss a reversible-controller implementation, finite-statistics certification from work data, robustness to imperfect battery readout, and cyclic bookkeeping showing that no positive net work is obtained once fuel restoration and memory erasure are included.

Real-time quantum error correction places the classical decoder inside the fault-tolerant control loop under strict timing and memory constraints. For quantum low-density parity-check (QLDPC) codes, practical deployment therefore depends not only on correction performance, but also on timely decoding under deadlines, finite on-chip memory, and time-varying load. However, existing decoder studies primarily emphasize correction performance without exposing operational viability under these constraints. We present DART-Q, a real-time QLDPC decoding framework that treats windowed workloads as discrete arrival, queueing, service, and completion events. DART-Q models each decode request as a deadline-driven online service job with queueing and non-preemptive Earliest Deadline First scheduling. It supports configurable admission control, service times, and bounded rescue policies. Through controlled studies of the SRAM-fit transition, tail latency, overload, and a capacity-scaling extension, DART-Q isolates the effects of memory pressure, rescue selectivity, admission control, and pooled service capacity on timely decoding. Our results show that real-time decoder viability is governed by state organization, overload policy, and service capacity. A cached-summary state organization lowers the SRAM-fit boundary by 4x relative to an edge-centric baseline. Under overload, relaxing the backlog cap increases queued work by approximately 20.1x and worsens p99 latency by approximately 17.6x, with little gain in useful throughput. In contrast, doubling decoder capacity reduces the MissRate from 97.64% to 0.98% and improves p99 latency from 3.861ms to 10$\mu$s. These results position DART-Q as a framework for exposing the regime changes that determine real-time QLDPC decoder viability under deadlines, finite memory, and time-varying load.

The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity – finding its capacity threshold – is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.

We study finite-temperature $P$-form $\mathbb Z_N$ homological codes via an exact finite-Trotter quantum-to-classical map to a $(d+1)$-dimensional spacetime model with electric and magnetic topological background charges. The resulting background-resolved partition functions admit an exact reformulation in terms of closed magnetic and electric defect polymers, with opposite-species interactions governed by linking phases. By bounding this complex polymer gas by positive same-species hard-core majorant gases, we obtain an explicit low-activity criterion under which all background-dependent partition functions are uniformly controlled and homologically nontrivial polymers are exponentially suppressed on the scale of the spacetime systole. We also derive an exact higher-form Kramers-Wannier duality exchanging electric and magnetic backgrounds, Wilson and 't Hooft operators, and $P$-form and $(d-P)$-form theories. Finally, for prime $N$, we identify an exact source-free gauge-theory specialization coupled to the plaquette random-cluster model, which imports sharp phase-transition results on special geometries into the spacetime framework.

Transfer learning under limited data is a challenging setting, where models must adapt to new tasks with minimal supervision. Prior work has primarily focused on improving absolute accuracy in transfer learning. However, empirical evidence comparing quantum and classical models in realistic transfer learning settings remains limited, especially in low-data regimes. In this work, we systematically study the robustness of quantum models under reduced training data. We evaluate multiple quantum and classical architectures across diverse transfer tasks and retraining configurations, and quantify robustness using accuracy degradation and relative performance retention (RPR). Our results show that, although classical models often achieve higher peak performance, they exhibit significantly larger degradation when training data is limited. In contrast, quantum models maintain more stable performance across data regimes, indicating improved robustness and data efficiency. These findings provide empirical evidence that quantum models can offer improved robustness in low-resource transfer learning scenarios.

We show how local periodic driving can be used to control dissipation in a structured environment in a highly selective manner. As a minimal setting, we consider two discrete levels coupled to a one-dimensional tight-binding continuum with a finite bandwidth, where only one level is driven while the other remains undriven. Without driving, both bare energies are placed outside the static continuum band so that neither level decays. We demonstrate that the drive can nevertheless activate a selective remote dissipation channel: the undriven level acquires a finite decay rate, whereas the driven level can remain long-lived. The mechanism is clarified within Floquet theory. Periodic driving generates photon-assisted channels shifted by integer multiples of the drive frequency, effectively creating a ladder of drive-shifted continuum sidebands (Floquet channels). A decay channel for the undriven level opens once its bare energy overlaps an open sideband accessed via drive-enabled pathways; in the tight-binding example, the decay is strongly enhanced near the sideband edge due to the increased density of states. The dominant remote pathway is controlled by Bessel-weighted couplings and can be switched and strongly suppressed by tuning the drive amplitude. We verify these predictions by direct numerical integration of the time-dependent Schrödinger equation. We also formulate a complex-eigenvalue problem for the Floquet Hamiltonian by eliminating the continuum via a Brillouin–Wigner–Feshbach projection, and show that the pole-implied decay rate quantitatively reproduces the time-domain decay envelope.

We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a rank-one projector for each copy using the previous outcomes, and performs the corresponding two-outcome projective measurement. The goal is to learn the state while keeping the chosen projectors close to the unknown state in order to minimize disturbance. The qubit solution relies on the special geometry of the Bloch sphere and does not extend directly to qudits, where pure states form a curved manifold. We show that this obstruction can be overcome by working locally on the pure-state manifold. The algorithm proceeds in epochs. In each epoch, it fixes a current estimate, measures pairs of nearby rank-one projectors obtained by moving in opposite tangent directions, and takes differences of the corresponding outcomes. This gives an exact linear observation of the tangent component of the error. The resulting local linear models are combined with a robust variance-adaptive estimator and a hot-start regularization that transfers precision across epochs. For every unknown pure state in dimension \(d\), after \(T\) measured copies, our protocol achieves cumulative regret \(\mathcal{O}(d^3\log^2 T)\), and at each intermediate time \(t\leq T\) its current estimate has online infidelity \(\mathcal{O}(d^3\log(T)/t)\). Hence, pure-state tomography with essentially no cumulative disturbance is not a peculiarity of qubits but a geometric phenomenon that persists for qudits.

The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths and cycles, a complete understanding of their query complexities remains elusive. In this work, we consider several variants of path- and cycle-containment problems in the adjacency matrix model, where we search for paths or cycles of constant length $k$. We compare the settings where the graphs are directed or undirected, where the goal is to detect or find the existence of a path/cycle, and where the path/cycle we are looking for has length exactly $k$, or at most $k$. We also consider several promise versions of these problems, where we suppose that the input graph has a certain structure. We characterize the relative difficulty of these variants of the path/cycle-containment problems, by relating them to one another using randomized reductions, and grouping them into equivalence classes. When we restrict our attention to path-containment problems, we get a dichotomy result. Some of the path-containment problems can be solved using a linear number of queries, and all the others are equivalent to one another (and additionally to several cycle-containment problems) under randomized reductions, up to constant overhead. For the latter equivalence class, we prove a novel quantum-walk-based algorithm that achieves query complexity $\widetilde{O}(n^{3/2-\alpha_k})$, where $\alpha_k \in \Theta(c^{-k})$ and $c = \sqrt{3+\sqrt{17}}/2 \approx 1.33$, beating the previous best upper bound $O(n^{3/2})$ on its query complexity. We also provide a conditional lower bound based on the graph-collision problem, which implies that this equivalence class does not admit linear-query quantum algorithms unless graph collision admits an $O(\sqrt{n})$ query algorithm.

We develop a resource-theoretic framework for quantum coherence directly in continuous basis, with emphasis on the position representation. Since position eigenstates are non-normalizable generalized eigenstates, the standard finite-dimensional dephasing map cannot be transferred directly to normal states. We therefore introduce a physically motivated dephasing channel based on random momentum kicks, equivalently described as the unconditional back-action of a finite-resolution position measurement. This yields a fixed-point notion of incoherence and a natural class of dephasing-covariant free operations. For physically relevant kernels, however, the fixed-point set contains no normal states, showing that continuous-basis coherence is tied to dephasing disturbance rather than to distance from a nonempty set of diagonal states. We study two quantifiers built from the channel action: a relative-entropy dephasing loss and a Hilbert-Schmidt dephasing loss. The former satisfies the main resource-theoretic properties under the free operations considered, while the latter is convex and experimentally transparent but fails monotonicity and strong monotonicity. We also formulate threshold witnesses for certifying coherence above a finite value and connect them, in a two-path setting, with interference visibility. Finally, we illustrate the framework with a Gaussian wavepacket evolving in a gravitational potential. The resulting theory provides a mathematically consistent and physically motivated treatment of coherence in continuous-variable systems.

We study an exactly solvable model that can be interpreted as an ideal one-dimensional electron gas confined with an anisotropic quantum wire potential of oscillator-shaped profile. The homogeneous nature of the quantum wire is broken by the introduction of the effective electron mass, which changes with radial distance. We solve the problem described both within the canonical and the non-canonical approach. Analytical expressions of the wavefunctions of the stationary states for both cases in terms of the Laguerre polynomials are obtained, as well as the discrete energy spectrum related to these wavefunctions. Additionally, an exact solution to the angular position part of the position-dependent mass Schrödinger equation within the non-canonical approach leads to the angular-part wavefunctions of the even and odd states expressed through the Gegenbauer polynomials. Possible limit relations and special cases are studied too.

Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not increase after the time evolution. In fact, this is the case if the reduced dynamics of the system is given by $\mathcal{E}_{A}\otimes \mathcal{E}_{B}$, where $\mathcal{E}_{A}$ and $\mathcal{E}_{B}$ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as $\Psi_{A}\otimes \Psi_{B}$, where $\Psi_{A}$ and $\Psi_{B}$ are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that exhibit entanglement exceeding. Furthermore, we demonstrate that this apparent entanglement increase in the two above procedures corresponds physically to the retrieval of pre-existing inaccessible entanglement stored across the global system-environment degrees of freedom, rather than genuine generation of the entanglement $\textit{ex nihilo}$.

Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.

The Bloch Siegert shift, a hallmark correction arising from counter-rotating interactions in driven two-level systems, has an exact counterpart in binary lattices under static forcing, where it governs resonant long-range tunneling between sites separated by odd lattice spacings. Here we report the first experimental realization of this correspondence using a 12 mode programmable photonic integrated circuit. By implementing a reconfigurable binary lattice with sub-percent control of on-site detuning, we observe coherent periodic jumps across four resonance orders and quantitatively verify the predicted period law over the full parameter space. The measured dynamics exhibit the extreme resonance sensitivity characteristic of Bloch Siegert physics and agree closely with the level-anticrossing picture of the semiclassical Rabi model. Exploiting the underlying parity structure, we further convert intrinsically bidirectional oscillations into cascaded unidirectional transport through adaptive sign reversal of the staggered potential, achieving fidelities exceeding 0.95 and 0.98 on the same hardware platform. Our results establish programmable photonic lattices as a scalable testbed for strongly driven quantum-optical phenomena and Floquet-engineered transport.

Let $(\mathcal{M},\tau)$ and $(\mathcal{N},\tau^{\prime})$ be tracial von-Neumann algebras and let $\phi:\mathcal{M}\to\mathcal{N}$ be a strictly completely positive, trace preserving map. Given a positive, invertible $B\in\mathcal{M}$ with $\tau(B)=1$, a state on $\mathcal{M}$ given by a positive $A\in L^1(\mathcal{M}, \tau)$ is said to be recoverable if $\mathcal{R}(\phi(A))=A$ where $\mathcal{R}$ is the Petz recovery map corresponding to $B$ and $\phi$. In this paper, we study recoverable states and show how an arbitrary state can be made close to a recoverable state via iterates of $\mathcal{R}\circ\phi$. We show that there exists a completely positive, trace preserving map $\psi:\mathcal{M}\to\mathcal{M}$ such that $\psi(A)$ is recoverable for all $A$ and $(\mathcal{R}\circ\phi)^n\to\psi$ in norm as operators on $L^p(\mathcal{M},\tau)$ for all $1\,\textless p\,\textless\infty$, and discuss potential applications to quantum information theory. We also show that this convergence holds strongly in $L^1$. Finally, we prove an interesting decomposition theorem for normal states on $\mathcal{M}$.

State-vector quantum circuit simulation is memory-bandwidth bound, yet the interaction between memory hierarchy, access pattern, and hardware parallelism remains incompletely characterized. We address this using the Apple M4 Pro Unified Memory Architecture (UMA), where CPU and GPU share identical physical LPDDR5X DRAM ($\sim$224 GB/s STREAM bandwidth for both), eliminating memory-technology and interconnect confounds. Using a thermally isolated, multi-trial methodology across 11 simulation backends on GHZ and QFT circuits from 3 to 30 qubits, we make three central contributions. First, a Roofline analysis confirms all gate implementations have arithmetic intensity $\leq$0.38 FLOP/byte, well below the ridge point for any plausible peak compute on modern hardware, establishing structural memory-boundedness. Second, we identify a reproducible 4.46$\times$ timing discontinuity at the 28$\rightarrow$29 qubit transition, confirmed under thermally isolated conditions and cross-validated across GHZ and QFT circuits; tensordot backends exhibit the full discontinuity while direct-index backends maintain $\sim$2$\times$ per-qubit scaling throughout. Third, despite STREAM predicting only 1.85$\times$ GPU speedup (MLX CPU 119.9 GB/s vs. MLX GPU 221.9 GB/s), all three algorithm classes exceed this prediction: tensordot 3.1–4.1$\times$, flat-index 3.5–5.9$\times$, and direct-index 6–10$\times$, demonstrating that peak streaming bandwidth does not predict simulation speedup for non-contiguous memory access patterns, with the gap widening as access irregularity increases. These findings provide a hardware-characterization framework for quantum simulation workloads on UMA.

Entanglement purification with two entangled resource pairs is widely employed in the literature on quantum repeater networks to counteract fidelity degradation introduced by noisy quantum memories and entanglement swapping across multiple hops. Standard purification protocols assume both resource pairs carry identical fidelity. In practice, entanglement generation is stochastic, the two resource pairs are heralded at different times, and so the first pair decoheres in memory while the second is being generated. Thus a fidelity asymmetry is a structural feature of any network operating under realistic memory conditions, leading to the question: when is it beneficial to perform purification? We derive a closed-form fidelity asymmetry tolerance delta(F) that governs whether a purification attempt is beneficial. We determine a universal upper bound delta_max of approximately 0.076 beyond which purification is always counterproductive. Our simulations show that with exponential memory decoherence, purification yields benefits in only approximately 14% of purification attempts on two resource pairs in a two-hop repeater chain. We define three network objectives: fidelity only, time only, and a combination of time and fidelity, to deliver end-to-end entanglement. We show that when the application fidelity requirement is achievable through swapping alone, no-purification is the superior policy, with its advantage increasing with the number of hops. When the fidelity requirement cannot be met with swapping alone and purification is necessary, to be effective, it must be conditioned on delta(F) between resource pairs. We introduce DeltaPurify, a policy that conditions purification decisions on local fidelity information, and show it reduces time-to-serve relative to both naive purification and no-purification across several fidelity thresholds and hops of a repeater chain.