arXiv subjects

Masayuki Ohzeki

Publications and source records attributed to Masayuki Ohzeki.

At least 37 records · Page 2Linked to original sources

arXiv2026

Existence of a Phase Transition in the One-Dimensional Ising Spin Glass Model with Long-Range Interactions on the Nishimori Line

Dyson [Commun. Math. Phys. 12, 91 (1969)] rigorously proved the existence of a phase transition in the one-dimensional Ising model with long-range interactions of the form $r^{-α}$ for $1 < α< 2$. In the present study, we extend this result to the Ising spin glass model with Gaussian disorder on the Nishimori line. Following Dyson's method, we first prove the existence of long-range order at finite low temperatures in the Dyson hierarchical Ising spin glass model on the Nishimori line, with power-law-like interactions $J(r) \sim r^{-α}$ for $1 < α< 3/2$. The key ingredients of the proof are the interpolation method developed in the rigorous analysis of mean-field spin glass models, the Gibbs--Bogoliubov inequality on the Nishimori line, and the Tsirelson--Ibragimov--Sudakov inequality (Gaussian concentration inequality). We then use the Griffiths inequality on the Nishimori line to rigorously establish the existence of a phase transition in the one-dimensional Ising spin glass model with long-range interactions on the Nishimori line for $1 < α< 3/2$. For $3/2 \le α\le 2 $, the existence of a phase transition remains an open problem.

math-ph↗

arXiv2026

Star-triangle duality estimates for triangular and honeycomb permutation models

We study a duality analysis in conjunction with the star-triangle transformation for symmetric-group permutation models on the triangular and honeycomb lattices. The calculation is motivated by the permutation-model description of random tensor networks and by earlier duality analyses of replicated spin glasses. The essential point is that the finite-basis unit is not a bare bond but a star-triangle block. Our analysis estimates the critical bond dimension for the honeycomb lattice to be 2.634929344884, and the associated single-bond duality relation yields the triangular-lattice estimate 1.475661534848.

cond-mat.dis-nn↗

arXiv2026

Coherent Quantum Schrodinger Bridge: Two-Boundary Optimal Control for Quantum Algorithm Design

Quantum algorithms are intrinsically two-boundary processes: an input state is prepared, and an output state or subspace is selected as the computational answer. We formulate this observation as a coherent Quantum Schrödinger Bridge (QSB), a pure-state Hamiltonian counterpart of Schrödinger bridge theory in which the endpoint constraint is imposed on state vectors and the transport cost is the quadratic control action. In this setting Aharonov's two-state vector becomes the natural optimal-control pair: a forward state from the input and a backward state from the target. Pontryagin's principle then yields a universal optimal Hamiltonian whose weak value is purely imaginary in the geodesic gauge. Thus weak values are not an auxiliary interpretation; they are the local response functions that quantify the drift of the pre-selected state toward the post-selected boundary. Applying this framework to unstructured search, periodicity finding, and matrix arithmetic, we reconstruct Grover's algorithm, the quantum Fourier transform underlying Shor's algorithm, and quantum singular value transformation (QSVT). The usual circuit components -- oracles, diffusion reflections, controlled phases, and signal-processing rotations -- emerge as Lie-algebraic syntheses of the optimal weak-value drift. This perspective unifies distinct algorithmic paradigms into a single geometric principle: algorithm design is the problem of choosing computational boundary conditions and realizing the corresponding optimal flow.

quant-ph↗

arXiv2026

Kernel Learning by quantum annealer

The Boltzmann machine is one of the various applications using quantum annealer. We propose an application of the Boltzmann machine to the kernel matrix used in various machine-learning techniques. We focus on the fact that shift-invariant kernel functions can be expressed in terms of the expected value of a spectral distribution by the Fourier transformation. Using this transformation, random Fourier feature (RFF) samples the frequencies and approximates the kernel function. In this paper, furthermore, we propose a method to obtain a spectral distribution suitable for the data using a Boltzmann machine. As a result, we show that the prediction accuracy is comparable to that of the method using the Gaussian distribution. We also show that it is possible to create a spectral distribution that could not be feasible with the Gaussian distribution.

quant-ph↗

arXiv2026

Non-Equilibrium Model Selection via Finite-Time Thermodynamics

Information criteria such as WAIC and WBIC extend model selection to singular learning machines, but they are usually derived for equilibrium posteriors. We formulate a finite-time analogue of WBIC by replacing the equilibrium posterior with an effective ensemble generated by learning dynamics under a resource constraint. When this ensemble admits an analytic effective potential, singular learning theory yields a resource-dependent real log canonical threshold. The resulting estimator gives a computable thermodynamic contribution to time-bounded MDL and identifies the finite-time singular complexity relevant to the structural information measured by epiplexity.

cond-mat.dis-nn↗

arXiv2026

Cavity method for permutation models on Cayley trees

Motivated by permutation statistical models arising in random tensor networks, we study permutation models on a Cayley tree whose variables take values in the symmetric group $\Sn$. The pair interaction is assumed to depend only on the cycle type of the relative permutation. Then the Boltzmann weight is written as a class function on $\Sn$. This property diagonalizes the edge convolution operator in irreducible representation sectors. As a result, the linear stability of the uniform paramagnetic cavity solution is controlled by the character eigenvalue ratios. For cycle-factorized weights, these eigenvalues can be expressed as specializations of Schur functions. We derive the instability criteria and also verify their validity by comparison with direct numerical iterations of the cavity equation.

quant-ph↗

arXiv2026

Daydreaming algorithm for Biased Patterns

The \emph{Daydreaming} algorithm has been recently proposed in Ref.~\cite{Serricchio2025} as a learning rule that simultaneously reinforces stored patterns and suppresses spurious attractors to improve the storage capacity of the Hopfield model. Its effectiveness has been reported for both uncorrelated and correlated data. However, the existing formulation has mainly assumed unbiased patterns, and the formulation for biased patterns has not yet been sufficiently established. Biased patterns are known to be much more problematic for models of associative memories. In this study, we reformulate Daydreaming for biased patterns motivated by the underlying rationale of the pseudo-inverse rule. Specifically, we introduce the retrieval dynamics and an energy function based on the centered representation, and we derive a corresponding update rule for centered Daydreaming. We compare the centered pseudo-inverse rule with centered Daydreaming for biased patterns and examine the retrieval maps and eigenvalue distributions of the coupling matrices. As a result, the centered Daydreaming yields larger basins of attraction than the centered pseudo-inverse rule, and such a beneficial property seems to be due to the broadness of the eigenvalue spectrum of the coupling matrix. To better understand this connection, we construct modified coupling matrices whose spectra interpolate between a pseudo-inverse-like spectrum and the Daydreaming one. The results clearly indicate that the broader spectrum generated by Daydreaming contributes to the enlarged basin of attraction.

cond-mat.dis-nn↗

arXiv2026

Nonreversible Gauge Fields in Fokker--Planck Dynamics: Supersymmetric Hamiltonians and Learned Finite Forces

We formulate stationary-density-preserving nonreversible perturbations of Fokker--Planck dynamics as gauge fields that deform relaxation spectra while leaving the invariant state fixed. When detailed balance holds, a similarity transformation maps the reversible Fokker--Planck operator to a Witten-Laplacian-type supersymmetric Hamiltonian; nonreversible gauges then appear as non-Hermitian perturbations that preserve the zero mode but modify the excited spectrum. This operator viewpoint gives a common language for relaxation gaps, circulating probability currents, hypocoercive acceleration, and finite control costs. We represent admissible gauge currents by antisymmetric tensor fields and identify the detailed-balance-violating Ohzeki--Ichiki force as a constant symplectic example whose infinite-strength limit is Hamiltonian dynamics. The continuous-time spectral gap alone does not select a finite gauge strength, so we introduce a finite-time regularized objective and an actor--critic procedure for learning the gauge. An exactly solvable anisotropic Gaussian Ornstein--Uhlenbeck benchmark separates the spectral transition from the finite-time optimum and shows that the learned gauge recovers the Lyapunov-equation optimum. A double-well benchmark then illustrates the same constrained selection in a nonconvex metastable landscape. Stochastic gradient methods enter this framework as physically relevant Fokker--Planck systems: mini-batch noise acts as an effective diffusion tensor, and adaptive methods such as Adam correspond to metric choices with possible nonequilibrium currents.

cond-mat.dis-nn↗

arXiv2026

Finite-Basis Duality Estimate for the Surface-Code Threshold under Correlated Bit-Flip Errors

We apply finite-basis duality to a statistical-mechanical model introduced by Chubb and Flammia for the surface code under spatially correlated bit-flip noise. Their mapping gives a random-bond Ising model with both two-body edge interactions and four-body face interactions. The single-equation estimate based on the duality analysis is slightly deviated from their Monte Carlo estimate $p_c=0.1004(6)$. Following the finite-basis and graph-polynomial strategy, we instead use periodic and twisted-periodic sectors on toroidal bases. We have obtained an improved estimate of the critical point, $p_c = 0.10348$.

cond-mat.dis-nn↗

arXiv2026

A Minimal Duality Estimate for the Surface-Code Threshold under Nearest-Neighbor Correlated Errors

We apply the single-equation duality criterion to the square-octagonal random-bond Ising model recently obtained from an exact error-edge map for a surface code with nearest-neighbor correlated errors. The calculation is performed for the minimal cell after the error-edge reduction. For the symmetric case $p_1=p_2=p_3=p$, this gives $p_c=0.0288427147$, in close agreement with the reported numerical threshold of about $3\%$.

cond-mat.dis-nn↗

arXiv2026

Attention-Like Hebbian Learning from Quantum Probability Flow and Quantum-Annealer Tests

We propose a quantum probability-flow principle for deriving local learning rules in associative memory. A transverse field defines leakage channels from data states, and minimizing the measured survival loss gives stability-driven updates. For imaginary-time, dephased dynamics, the local leakage free energy is the log-sum-exp of energy gaps; its gradient is a softmax-weighted Hebbian rule. Real-time stability instead yields a power-law weighting. D-Wave standard- and fast-anneal tests of a one-hot attention forward map are better fitted by an effective softmax than by a Lorentzian power law.

quant-ph↗

arXiv2026

Analytical Singular-Value Structure of Analytic-Continuation Kernels from Slepian Information Theory

Analytic continuation from imaginary-time Green's functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian's finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, producing self-adjoint effective potentials but no numerical kernel diagonalization. The Shannon number, $N_c=β\wmax/π$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches.

quant-ph↗

arXiv2026

Analysis of Critical Points in a Permutation Model on Hierarchical Lattices by Real-Space Renormalization Group

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.

cond-mat.stat-mech↗

arXiv2026

Improving search efficiency via adaptive acquisition function selection in discrete black-box optimization

In discrete-variable black-box optimization, the number of candidate solutions grows combinatorially, while each evaluation is often expensive. Therefore, it is important to identify promising solutions efficiently within a limited number of trials. Bayesian Optimization of Combinatorial Structures (BOCS), an existing parametric method, works effectively when only a small amount of data is available. However, as the number of observations increases, BOCS tends to repeatedly propose points that have already been evaluated, which leads to search stagnation. A random-point addition strategy has been proposed to address this issue when an evaluated point is proposed, but it cannot sufficiently exploit information from promising data obtained so far. In this study, we propose a hybrid method that uses BOCS as the main search framework and generates alternative unevaluated points using a Gaussian process only when search stagnation is detected. In the Gaussian-process-based component, multiple Lower Confidence Bound (LCB) acquisition functions are adaptively selected to dynamically control the balance between exploitation and exploration. Numerical experiments using fully connected Quadratic Unconstrained Binary Optimization (QUBO) and Higher-order Unconstrained Binary Optimization (HUBO) as black-box functions show that the proposed method finds solutions with better objective values than the conventional random-point addition method in both settings. Additional analyses show that its effectiveness comes from selecting points that promote search progress within Hamming-distance neighborhoods, rather than simply adding low-energy points near promising solutions. Experiments with sparse surrogate models for quantum annealer applications further suggest the importance of retaining near-fully connected representational capacity.

quant-ph↗

arXiv2026

Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line

We consider a class of gauge glass models with Gaussian disorder on the Nishimori line, including the Ising spin glass, the $XY$ gauge glass, the $Z_q$ gauge glass, and the gauge-invariant Potts model. We prove that the first and second Griffiths inequalities hold for these models on arbitrary lattice structures. As a consequence, both the pressure and the correlation functions are monotonically increasing with respect to the inverse temperature along the Nishimori line. Furthermore, we establish an analogue of the Gibbs--Bogoliubov inequality for this class of models. This result implies that, on the Nishimori line, the approximate quenched free energy obtained via the replica method with a replica-symmetric mean-field approximation is always greater than the true quenched free energy. Our results provide a broad generalization of previous results established for the Ising spin glass with Gaussian disorder on the Nishimori line.

math-ph↗

arXiv2026

Phase transition in compressed sensing using log-sum penalty and adaptive smoothing

In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching the Bayes-optimal reconstruction limit. Nonconvex alternatives, such as the log-sum penalty, have been proposed to promote stronger sparsity. However, maintaining their algorithmic stability is challenging. To address this challenge, we introduce an adaptive smoothing strategy within an approximate message passing framework to mitigate algorithmic instability. Furthermore, we evaluate the typical exact-recovery threshold for Gaussian measurement matrices using the replica method and state evolution. The results indicate that the adaptive method achieves exact recovery over a broader region than $\ell_1$ norm minimization, although metastable states hinder reaching the information-theoretic limit.

cs.IT↗

arXiv2026

Population Annealing as a Discrete-Time Schrödinger Bridge

We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schrödinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically solving the Schrödinger system without iterative computation via instantaneous projection. In addition, we identify the thermodynamic work as the optimal control potential that solves the global variational problem on path space. This perspective unifies non-equilibrium thermodynamics with the geometric framework of optimal transport, interpreting the Jarzynski equality as a consistency condition within the Donsker-Varadhan variational principle, and elucidates the thermodynamic optimality of PA.

cond-mat.stat-mech↗

arXiv2026

Accelerating Extended Benders Decomposition with Quantum-Classical Hybrid Solver

We propose a quantum-classical hybrid method for solving large-scale mixed-integer quadratic problems (MIQP). Although extended Benders decomposition is effective for MIQP, its master problem which handles the integer and quadratic variables often becomes a computational bottleneck. To address this challenge, we integrate the D-Wave CQM solver into the decomposition framework to solve the master problem directly. Our results show that this hybrid approach efficiently yields near-optimal solutions and, for certain problem instances, achieves exponential speedups over the leading commercial classical solver. These findings highlight a promising computational strategy for tackling complex mixed-integer optimization problems.

quant-ph↗