Papers

Quantum heat transport governs energy exchange processes and statistical laws in non-equilibrium quantum systems, and plays a pivotal role in quantum thermodynamics. We investigate the steady-state thermal transport of a noncommuting coupled spin system. We employ the quantum dressed master equation approach within the framework of open quantum system theory to accurately analyze the non-equilibrium dynamics, ensuring the validity of transport results in the strong coupling regime. Our results demonstrate that noncommuting spin coupling serves as a significant resource for modulating the nonlinearity of the heat current. Specifically, in the weak spin-coupling regime, the system exhibits robust negative differential thermal conductance (NDTC) across various spin numbers. By deriving analytical expressions for the heat current in both the single-spin and large-spin limits, we reveal that this NDTC behavior is governed by microscopic cycle fluxes. Physically, this arises because spin excitation channels induced by the cold reservoir are suppressed under a large temperature bias, thereby blocking energy exchange cycles. Conversely, in the strong spin-coupling and large temperature bias regime, the quantum system demonstrates pronounced thermal rectification. This high rectification efficiency originates from the unidirectional saturation of the heat current, rendering the system a promising candidate for high-performance thermal diodes. Furthermore, we extend the model to a three-terminal configuration to construct a quantum thermal transistor. By manipulating the temperature of the gate reservoir, we achieve efficient modulation and amplification of heat flow between the source and drain. The heat amplification factor is shown to far exceed unity in specific operating regions, confirming significant thermal amplification.

Integrated quantum photonic circuits are a key enabling technology for the scalability of quantum information systems. Among the available platforms, silicon photonics offers an unrivalled capability for the large-scale integration of photonic components within compact footprints. However, the strong index contrast that enables ultra-compact silicon devices also makes them highly sensitive to fabrication imperfections. As circuit complexity increases, active tuning is generally required to maintain spectral alignment among the different components, leading to significant power consumption that ultimately limit scalability. Here, we demonstrate a fully integrated silicon quantum photon-pair source operating without active tuning of any component. The circuit combines photon-pair generation in a micro-ring resonator, pump rejection using Bragg filters, and signal/idler demultiplexing through modal add-drop filters with building blocks engineered to minimize sensitivity to fabrication variations. The resulting circuit achieves excellent experimental quantum performance. Coincidence rates up to 4000 counts s^-1 with coincidence-to-accidental ratios as high as 100 are obtained across the generated spectrum, while separate two-photon interference measurements yield raw visibilities exceeding 93% for individually selected ITU wavelength-channel pairs. By eliminating the need for active spectral tuning while maintaining high quantum performance, this work addresses a major bottleneck in the scaling of complex silicon quantum photonic circuits.

Quantum circuit optimization is critical for mitigating the noise inherent in current quantum hardware. Quantum compilers typically sequentially apply multiple optimizations (also called “optimization passes”) to improve the circuit. The impact of the order in which these passes are executed has yet been largely unexplored. This paper investigates the significance of the order of optimization passes within quantum circuit compilation, specifically analyzing interactions between different optimization methods and quantifying their mutual influences. Using Qiskit's compiler, we systematically evaluate pairwise combinations of 16 selected optimization passes, measuring circuit depth and gate count across various benchmark circuits. Our findings indicate dependencies between certain optimization passes, demonstrating that the order of the passes affects the optimization quality. In some cases, the worse performing sequence can be corrected through repeated pass application. %such that they are as good as the best performing one by extending the sequence. Experiments on multi-pass sequences show that more than two optimization passes may have an impact on each other but that this always links to the previously found pairwise effects. We observe that it is important to initially choose the best order of optimization passes to get the best possible optimization for the given circuit. The experiments reveal some factors which are important to choose the best, or at least a good, order; among those, the resulting optimization sequence depends the most on the native gate set.

Phase-space representations reveal the geometry of quantum mechanics and distinguish quantum features from classical ones. However, the positivity of a density operator is among the properties of quantum states that phase-space representations capture least directly: deciding whether a phase-space function describes a physical quantum state has so far required global conditions coupling distant points in phase space. Here we show that these conditions can in fact be made local, by considering the Husimi representation in phase space. We establish a complete set of conditions which captures when a phase-space function $f$ is the Husimi function of a quantum state, with each condition involving only the derivatives of the function $f$ evaluated at a single phase-space point. We further show that each condition has an equivalent algebraic characterization, which takes the form of the nonnegativity of a determinant of the underlying operator in a displaced Fock basis. As a result, these conditions obey a recurrence relation organizing them into a differential hierarchy, which terminates based on the rank of the operator. Our results thus show that operator rank and positivity are local properties in phase space, reinforcing the role of phase-space representations as a geometric description of quantum mechanics.

We reveal that the information geometry of entropy production exhibits an intrinsic anisotropy, providing a unified origin for the inequivalent geometric constraints obeyed by its different components. Using a hierarchical projection structure of quantum relative entropy, we derive an exact orthogonal decomposition of entropy production into three distinct geometric contributions associated with the deviation of the Gibbs projection temperature from the reference temperature, the deviation of the environment from its Gibbs projection state, and system–environment correlations. We demonstrate that these contributions obey fundamentally different geometric bounds: the first reduces to a classical Kullback–Leibler divergence and admits no universal upper bound in terms of the trace distance and the system and environment dimensions alone, whereas the latter two admit rigorous distance-based bounds with dimension-dependent factors. The framework also applies to classical Markovian dynamics described solely in terms of the system state, for which the system–environment correlation contribution is absent from the decomposition. Combining this geometric decomposition with dynamical speed limits, we obtain rigorous bounds on entropy production expressed solely in terms of physically accessible quantities, such as the mean energy and Hamiltonian variance.

A quantum measurement transforms a quantum statistical experiment into a classical one, but different measurements generally yield experiments with different statistical information. We introduce quantum-to-classical sufficiency: relative to a prescribed measurement class, a measurement is sufficient if its induced classical experiment Blackwell-dominates those from every other measurement in the class. This separates two components of quantum inference: reducing the measurement class through symmetry or decision-theoretic arguments, and identifying a canonical measurement in the reduced class by an experiment-level sufficiency condition. We establish a factorization criterion where the parameter enters the group-averaged experiment only through weights of an orthogonal block decomposition. The block-label measurement is then sufficient relative to all invariant measurements. For tensor-product models under unitary conjugation, this identifies weak Schur sampling as the sufficient measurement for spectral inference. Combined with risk-preserving symmetrization, it reduces invariant Bayes and minimax problems over all measurements exactly to classical decision problems based on Young diagrams. We derive sharp first-order asymptotic Bayes and minimax risks for smooth spectral functionals. We establish an analogous reduction for a noncompact group action in a continuous-variable setting. We consider displaced thermal states and functionals of the thermal parameter with an unknown displacement. Within displacement-invariant measurements, total residual photon number measurement emerges as the sufficient measurement. Combined with Hunt-Stein reduction, this yields exact finite-sample reductions of Bayes-minimax and minimax problems over all measurements to classical decision problems based on the total residual photon count, which follows a negative binomial distribution.

Dynamical simulation of quantum many-body systems is a central task in quantum chemistry and requires efficient wavefunction representations. Although tensor-network and neural-network quantum states have achieved considerable success in ground-state calculations, entanglement growth hinders their application to quantum dynamics. Quantum computing may offer a route to quantum advantage, but algorithms such as Trotterization generally require fault-tolerant quantum computers, whereas near-term hardware supports only limited circuit sizes. Variational quantum simulation (VQS) instead represents the evolving state with a single shallow, fixed-size parameterized quantum circuit (PQC). Here, we introduce nonorthogonal variational quantum simulation (NOVQS), which applies linear combinations of parameterized quantum states to real- and imaginary-time evolutions. We design a shallow, hardware-friendly ansatz tailored to second-quantized electronic-structure Hamiltonians, together with resource-efficient protocols for measuring the matrices and vectors in the parameter equations of motion. Error analysis and resource estimation are also provided. Numerical simulations of hydrogen chains and the nitrogen molecule demonstrate that a collection of shallow, or even single-layer, PQCs can match or outperform a much deeper PQC in VQS. In particular, we identify a trade-off between circuit number and depth. NOVQS therefore provides a flexible route to enhancing wavefunction expressivity under circuit-depth constraints, making it a promising framework for quantum dynamics simulations on near-term quantum processors.

Hybrid quantum-classical compilers exchange programs among circuit, control-flow, pulse, device, and physical representations. Existing formats make different abstraction choices, so the properties that must survive a lowering step are often enforced by tool-specific code rather than stated in a common intermediate representation (IR). We present QaiJi IR, an eight-layer family organized by a five-axis semantic contract for data, semantics, lowering, runtime, and verification. Its L4 SemanticIR records the operation class, declared equivalence level, optimization role, and classical-feedback model as attributes, and maps operation classes to ISA-neutral hardware actions. The prototype provides typed quantum and classical circuit nodes, OpenQASM~2 compatibility input, canonical OpenQASM~3 output, explicit rejection of unsupported constructs, and executable gate-convention checks. A representative measurement-conditioned program reaches a canonical QASM fixed point, acquires a measurement-to-condition edge, passes an exact aggregate consistency check, and produces a symbolic pulse template. For a one-bit active-reset case, device lowering materializes ALU/FPROC records and a conditional branch. Running the resulting virtual pulse processing unit (VPPU) program with externally supplied outcomes 0 and 1 respectively skips and executes the conditional drive. These tests validate the represented compiler path and binary branch behavior. They do not establish a physical feedback loop, because the simulator cannot yet apply mid-circuit measurement collapse and continue the same dynamical trajectory.

True random number generation is a critical capability for fault-tolerant quantum computing at millikelvin temperatures. Yet existing Josephson-junction-based TRNGs all rest on a widely accepted but untested assumption: that reliable entropy extraction requires precisely controlled device parameters. Here we show that this assumption does not always hold. We demonstrate a counterintuitive finding: a single current-biased Josephson junction, regardless of its parameter quality, can serve as a cryptographic-grade true random number generator. To establish the universality of this conclusion, we deliberately selected the most extremely deviated devices from fabrication, with critical currents three orders of magnitude away from theoretical predictions and $I_cR$ products an order of magnitude above conventional values, as the ultimate stress test. Even under these extreme conditions, the raw Shannon entropy reaches 0.9981~bit (99.8% of the theoretical maximum), with a min-entropy of 0.9271~bit. Using a square-wave pulsed-bias scheme, we tune the switching probability to $P\approx0.5$. After SHA-256 post-processing, the bitstreams pass all 15 NIST SP 800-22 tests under a conservative $m=3$ criterion that is more demanding than the standard recommendation, and this certification holds across the entire 100-700~mK operating window of a dilution refrigerator.

Magic-state cultivation offers a promising alternative for lowering the cost of non-Clifford operations in fault-tolerant quantum computing (FTQC). However, realizing cultivation in practice exposes two challenges: (i) the lack of an open-source classical runtime layer between logical software and physical control, and (ii) the latency constraints on protocol-specific decisions that determine magic-state readiness. To address these challenges, we adopt an algorithm–hardware co-design approach. At the algorithm level, we develop a two-stage early-escape scheme that identifies an informative subset of detectors offline, constructs a compact decoding problem, and performs partial decoding in parallel with complete decoding at runtime, allowing high-confidence attempts to advance before full decoding completes. At the hardware level, we present MagiCFirm, a configurable runtime that combines offline-compiled microprograms with dedicated datapaths for detector construction, event processing, and protocol control, enabling end-to-end execution of magic-state cultivation. Across evaluated configurations, MagiCFirm reduces wall-clock magic-state preparation time by up to 39.3% at matched logical error rate. For a representative magic-state-bound workload, this translates to an estimated 11% reduction in overall application runtime.

Quantum uncertainty emerged from two strikingly different routes to quantum mechanics. Heisenberg's matrix mechanics replaced the classical description of atomic orbits by relations among observable transition quantities and led, in 1927, to the uncertainty relation and its influential measurement-based interpretation. Schrödinger's wave mechanics grew instead from the Bose–Einstein and de Broglie developments and restored a continuous space-time description through matter waves. The two formalisms were soon shown to be closely related, but neither historical route by itself settles the ontological question of whether particles may possess underlying trajectories. After reviewing these developments, including Einstein's criticism of a simple observability doctrine and Mott's wave-mechanical account of straight cloud-chamber tracks, we distinguish precise quantum uncertainty relations from the stronger claim that quantum mechanics excludes definite microscopic histories. We then compare Feynman paths, Bohmian trajectories, Nelson's stochastic mechanics, and finite-speed persistent Goldstein–Kac dynamics. The Kac process has continuous, piecewise differentiable finite-speed paths; its diffusion limit approaches Wiener kinematics, while analytic continuation of its two-sector dynamics is related to Dirac evolution. These examples show that quantum uncertainty relations constrain observable statistics without, by themselves, uniquely determining an underlying path geometry.

Random matrix spectral statistics are widely used to diagnose quantum chaos in open systems, but whether chaotic eigenvalue correlations are accompanied by Haar-typical eigenoperators remains unclear. We study the operator-entanglement statistics of Liouvillian eigenoperators with near-maximal entanglement, analogous to states near the middle of the spectrum in Hamiltonian systems. Using the Kullback-Leibler divergence, we show that Haar-random statistics accurately describe both the Ginibre and class-AI$^\dagger$ Gaussian ensembles. For purely dissipative random Lindbladians, we find that locality of the jump operators drastically alters the eigenoperator-entanglement statistics. Nonlocal Lindbladians remain relatively close to Haar-random behavior, whereas local Lindbladians deviate increasingly from random-matrix statistics with system size. Moreover, unlike in Hamiltonian systems, the most highly entangled eigenoperators of local Lindbladians do not generally lie in the region of largest density of states, owing to the clustered structure of the complex eigenspectrum. We introduce an iterative $\sigma$-clipping scheme to extract the high-entanglement distribution without preselecting a spectral window, and find that it is Gaussian for nonlocal Lindbladians but log-normal for local ones. Remarkably, the same log-normal distribution, with no additional fitting, also describes dissipative mixed-field Ising chains belonging to distinct non-Hermitian symmetry classes. Our results therefore point to a universal eigenoperator-entanglement distribution for local Lindbladians that is not captured by generic non-Hermitian random-matrix ensembles.

Fault-tolerant compilation can disperse high-level structure: schedules split an accumulated phase across rounds, gate synthesis replaces an angle by a Clifford+$T$ word, and randomized compiling spreads rotations over sign-randomized fragments. They preserve the computation but change how cheaply a downstream compiler can recover the aggregate phase data. We formalize this representation-dependent recoverability by charging two channels: output committed before the suffix arrives, and a serialized restart state crossing the cut. For an $r$-round accumulation of a commuting layer with $m$ generators at accuracy $\epsilon$ ($K_\epsilon=\Theta(1/\epsilon)$), any $p$-pass compiler correct on every valid stream with failure probability at most $\delta$ obeys $\overline{A}_p+(2p-1)S\geq(1-\delta)m\log_2 K_\epsilon-h_2(\delta)$, where $\overline{A}_p$ is committed output and $S$ is the crossing-state cap. The bound covers compile-time randomized compiling; a memory-capped block compiler attains it within a constant factor, and direct semantic aggregation reaches compact output with logarithmic state. The two channels are not always interchangeable. A compiler whose committed prefix is executed at the cut pays a toll the state channel never pays: the entropy $\log_2\binom{m}{k}$ of the mask naming which $k$ coordinates it commits early. Compilers that defer or buffer pay none of it. We prove both directions and, with instrumented compilers under a preregistered protocol, measure a per-generator toll matching $\log_2\binom{m}{k}/k$ that vanishes for a public mask and a buffered control. Under a disclosed fixed-total-error Clifford+$T$ and surface-code model, a materialize-first pipeline costs orders of magnitude more logical $T$ states and spacetime volume than a semantic-first one. Phase semantics should therefore be preserved until aggregation whenever the interface permits.

We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.

Variational quantum algorithm is a leading approach for quantum chemistry and many-body physics on noisy intermediate-scale quantum devices. The performance depends strongly on the structure of the parameterized quantum circuits. Quantum architecture search (QAS) can automate ansatz design. However, it requires repeated training and evaluation of many candidate circuits, leading to high evaluation cost. In this work, we propose a noise-aware quantum architecture search framework based on ZX-calculus topological reuse (ZX-QAS). The framework encodes the search space with a ternary Gray-code mapping and integrates a noise-aware quantum neural network with a ZX-calculus topological reuse mechanism. The effectiveness of the framework is validated through ground-state energy estimation tasks and one-dimensional transverse-field Ising model tasks under noisy conditions. The results show that the ZX-QAS exhibits stable convergence and remarkably reduces the cost of expensive evaluations under noisy conditions.

Quantum error-correcting decoders provide both corrections and confidence estimates for the logical-error risk of individual measurement records. Such confidence can guide postselection, but it depends on the accuracy of the decoder noise model. When the physical device drifts away from that model, confidence measures such as the logical gap can become miscalibrated. We show that this mismatch can itself provide useful information. On IBM quantum hardware, syndrome statistics drift across consecutive acquisition windows, and the resulting detector histories differ substantially from those predicted by the stationary detector error model used for decoding. We observe a similar hardware-model mismatch in independent Google surface-code memory data. We exploit this effect by assigning additional rejection weight to detector histories that are unlikely under the assumed model. For minimum-weight perfect matching (MWPM), the minimum weight $W$ provides an inexpensive proxy for syndrome surprisal. On held-out IBM repetition-code memories, likelihood-aware postselection reduces the retained logical-error probability (LEP) by $10.6\%$ at $d=7$ and $28.8\%$ at $d=9$, both at $15\%$ rejection. On Google ten-round $d=5$ XZZX surface-code memory data, it reduces retained LEP by $75.4\%$ at $90\%$ rejection. Applied to Google's magic-state cultivation experiment with the Tesseract decoder, it reduces tomography infidelity by $34.7\%$ with $30\%$ additional grafting-stage rejection, or increases accepted yield by $30.4\%$ at a target fidelity of $97.0\%$. Burst-noise simulations show that the advantage persists as code distance and syndrome-extraction volume increase. The method reuses quantities already produced during logical-gap decoding and requires only an additional fitting step.

The simulation of nonlinear ordinary differential equations on quantum computers is inherently challenging, as quantum gates are linear operators on qubit states. In this paper, we put forth a Koopman-von Neumann (KvN) operator based algorithm for solving nonlinear ordinary differential equations on a quantum computer which overcomes the innate limitations of quantum operations. In this approach, a Liouville probability density is embedded into a wavefunction, the evolution of which is governed by an operator dual to the Koopman operator. The trajectories corresponding to the nonlinear differential equations are reconstructed from the average value of Koopman observables evaluated through quantum measurements. We specifically evaluate the computational limitations of solving nonlinear equations within this Liouville embedding framework. An Ehrenfest-type estimate is derived that relates the reconstruction error to the covariance of the transported density, highlighting the competition between linear stretching and Hessian-induced folding.This leads to a key stability criterion, which depends on the local Ehrenfest-Reynolds number. We discuss the effects of measurement-induced errors including those due to Hadamard-test sampling, amplitude estimation, and bias due to covariance in probabilistic Grover-type inference on the evaluation of trajectories. The limiting bounds on the accuracy of quantum computations are numerically verified for the Lotka-Volterra system and for the quartic oscillator. We observe a rapid growth in computational errors when the Ehrenfest-Reynolds number approaches the predicted threshold. The bounds resulting from our analysis provide key guidelines for selecting the width of the initial Gaussian probability distribution associated with a system of nonlinear ordinary differential equations.

The dissipative transverse-field Ising (TFI) model provides a paradigmatic setting for nonequilibrium quantum many-body physics. We show that a class of boundary-driven TFI models subject to dissipation at only one boundary possesses hidden time-reversal symmetry, which enables an exact construction of their nonequilibrium steady states. The solution admits a matrix-product representation and defines a nonequilibrium partition function from which steady-state observables can be evaluated efficiently. We use the exact solution to characterize the microscopic structure of the steady state through its z-magnetization and two-point correlations. A striking feature is that the local field at the dissipative boundary governs the spatial organization of the steady state throughout the chain. The steady state typically exhibits boundary-localized magnetization profiles and exponentially decaying correlations, whose characteristic length scales are set by the dissipative boundary. In the weak-driving limit, suitably tuned boundary fields can reorganize the NESS into a delocalized single-interface structure, giving rise to long-range correlations that decay linearly with distance.

Maximizing the number of addressable spins within a fixed volume can improve ensemble quantum sensor sensitivity, but dense packing usually increases dipolar interactions and excited-state transport, shortening coherence and suppressing optical readout. Here we report a 2:1 cocrystal of 6,13-dihydropentacene and pentacene (DHP/Pc) containing 33.3 mol% pentacene ($3.3\times10^{5}$ ppm; $9.51\times10^{20}$ cm$^{-3}$), a volumetric spin-site density more than two orders of magnitude above previous benchmarks, NV-diamond and pentacene-doped p-terphenyl (PDP). Despite this density, DHP/Pc exhibits microsecond spin coherence, room-temperature optically detected magnetic resonance and coherent control. Time-resolved measurements indicate that the long-lived triplet population is generated predominantly by intersystem crossing and exhibits strong, non-thermal sublevel polarization. Density-functional theory calculations further suggest that the native cocrystal geometry weakens electronic coupling between neighboring pentacenes, while the higher DHP triplet energy creates a barrier to triplet migration. These results identify molecular packing and coformer triplet energetics as complementary design parameters for preserving coherence in high spin-site density systems, demonstrating cocrystallization as a promising route to dense, optically addressable spin materials for room-temperature ensemble quantum sensing.

A quantum circuit for Gaussian elimination is developed in this work. While previous quantum implementations of Gaussian elimination were restricted to $\mathrm{GF}(2)$, the proposed design is generalized to any finite field. Compared with previous works in $\mathrm{GF}(2)$, the developed circuit achieves garbage-free construction while retaining the best known asymptotic Toffoli depth up to logarithmic factors.

Superconducting strip single-photon detectors (SSPDs) have emerged as scalable, wide-strip variants of traditional nanowire counterparts. Despite practical advantages including improved optical fill factors and enhanced signal-to-noise ratios the fundamental detection physics governing these micro-scale geometries remains largely unexplored. Here, we investigate the underlying photoresponse of a 20 um-wide tungsten silicide SSPD, demonstrating a slew-rate-corrected timing jitter of 13.2 ps at 532 nm and 20.5 ps at 1550 nm, alongside saturated internal detection efficiency up to 1550 nm. Using focused free-space optical scanning, we reveal that detector timing jitter is strongly influenced by a spatially dependent slew rate between edge and center absorption events. To mitigate this impact, we utilize a parallel superconducting rail architecture to actively redistribute supercurrent. This in-situ tuning minimizes the latency mismatch and mitigates thermally activated intrinsic dark counts, extending the device's ability to operate at higher temperatures. Finally, comparing these dynamics with time-dependent Ginzburg-Landau (TDGL) modeling elucidates the physical origins of the position-dependent photoresponse, highlighting how superconducting rails or specialized readout electronics can mitigate negative impacts on timing jitter.

Many optimization problems reveal inexpensive structural information before requiring costly final evaluation, whereas the conventional quantum approximate optimization algorithm (QAOA) applies a single aggregate objective throughout. We introduce the learned-projector quantum alternating operator ansatz (LP-QAOA), a multistage protocol that freezes optimized circuits and uses their output states to define later projector mixers. We prove a stability theorem for LP-QAOA that bounds the propagation of approximation errors through successive frozen stages. Our analysis also shows how learned-projector mixing avoids the high-order tunnelling suppression of local mixers. We conduct state-vector simulations on block-constrained spin tiling (BCST) instances, where LP-QAOA achieves higher probabilities of sampling the optimum, lower estimated logical-resource requirements, and better trainability than the tested baselines. A supporting stochastic block model experiment extends LP-QAOA to optimization problems with soft hierarchical structure. Our results highlight the potential of LP-QAOA to improve variational quantum optimization by exploiting hierarchical problem structure.

We study reversible secp256k1 point-addition circuits developed through ECDSA.Fail for Shor's elliptic-curve discrete-logarithm algorithm. Two complementary constructions improve record-and-replay GCD arithmetic: Jump-2 groups binary-GCD steps and compresses their decisions using base-5 encoding, while ping-pong uses fixed register alternation and one-bit decisions to avoid full-width comparisons and data-dependent swaps. Fused replay combines doubling and signed addition into one modular correction. Both constructions support quantum-addressed window selection with measurement-based lookup cleanup. We compare three circuits on 100,000 fresh inputs across nine lookup-table configurations. A separately tested repair uses 1,419 qubits and 1.356 million mean executed Toffolis, with no detected failures on another 100,000 inputs. Structured supported-input counterexamples remain, so these tests do not establish all-input correctness. We also provide conditional coherent-error analysis and reversible safegcd comparisons. Under the stated window allowance, repaired-circuit resources lie below Google's low-gate caps and Schrottenloher's low-gate estimates, but differing accounting and correctness evidence preclude formal dominance. The results concern individual window-selected additions, not complete Shor computations.

Scaling superconducting quantum processors requires interconnects that provide both non-local connectivity and parallel entangling operations. While current quantum routers offer greater connectivity than nearest-neighbour topologies, their support for parallel, independently addressable two-qubit gates remains fundamentally limited, imposing severe compilation overheads that constitute a critical bottleneck. Here we introduce a bus-based reconfigurable quantum router that enables parallel controlled-$Z$ (CZ) gates for modular superconducting processors. Constructed from a flux-tunable SQUID network, the router selectively connects interface qubits to two shared buses, allowing destructive interference to suppress idle interactions while supporting two disjoint CZ gates in parallel. Full-system Hamiltonian simulations yield parallel-gate infidelities ranging from $7.9\times10^{-4}$ to $1.8\times10^{-3}$ under the operating conditions considered, and an open-system analysis identifies the coherence requirements for high-fidelity operation. We further assess the circuit-level consequences using hardware-aware compilation and resource-constrained scheduling. For the 36-qubit quantum Fourier transform (QFT), QAOA-MaxCut, and random-pairing circuits, the router reduces the median SWAP count by up to $34\%$ and the native CZ count by up to $20\%$ relative to a matched two-dimensional grid. Circuit-depth reductions are workload-dependent, reaching $20\%$ for QAOA-MaxCut but remaining negligible for the QFT despite its lower gate count. These results show that enhanced connectivity and schedulable parallelism provide complementary benefits for connectivity-intensive algorithms, establishing the router as a compiler-visible hardware resource and providing a scalable architectural pathway toward constructing highly connected modular superconducting quantum processors.

Jarzynski's equality recovers an equilibrium free-energy difference from nonequilibrium work trajectories, but its exponential average can converge very slowly because rare trajectories carry large weight. We show that coarse thermodynamic information measured at the nonequilibrium endpoint can reduce this sampling burden while keeping the same microscopic trajectories and the same free-energy target. The endpoint mean energy and a coarse spatial record define a maximum-entropy state and select one member of an exact family of fluctuation relations. That physically selected member provides an exact statistical control for the ordinary Jarzynski estimator, even when the final energy and retained record do not commute. In a finite Bose–Hubbard system, this control substantially lowers the finite-confidence sampling cost, while a small controlled departure from exact endpoint matching produces a square-root information–sampling tradeoff.

Exceptional points (EPs) are spectral singularities, but whether they can be used to control a distinct criticality of coherent interference remains largely unexplored. Here we show in nonlocal superconducting transport how spectral and interference criticalities can be controllably synchronized. In a minimal superconducting double-quantum-dot system, loss imbalance selectively drives one Bogoliubov sector through an EP. The spectral EP and the CAR-ECT interference criticality form distinct structures in control space whose relative ordering can be continuously tuned. At their synchronization point, the interference boundaries between crossed Andreev reflection (CAR) and elastic cotunneling (ECT) coalesce at the EP and bifurcate beyond it, creating a finite CAR-dominated window. The resulting interference window opens with a square-root critical law, whose exponent also governs the finite-temperature observability scale. Detuning unfolds the two criticalities, while retuning restores their intersection, establishing the synchronization as controlled rather than generic. The bifurcation is directly observable in nonlocal conductance. Our results establish exceptional points as spectral control points for independently defined interference criticalities, opening a route to non-Hermitian control of critical quantum interference.

Quantum computing offers a new, orthogonal direction for investigating fundamental physics, extending beyond classical numerical methods and conventional observables. Realizing this potential requires directly confronting the noise limiting currently available quantum computers. Progress rests on advancing algorithms, interpreting their results, and managing their errors together. This thesis presents several advancements in the use of quantum simulation and quantum information to probe fundamental physics. The first is in the use of quantum computers to simulate collisions in quantum field theories. Central to these simulations are new wavepacket preparation, time evolution, and error mitigation techniques, which allow for simulations with some of the largest effective circuit volumes to date. These methods enable the first quantum simulation providing numerical evidence for inelastic particle production, a key process in fundamental physics. The second advancement centers on the role quantum-information-theoretic quantities play in physical processes. Beyond mere correlations with the physics of the process, entanglement and magic are shown to probe the interactions present in scattering and hadronization dynamics. A precision study requires a complete quantification of algorithmic and hardware uncertainties, an outstanding goal as quantum simulations mature. The third advancement in this thesis addresses error management. A framework minimizing the effect of algorithmic errors in analog quantum simulations is presented. In a step toward fault tolerance, error detection in encoded quantum simulations is shown to improve estimation of local observables relative to unencoded runs. Together, the developments in this thesis mark practical progress toward fault-tolerant quantum simulations of fundamental physics capable of scientific discovery.

Quantum generative models are often motivated by circuit families whose output distributions are believed to be classically hard to sample from. When such models are trained on ordinary classical datasets, however, this hardness does not automatically transfer to the unknown data-generating distribution. We show that transferring sampling hardness via total-variation closeness from a quantum model to an unknown source requires certifying a global relation between the two distributions, thereby reducing the problem to distribution certification. Combining this reduction with existing certification lower bounds yields an exponential sample requirement for the high-entropy distributions relevant to many sampling-hardness proposals. Consequently, polynomially many samples cannot, in general, justify attributing sampling hardness to an unknown data-generating distribution. Moreover, even classically trivial distributions, such as the uniform distribution and product distributions, require exponentially many samples to certify in the absence of structural assumptions. Our results clarify the role of sampling hardness in quantum generative modeling and distinguish generator-level hardness from source-level hardness when learning from ordinary datasets.

We propose a hybrid quantum state preparation method based on the Walsh–Hadamard transform within the dense-to-sparse quantum state preparation framework. The method approximately prepares structured classical data in a quantum circuit through an indirect approach. Instead of directly preparing the dense amplitude-encoded state, the method first transforms the classical data into the Walsh domain and prepares only the largest-magnitude coefficients using a sparse state-preparation algorithm. The original state can then be approximately recovered through a parallel layer of Hadamard gates. Since this reconstruction requires no CNOT gates and has circuit depth 1, the proposed method introduces no additional CNOT or circuit-depth overhead, and its quantum preparation cost is determined by the underlying sparse state-preparation algorithm. Numerical results on representative benchmark signals demonstrate that the proposed method enables accurate state preparation for signals admitting sparse or approximately sparse representations in the Walsh domain.

We introduce a generalized classical long-range stochastic cellular automaton that exactly captures the entanglement dynamics and transitions of a measurement-only monitored quantum system. The corresponding quantum model consists of a one-dimensional qubit chain subject to competing single-site and long-range Bell measurements, with separations drawn from a power-law distribution. At every step of each trajectory, the state remains a tensor product of Bell pairs and unpaired qubits, with bipartite entanglement entropy fully encoded in a classical matching of the sites. This exact representation allows us to solve the dynamics analytically in several limits and to determine the steady-state scaling of the entanglement entropy. We find volume-law, fractal, and area-law regimes. Numerical results show that these regimes persist beyond the analytically solvable limit. Because Bell measurement outcomes change only the Bell-state labels and leave the matching unchanged, all subsystem entropies are outcome independent, avoiding the exponential cost of trajectory postselection often encountered in experimental studies of measurement-induced entanglement dynamics.