Papers

Complex zeros of wavefunctions represented as entire functions in Bargmann–Fock space encode structural information about the underlying quantum state. Prior work employed zero galleries of randomly generated polynomial superpositions of Fock states as visual fingerprints suitable for classification. Here we examine whether Bargmann zeros of physically realized eigenstates of one-dimensional anharmonic and double-well Hamiltonians carry a recognizable signature of the tunneling transition in the symmetric double well. Ground and first-excited eigenstates are obtained from a variational ansatz consisting of a physically motivated symbolic envelope multiplied by a small flexible correction network, trained by Rayleigh–Ritz minimization of the finite-difference Hamiltonian expectation value and validated to reproduce energies to within $\sim 10^{-5}\,\mathrm{Ha}$. The resulting wavefunctions are projected onto the harmonic-oscillator basis and the complex zeros of the truncated Bargmann polynomial are located by numerical root-finding. For harmonic and quartic-anharmonic potentials the zeros show no preferred orientation. For double-well eigenstates, by contrast, the zeros condense onto the imaginary axis. A sweep of the barrier parameter $a$ from $0.5$ to $2.3$ reveals a continuous migration of zeros toward the imaginary axis, concurrent with the exponential collapse of the tunneling splitting $\Delta(a) = E_1 - E_0$ over $3.5$ decades. This condensation is traced to a sign-alternation pattern in the Fock-coefficient spectrum that is characteristic of bimodally localized wavefunctions. The complex zero set of the Bargmann-represented wavefunction thereby provides a compact, purely analytic diagnostic for the tunneling regime of one-dimensional double-well Hamiltonians, extending the random-polynomial zero-image framework to physical eigenstates.

This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.

The expressions of the eigenfunctions of the Hawton photon position operator in configuration space are derived for several classes of wave function, including the Riemann–Silberstein and Landau–Peierls cases. Although these eigenfunctions have a simple form in momentum space, the explicit characterization of their representations in configuration space is rather more involved. We provide closed expressions of these eigenfunctions in terms of linear combinations of the complete elliptic integrals $K(\kappa)$ and $E(\kappa)$ with modulus $\kappa$ depending on trigonometric functions of the polar angle. We show that they diverge not only at the value $\mathbf q$ of the position eigenvalue, but also on a plane containing $\mathbf q$ and that they decay as inverse powers of the distance from $\mathbf q$.

Measurements can drive quantum many-body systems into nontrivial steady states and induce interesting dynamical phase transitions, rendering measurement-only quantum circuits a useful platform for exploring quantum many-body phases beyond those of equilibrium Hamiltonian systems. Here we study a class of long-range measurement-only quantum circuits with competing two-qubit and three-qubit measurements. We demonstrate that these circuits exhibit rich steady-state structure and uncover a strong influence of the measurement range on the resulting phases. In particular, states with symmetry-protected topological (SPT) order can emerge with sufficiently short-range measurements beyond the nearest-neighbor limit. These states feature robust topological edge modes, which can also be detected from circuit dynamics. With longer-range measurements, an extended parameter regime emerges in which conventional order parameters are suppressed while spatial correlations remain nontrivial. Moreover, we show that in this circuit model sufficiently long-range measurements can produce significant entanglement with scaling beyond an area law despite the absence of any unitary evolution.

Dissipation engineering has attracted growing interest as an approach to controlling open quantum systems through engineered system-environment interactions. Standard variational quantum circuits are usually built from unitary operations and therefore explore only a restricted family of states. To go beyond this limitation, we introduce a variational dissipative framework in which ancilla-assisted engineered dissipation is incorporated into parameterized quantum algorithms. In this framework, system-only variational layers are combined with trainable dissipative modules, so that the circuit can prepare a broader class of mixed states through ancilla-assisted nonunitary transformations. Within this framework, the same ancilla-assisted dissipative block is used in two representative settings with different objectives. For ground-state search, it is integrated into a dissipative variational quantum eigensolver to improve the convergence toward low-energy states. For state recovery, it is trained as a recovery channel to suppress preparation noise and enhance fidelity with the target state. In both cases, the block is realized through parameterized system-ancilla couplings followed by ancilla reset and trace-out. Our results show that engineered dissipation can be incorporated into variational quantum circuits as a reusable trainable primitive rather than treated only as a source of noise. In this sense, the proposed framework identifies ancilla-assisted dissipative channels as a concrete variational resource that can support both optimization and recovery tasks within a unified design.

Open quantum systems are central to quantum optics, condensed matter, and chemistry, yet their simulation remains challenging for both classical and near-term quantum hardware. In this work we implement and execute utility-scale quantum circuits that accurately reproduce the dissipative dynamics of interacting qubits. We consider a one-dimensional chain of many qubits weakly coupled to a common Markovian bath. The Markovian time evolution of the system is implemented through Trotterized evolution with the introduction of ancilla-assisted dissipative channels, including single-qubit and two-qubit dissipators to capture collective decay. Mid-circuit measurements, conditional gates, and hardware-aware transpilation significantly reduce circuit depth. We further implement a biased Clifford data regression (biased CDR), an error mitigation strategy that outperforms the uniform Cliffordization baseline and a variety of zero-noise extrapolation protocols. We execute large-scale quantum experiments of the dynamics of chains comprising up to 86 emitters on the IBM System Two ibm\_basquecountry. In order to do so, we use 129 total qubits (including ancillas), with the largest circuits contain about 8000 two-qubit gates. To validate these experiments we develop a classical Monte Carlo-Time-Evolving Block-Decimation (MC-TEBD) tensor-network method that incorporates reset operations through stochastic pure-state trajectories, obtaining very good agreement. The approach presented here opens a practical route for utility-scale quantum simulation of dissipative dynamics, enabled by dynamic circuits, targeted error mitigation, and tensor-network validation, and enables to tackle complex dynamics of systems such as quantum emitters in dissipative optical cavities.

Quantum wave mixing on a single superconducting qubit produces a hierarchy of coherent side peaks associated with elastic multiphoton scattering pathways. In a cascaded source–probe geometry these pathways become sensitive to the photon statistics of the radiation emitted by the source qubit. We develop an analytical theory of this effect starting from the cascaded master equation in the weak-driving regime. In the coherent-filtering limit when the decay rate of the probe qubit is less than that of the source, the standard coherent–coherent wave-mixing hierarchy is recovered. In the opposite limit, side peaks associated with multiphoton absorption from the antibunched source field are parametrically suppressed. Numerical solutions confirm the analytical scaling laws. The resulting sideband hierarchy provides a frequency-domain fingerprint of antibunched itinerant microwave light.

We formulate a one-dimensional flux-controlled anomalous Floquet quantum walk and show that it admits a direct microscopic realization in a driven bipartite lattice. The walk consists of a coin-dependent drift step and a momentum-dependent coin mixing step, so the same evolution operator governs quasienergy bands, boundary modes, and bulk dynamics in real space. Because the walk is chiral, the quasienergy gaps at $0$ and $\pi/T$ carry independent topological information, which organizes trivial, $0$-only, $\pi$-only, and coexistence sectors in the $(M,\phi)$ plane. In the coexistence sector, a $0$ mode and a $\pi$ mode reside on the same edge and span a natural boundary logical subspace. One Floquet period acts there as a relative phase operation and produces a clear $2T$ response in local boundary observables. In the bulk, the same anomalous Floquet structure is probed dynamically in two complementary ways. Frame-resolved mean chiral displacements approach the two winding numbers in the clean pre-reflection window of the symmetric time frames, while selected benchmark cuts at a representative $0$ gap closing and a representative $\pi$ gap closing exhibit distinct local stroboscopic responses, with the $\pi$ gap benchmark showing a much stronger odd-even alternation. The boundary logical subspace and the bulk dynamical probes are therefore organized within one flux-controlled anomalous Floquet quantum walk, suggesting a symmetry-protected route to quantum-walk information primitives in driven microstructured lattices.

Quantum federated learning (QFL) on NISQ hardware is highly sensitive to backend heterogeneity: some clients contribute informative updates, while others contribute noise-dominated drift that uniform averaging cannot distinguish. We propose Q-RAIL (Quantum Reliability-Aware Federated Inference and Learning), a circuit- and calibration-aware aggregation method for hardware-heterogeneous QFL. Q-RAIL computes a client-specific effective noise budget from backend calibration metadata together with transpiled circuit statistics. This budget is converted into stabilized aggregation weights using temperature scaling, uniform mixing, and a minimum-weight floor. Q-RAIL was evaluated across multiple experimental settings, including an ablation study, and benchmarked against state-of-the-art methods on three datasets: MNIST, Fashion-MNIST, and OrganAMNIST. On the primary MNIST benchmark under strong hardware skew, Q-RAIL improves final test accuracy from FedAvg's 0.777 to 0.877, a +10.0-point gain corresponding to about 44.8% relative error reduction, while also exceeding the strongest wpQFL baseline (0.833). At the same time, test loss drops from 0.722 to 0.585, and test AUC rises from 0.920 to 0.973. Under non-IID MNIST, Q-RAIL reaches 0.813 vs 0.722 for FedAvg. It also outperforms FedAvg in 12/12 ansatz/CX-fold stress configurations and remains stronger at 4, 10, and 15 qubit setups. Overall, the results support calibration-driven, circuit-aware aggregation as a practical path toward robust QFL on heterogeneous quantum hardware.

Hybrid quantum neural networks (HQNNs) integrate parameterized quantum circuits (PQCs) within classical networks, where the behavior of the underlying PQCs is often the primary focus of analysis. In this context, expressibility and trainability are widely used to characterize PQC's performance and are commonly assumed to exhibit a trade-off, where highly expressive circuits are more susceptible to barren plateaus. However, the validity of this relationship in HQNNs remains unclear. In this paper, we systematically analyze the expressibility–trainability relationship in HQNNs across varying circuit depths, qubit counts, entanglement topologies. We consider different training configurations, including pure PQCs, quantum-only training in hybrid setting, and full end-to-end training of hybrid models. Our results show that pure PQCs exhibit only a weak and regime-dependent trade-off, while hybrid architectures increasingly disrupt and can eliminate this relationship under full hybrid training. This indicates that classical components reshape the optimization landscape, decoupling trainability from PQC expressibility. We further propose a multi-objective neural architecture search (NAS) framework that jointly optimizes expressibility, trainability, and task performance over a combined classical–quantum design space, revealing different Pareto-optimal solutions under full end-to-end and quantum only training in hybrid setting. different trainability definitions. Our results suggest that hybridization is not just an implementation detail, but a defining factor in the performance of quantum machine learning models.

We investigate the dynamics of a qubit chain locally coupled to a thermal reservoir, modeled through repeated collisions with particles drawn from a heat bath. Under suitable conditions, the resulting Lindblad equation is thermodynamically consistent – it drives the system toward thermal equilibrium – while remaining local at short times. This framework reveals a crossover between the global Lindblad equation derived from the secular approximation in weak-coupling theory and the local dissipative models often employed in the literature, which generally fail to ensure thermodynamic consistency.

Power side-channel attacks on AES exploit data-dependent physical leakage to recover secret keys, but turning noisy leakage observations into a verified AES-128 key remains a hard combinational search problem. SAT-assisted power side-channel cryptanalysis addresses this challenge by encoding AES semantics, key constraints, plaintext/ciphertext consistency, and leakage predicates as CNF, so that candidate keys must satisfy the exact cryptographic specification. These cryptanalytic SAT formulas are large and highly structured; our largest controlled AES-oriented power-SCA instances contain up to 39,389 variables and 137,712 clauses, making a full-formula Grover search well beyond the scale studied here and beyond currently practical near-term implementations. We propose QGCL, a Quantum-Guided Conflict-Driven Clause Learning (CDCL) framework in which Grover search is invoked only on small subformulas extracted dynamically around CDCL conflict cores. The quantum subsolver returns candidate assignments and violation scores that bias branching heuristics, while final SAT/UNSAT decisions and key verification remain classical. We evaluate QGCL on AES-oriented cryptanalytic SAT instances derived from power side-channel CNFs with leakage-derived hint configurations, measuring conflicts, restarts, decisions, and propagations. The experiments show consistent reductions in these solver-internal statistics on harder instances, with up to an 86% reduction in conflicts compared with the classical conflict-learning baseline. Parameter sweeps over the number of Grover oracle calls and the subproblem size identify a regime in which a modest quantum resource allocation captures most of the observed improvement.

Photons in a two-path interferometer best embody wave-particle duality (WPD), which is a core concept of quantum theory. So far, the WPD relation is commonly written as $V^2+D^2 \leq 1$, where $V$ is the interference fringe visibility and $D$ is path distinguishability, i.e., the distinguishability of which path a photon passed. This inequality is saturated only when the which-way marker (WWM), which embodies which-path information (WPI) via an internal degree of freedom of photons, such as polarization, is in a pure state. For mixed-state WWM, conventionally defined distinguishability underestimates the amount of WPI and thus does not saturate the WPD relation. Here, we introduce a generalized measure of distinguishability $D$ that properly quantifies the WPI and saturates the WPD relation for all pure- and mixed-state WWM within a purification-based framework. To this end, mixed-state WWM is treated as a result of entanglement formation between the WWM and an external degree of freedom, e.g., environment, and $D$ is defined so that it incorporates the total WPI shared between the WWM and the environment. We show that $D$ thus defined is experimentally quantifiable, independently of $V$, without access to the environment. We experimentally evaluate $V$ and $D$ using true single photons generated in the completely mixed (unpolarized) state, and thus verify the saturated WPD relation.

Formal verification of power side-channel leakage and its countermeasures in cryptographic algorithms is challenging, as SAT-based methods fail to scale on XOR-heavy, time-unrolled cryptographic circuits with realistic leakage models. We construct compact Conjunctive Normal Form (CNF) cases modeling one-bit leakage under two-trace conditions, linking key dependence and state evolution. Classical solvers quickly reach complexity limits, so we propose Q-LEAK, a quantum-based verification approach using Grover's algorithm, compiling each CNF into an oracle and applying amplitude amplification to search in O(sqrt(N)) oracle calls, with oracles that encode the two-trace leakage predicate and the CNF constraints. Benchmarking against classical SAT shows both potential gains and practical resource limits. In noiseless tests on 5-7 variable benchmarks, Q-LEAK consistently recovered a satisfying assignment within 1-4 tries, with marked bitstrings amplified clearly above the background distribution, exceeding 20 percent probability. The evaluation of Q-LEAK on real quantum hardware revealed at least one classically verified SAT assignment, despite the presence of noise. These results point to a potential path toward quantum-assisted verification of side-channel protections.

We study the algebraic compatibility between quantum homomorphic encryption and stabilizer quantum error correction in an honest-but-curious model, restricting the encryption to the transversal block-Pauli mask $(X^aZ^b)^{\otimes n}$ controlled by two secret key bits $a$ and $b$. We prove a necessary and sufficient criterion for an $[[n,1,d]]$ stabilizer code to remain compatible with this mask, namely that the transversal $X$ and $Z$ operators commute with every stabilizer generator, and we specialize it to a classical-code criterion for Calderbank–Shor–Steane codes. Combining code-space preservation with the logical action of the mask, every stabilizer code falls, with respect to each of the two transversal mask operators, into exactly one of three classes: incompatible, compatible but trivially acting, or compatible with a nontrivial logical Pauli action; the two operators need not fall into the same class. We verify this classification by exact symplectic computation for rotated and planar surface codes, toric codes, triangular and toric color codes, the $[[15,1,3]]$ code and several small codes, and find that the class is fixed by the lattice size and the boundary presentation rather than by the topological phase: the surface-code family realizes all three classes, whereas color codes realize only the two compatible ones. For encrypted computation we show that the Shor code does not implement the logical $T$ gate by a transversal $T^{\otimes 9}$, whereas suitable triorthogonal codes do so up to a Clifford correction. We formulate logical-Pauli masking as a code-independent algebraic template. Syndrome extraction and recovery are key-independent whenever the mask preserves the code space, so that the client only needs the block size and the class of the code to decrypt.

The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random tensor networks. In these contexts, the entanglement entropy undergoes a transition between area-law and volume-law scaling, depending on the model parameters. This transition point has attracted considerable attention. In the present work, we investigate the ferromagnetic-paramagnetic phase transition of the permutation model, which corresponds to the entanglement entropy transition. Using exact real-space renormalization group calculations on self-dual hierarchical lattices, we numerically determine finite-replica critical points for (q=mn=2,...,6). We compare the results with the duality prediction based on the Fourier transform of the symmetric group and then extrapolate the b=3 data toward the replica limit $mn\to0$, where the effective dimension is two. The comparison supports the duality-based estimate while also clarifying the systematic uncertainty associated with the extrapolation formula.

Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural route beyond periodic order, enabling dissipative time quasicrystals without externally imposed quasiperiodic driving. We consider a collectively driven-dissipative four-level ensemble with two degenerate excited states and two degenerate ground states. In the thermodynamic limit, the exact mean-field dynamics reduces to an irrational flow on a two-dimensional torus, yielding quasiperiodic order parameters with discrete spectra generated by two incommensurate fundamental frequencies. Vanishing maximal Lyapunov exponents demonstrate that the nonlinear self-consistent dynamics remains nonchaotic. Our results establish a minimal interference-induced mechanism for time-quasiperiodic order and open a route toward higher-dimensional quasiperiodic dynamics in multilevel systems.

Photonic hyperentanglement enables increased information capacity and enhanced functionality for quantum communication and networking. However, synchronization of hyperentangled photon pairs requires maintaining correlations simultaneously across multiple degrees of freedom (DOFs). The preservation of polarization and energy-time entanglement in hyperentangled photon pairs is demonstrated using a free-space optical delay line based on nested Herriott cells. After a delay of 647 ns, a two-photon interference visibility of 93.9(3)% is observed in the energy-time DOF, while a CHSH parameter of 2.758(5) is obtained in the polarization DOF. These results confirm that entanglement correlations in both DOFs are preserved after propagation through the delay line. They demonstrate that free-space optical delay lines are compatible with complex photonic quantum states and provide a promising route toward delay-based memories for synchronization and multiplexing in quantum networks.

We investigate the fidelity susceptibility, which quantifies the sensitivity of single-particle eigenstates to perturbations, in the three-dimensional Anderson model. As a function of disorder strength $W$, it exhibits two distinct peaks. The first peak signals a crossover at weak disorder strength from plane-wave states to single-particle quantum chaos, and its position shifts toward $W\to 0$ in the thermodynamic limit. The second peak emerges, to high numerical accuracy, at the critical disorder strength associated with the Anderson localization transition. We further show that the divergence of the first peak is maximal, scaling as the square of the inverse frequency cutoff, whereas the divergence of the second peak is submaximal. We relate the latter suppression to the fractal structure of single-particle eigenstates at criticality. We discuss two distinct scenarios that give rise to the peaks in the fidelity susceptibilities. Moreover, studying the scaling of typical fidelity susceptibilities above the Anderson transition, we find evidence of two distinct regimes of nonergodic behavior.

We investigate the renormalized fermion-gluon vertex, the fermion effective mass, and the fermion condensate when the fermion propagates in an external Yang-Mills gauge field. We use an exact Green's function for the Dirac operator in a non-Abelian plane-wave gauge field to construct the renormalized vertex function, calculate the on-shell fermion self-energy, and the background-dependent condensate. We consider both the background and operator fields in the axial gauge $k^{\mu } \mathcal{A}_{\mu }^{a}=0$, thereby preserving the gauge. Its applications to strong-field QCD and non-Abelian Schwinger physics are discussed.

Variational quantum algorithms (VQAs) rely on parameterized quantum circuits (PQCs), whose performance is governed by expressibility and trainability. Existing studies typically evaluate these properties at the logical circuit level, implicitly assuming that designed PQCs remain unchanged during hardware execution. In practice, however, hardware-aware transpilation modifies circuit structure through qubit mapping, routing, and basis decomposition, potentially altering PQC behavior. In this paper, we perform a systematic hardware-aware analysis of expressibility and trainability by comparing logical and transpiled PQCs across multiple ansatz families, qubit counts, and circuit depths. Expressibility is measured using fidelity-based KL divergence, while trainability is quantified through gradient variance. Our results show that transpilation acts as an implicit architectural perturbation, producing strongly ansatz-dependent effects. Expressibility deviations exceed upto 125% in some cases, while trainability variations reach up to 25%. Structured ansatzes are generally more robust, whereas highly entangled architectures are more sensitive to transpilation-induced transformations. We further show that transpilation can alter the commonly assumed expressibility-trainability trade-off, demonstrating that logical-level analyses may not reliably predict hardware-level behavior. These findings highlight the importance of hardware-aware evaluation for accurate characterization of VQAs.

Correlations distributed by a mediator can be useful for coordination but vulnerable to inheritance by a colluder. We formalize the obstruction to such inheritance as a source-certified resource theory of strategic non-shareability. The free objects are symmetrically extendible sources, the free operations are shareability-preserving maps, and the trace distance to the free set is a faithful convex monotone. For Werner and isotropic sources in arbitrary local dimension, the resource has the exact form $D_m=c(d)(p-p_m^{*})_{+}$, with $p_m^{*}$ the Johnson–Viola shareability threshold. For qubit Werner sources, tomographically complete Pauli measurements yield the exact one-colluder capacity\[ C^{\rm tomo}_1(p)=\frac{1}{12}\Bigl[(3p-1)-\sqrt{(3p+1)(1-p)}\,\Bigr]_{+}.\] We prove that this anti-collusion resource is independent of Bellnonlocality: the Bell and shareability orderings cross, so some Bell-nonlocal states are strictly less collusion-resistant than Bell-local ones. Finally, we give an aligned Pauli coordination game whose observed behaviour has a local hidden-variable model for every visibility, making device-independent certification empty, while source-certified quantum anti-collusion is positive exactly above the extendibility threshold. These results identify symmetric non-extendibility, rather than Bell nonlocality, as the boundary of source-certified collusion resistance.

Quantum chaos plays a key role in understanding complex quantum dynamics, while integrated photonics offers unique advantages for quantum applications, including high-speed operation, scalability, and programmable unitary transformations. However, integrated photonic approaches to probing quantum chaos remain largely unexplored, owing to the absence of a clear connection between programmable photonic dynamics and established chaos diagnostics. In this work, we establish Fock-state boson sampling as a practical probe of quantum chaos by exploiting the sensitivity of multiphoton interference to the random-matrix properties of underlying single-particle unitary dynamics. More importantly, we design and fabricate a programmable quantum photonic chip to experimentally implement this framework, achieving the first integrated-photonic demonstration of quantum-chaos probes based on boson sampling. Experimental results show that the three complementary probes proposed in this work, namely the distance to Porter–Thomas statistics, Shannon entropy, and Out-of-Time-Ordered-Correlator-equivalent observables, exhibit close agreement with theoretical predictions and consistently distinguish chaotic and integrable dynamics. Our work provides a scalable route for investigating complex quantum dynamics on programmable photonic platforms while leveraging the intrinsic advantages of boson sampling through multiphoton interference and complex output statistics.

The non-Hermitian skin effect (NHSE) is a hallmark of non-Hermitian system, yet its generalized Brillouin zone (GBZ) description is restricted to periodic systems. We develop a site-resolved theory via a local scaling transformation (LST), introducing local twisting $T_n$ to quantify metric operator $\xi$ nontriviality. This elucidates the NHSE's origin and uncovers the generalized multiple-channel skin effect (MCSE). Exploiting $T_n$'s translational independence, we define the Zahlen-Brillouin Zone (ZBZ), extending non-Hermitian band theory to nonperiodic and disordered lattices. Furthermore, we unify the $\xi$ with GBZ Riemannian geometry, establishing the metric and state correspondence (MSC) as the principle for real-space localization. With a global skin index $\mathbf\Gamma$ for phase transitions, our results provide a universal paradigm for non-Hermitian physics in both crystalline and amorphous media.

Transformer now underpins modern AI as its core infrastructure. Its defining capability-dynamically focusing on the most relevant information in complex inputs-is bounded above by the self-attention scoring function. Quantum computing, with its superposition, entanglement, and probabilistic outputs, offers a fundamentally distinct computational framework for exploring beyond the design constraints of classical scoring functions. While quantum attention mechanisms have shown initial promise, existing works remain largely confined to redefining feature similarity measures, leaving the systematic use of parameterized quantum circuits (PQCs) as scoring functions largely unexplored; a substantial portion of existing schemes further rely on purely quantum architectures, precluding effective encoding of high-dimensional image inputs in the Noisy Intermediate-Scale Quantum era. We propose the Quantum Parameterized Self-Attention Network (QPSAN), implementing the self-attention scoring function via PQCs with only 5 trainable quantum parameters per layer. QPSAN computes query-key attention scores through quantum state encoding and joint measurement, yielding naturally bounded outputs without the explicit scaling of classical dot-product attention. We further establish a theoretical framework of the mathematical properties of this scoring function, demonstrating its potential to capture complex nonlinear query-key interactions, and quantifying the structural constraints of the encoding layer via effective degrees of freedom analysis. Experiments on four vision datasets show that QPSAN significantly outperforms the Vision Transformer (ViT) baseline, with the quantum representational advantage amplifying as data complexity increases. Ablation studies indicate that the performance gains may stem from the structural inductive bias of the quantum circuit rather than from parameter scale.

Dense linear maps carry much of the parameter and computational burden of modern neural networks, yet their dense form leaves the organization of learned couplings implicit. Quantum many-body physics organizes exponentially large operators by writing a global Hamiltonian as a sum of local terms, \(\hat H=\sum_k\hat h_k\). Whether the same structural principle can carry learned neural maps is unknown. We introduce Tensor Mixture (MixT), which represents a dense map as a natively executable sum of overlapping local tensor operators without imposing an explicit matrix-rank constraint. The local-term count \(N_T\) sets the effective nonlocality and operator complexity, while the number of replaced Transformer blocks \(N_B\) extends this structural coordinate across network depth. Tests on Qwen3-8B and LLaMA2-7B reveal a broad recoverable regime followed by an abrupt, model-specific boundary that is remarkably stable against changes in \(N_T\). Accuracy and output-distribution statistics reorganize together across the boundary; in LLaMA2-7B, the same depth separates two scaling regimes of inter-layer geometry drift. The directly executed structure also reduces parameters, arithmetic, storage, and memory. These results establish the local-sum structure as a viable organizing principle for learned linear maps at billion-parameter scale and expose a sharp boundary in their tolerance to structural simplification.

Nondispersive wave packets in driven helium are long-lived quantum states that follow classical resonant orbits without spreading. Their identification typically requires detailed analysis of phase-space structures and extensive exploration of parameter regimes. In this work, we introduce an unsupervised learning approach to automate the identification of physically relevant states in the driven helium atom. Using a Floquet-based description, quantum states are computed and represented as probability distributions in configuration and phase space, which serve as input to a convolutional neural network that constructs a low-dimensional embedding of the data. Clustering in the embedding space reveals distinct classes of quantum states. By combining geometric analysis, physical parameter inspection, and time-evolution studies, we identify clusters corresponding to frozen planet states and nondispersive wave packets. The method successfully recovers known NDWP regimes without prior labeling, demonstrating that the learned representation captures physically meaningful structures in a systematic and automated manner. These results establish unsupervised representation learning as an effective tool for the systematic analysis of complex quantum datasets.

We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM codes with column and row weights that result in measured stabilizers that have constant weight, thus preserving the desirable properties of the underlying QLDPC code. This process allows for control over stabilizer weights and SM code distance, resulting in significantly better performance than repeated syndrome extraction and allowing for both higher distances and fewer syndrome measurements. We implement these SM codes on a distance-5 rotated surface code, and show that this procedure results in a lower probability of logical error. As syndrome measurements performed are a reasonable metric for the time a circuit takes to implement, we conclude that these LDGM codes allow for improved implementation of QLDPC codes without sacrificing the low weights of the syndrome measurements performed.

We present a microscopic statistical-mechanical foundation for interpreting the horizon area of a scrambling black hole as coherent information, equivalently negative conditional quantum entropy, in Hawking's pair-creation picture. We derive the entropy increase induced in a black hole when an infalling object is absorbed and scrambled into its microscopic degrees of freedom. Up to finite-reservoir corrections, this increase takes a canonical form at the Hawking temperature, regardless of the initial entropy carried by the infalling object. Applying this entropy formula to an incoming mode paired by time reversal with an outgoing Hawking radiation mode, we show that their partition-function contributions cancel in the coherent-information balance associated with the horizon area. The resulting area response is then determined only by the energy flux, in agreement with the black-hole first law.

We present an efficient scheme to randomize a spin-state ensemble in a nonlinear spin-1 system by tuning chaos with an external periodic drive. Without modulation, the system exhibits a mixed phase space featuring regular islands embedded in a chaotic sea, where global mixing is inhibited by energy conservation. Using numerical simulations, we demonstrate that weak modulation of a linear Zeeman field not only facilitates transport between different energy shells but also drives ensembles toward a Haar-random distribution over spin states. Under optimized conditions, complete randomization is achieved on a timescale set by the inverse nonlinear interaction energy. In the overdriven regime, randomization is unexpectedly suppressed at specific modulation amplitudes, accompanied by the formation of sticky regions in phase space. We attribute this behavior to the dynamical cancellation of the leading low-order harmonic component of the periodic drive. These results illustrate how time-periodic driving can be used to engineer chaotic systems and achieve controllable randomization in nonlinear spin systems.