arXiv subjects

Masayuki Ohzeki

Publications and source records attributed to Masayuki Ohzeki.

At least 19 recordsLinked to original sources

arXiv2026

Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization

Regularization choice changes the recovery phase diagrams of annealing-based binary compressed sensing. We develop a regularization-selection method that combines systematic parameter search with random forest regression. Under noiseless Gaussian measurements with known sparsity, reference parameters are selected from a candidate grid by minimizing mean squared reconstruction error over repeated simulated annealing (SA) trials. The fitted model predicts these reference values from signal dimension, sampling ratio, and sparsity. With predicted regularization, the SA recovery transition broadly follows the asymptotic reference boundary for box-constrained $\ell_1$ recovery at the larger signal dimensions examined. Without retraining, the same predictor supplies identical regularization values to SA and a quantum--classical hybrid solver. On matched problem instances, the hybrid solver yields smaller mean squared reconstruction errors than SA in parts of the evaluated parameter space. The resulting rule reuses the searched information for subsequent reconstruction without repeating candidate searches at each setting. The results quantify empirical performance under the stated finite candidate grid and solver settings; they do not constitute a solver-independent recovery guarantee or a time-to-solution comparison.

quant-ph↗

arXiv2026

Information Erasure and Quantum Imprint in Quantum Measurement and First-Order SPAM Error Separation

We introduce information erasure and quantum imprint as two properties that classify quantum instruments. Information erasure is the property that an appropriate postselection can render the distribution of earlier measurement outcomes independent of the initial quantum state while retaining all outcome branches. Quantum imprint is the complementary property that no admissible postselection can eliminate this state dependence. We show that this classification has a nontrivial structure and that the natural intuition that measurements providing more information about the initial quantum state should be less likely to exhibit information erasure does not hold in general. We further show that, under a sufficiently reliable postselection, information erasure enables first-order separation of state-preparation and measurement (SPAM) errors. Specifically, the first-order contribution of state-preparation error vanishes from the posterior distribution, whereas visible first-order contributions of measurement error remain. This result recasts SPAM error separation from the problem of simultaneously characterizing state preparation and measurement into the problem of realizing a reliable postselection.

quant-ph↗

arXiv2026

Boundary-Cancelled Score-Hamiltonian Sampling

Diffusion sampling can be viewed as imaginary-time annealing of probability densities. From a forward/backward Euclidean Schrödinger pair, we show that fixing the noising drift forces the reverse score term, and that the same logarithmic force is the one-sided imaginary-time counterdiabatic connection of a supersymmetric Score Hamiltonian. The correspondence turns score-learning error into a Hamiltonian perturbation and yields a schedule principle: if the first $r$ terminal derivatives vanish, Morita--Nishimori boundary cancellation suppresses the residual Hellinger error from $T^{-2}$ to $T^{-2r-2}$ until score or sampling floors are reached. Reverse-SDE benchmarks, including two-dimensional learned-score tests, confirm the predicted improvement.

quant-ph↗

arXiv2026

Sparse Signal Recovery Using Log-Sum Regularization and Adaptive Smoothing

We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but its nonconvexity can make reconstruction algorithms unstable. To mitigate this instability, we use an adaptive smoothing strategy that determines the smoothing parameter so that the scalar proximal operator remains continuous. Using this proximal operator, we formulate the approximate message passing (AMP) algorithm and derive the corresponding state evolution (SE) recursion. The fixed point of the SE recursion predicts the final mean squared error (MSE) and, in the noiseless limit, the exact-recovery phase transition. To further investigate finite-dimensional reconstruction behavior, we implement an alternating direction method of multipliers (ADMM) algorithm. In the noiseless setting, we find that the empirical success boundary of ADMM closely agrees with the SE-predicted phase transition. In the noisy setting, we observe that AMP closely follows the SE prediction, whereas ADMM qualitatively reproduces the SE-predicted dependence of the final MSE on the regularization parameter. A comparison with $\ell_1$ regularization shows that log-sum regularization is beneficial in low-density or high-measurement-rate regimes, whereas $\ell_1$ regularization remains preferable at higher densities and lower measurement rates.

cs.IT↗

arXiv2026

Optimal control theory for measured quantum Schrödinger bridges

Schrödinger bridges and entropic optimal transport are usually formulated as stochastic interpolation problems between initial and final probability distributions. In their computational form, the bridge potentials are obtained by Sinkhorn or iterative proportional fitting, and are often regarded as auxiliary scaling functions. We show that for continuously monitored quantum systems, these potentials acquire a direct measurement-theoretic meaning. The mathematical structure of conditional quantum trajectory theory induces a Fokker--Planck equation on quantum state space. Conditioning this diffusion on a terminal distribution or a terminal measurement effect produces a Doob/Sinkhorn potential whose directional derivative along a unitary control vector field is the imaginary part of a generalized weak value. The same construction connects the Schrödinger-bridge viewpoint to the optimal-path framework for continuously monitored trajectories: the backward bridge potential plays the role of an effect-like costate, and its weak-value directional derivative gives the local control signal. By specifying the desired endpoint distribution, the induced drift produced by the Schrödinger bridge solution is the control solution that minimizes the quadratic cost feedback law, guiding the distribution to its desired endpoint. We quantify the control score of the available control Hamiltonian as a logarithmic directional derivative of the bridge potential, or an imaginary weak value. Three explicit examples identify weak measurement as a natural entropic regularization mechanism for quantum state transport and gives a route from Sinkhorn scaling to quantum feedback and Hamiltonian control synthesis for practical optimal control.

quant-ph↗

arXiv2026

Simulation-free and finite-time diffusion model

The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.

cs.LG↗

arXiv2026

Maxwell's Demon in Markov Chain Monte Carlo: Cooling Information Flow and Entropy Balance

Markov chain Monte Carlo algorithms can be viewed as feedback devices that compare a proposed move with the target distribution and then accept or reject it. In this paper the Maxwell demon is identified with the acceptance module: it measures a proposed edge, stores the outcome in the accept/reject bit, and uses that bit to shape the probability current. The decision bit carries a genuine Shannon mutual information about the proposal, whereas only its directional part is converted into a cooling information flow. The relative-entropy relaxation rate obeys $v(t)=\dot{\mathcal I}_{\rm cool}(t)+\dot S(t)$, which separates useful cooling from housekeeping circulation in nonreversible chains.

cond-mat.dis-nn↗

arXiv2026

Slepian Bounds on the Success Probability of Virtual Distillation

Virtual distillation is a powerful near-term error-mitigation primitive, but it is also a spectral filter: it amplifies the dominant eigenvector component already present in the noisy density matrix. We show that, for a finite-band variational state, this filtering cannot create new concentration inside a set of accepted measurement outcomes. The asymptotic success probability after distillation is bounded by the leading eigenvalue of a Slepian concentration operator built from a specified variational band and that outcome window. Moreover, the number of robust high-success spectral components is limited by the Slepian active dimension. \rev{For bit-string outcome windows, an explicit Walsh-band realization has a Krawtchouk kernel on the Boolean hypercube. Finite-size noisy-QAOA calculations for 2-regular Max-Cut illustrate both the in-band improvement and the out-of-band failure modes predicted by the branch-resolved result.

quant-ph↗

arXiv2026

Robust Wavelength Selection for Partial Least Squares Sugar Content Estimation Using Combinatorial Bayesian Optimization

Wavelength selection is one of the important preprocessing methods in near-infrared spectroscopy to improve prediction accuracy and interpretability of spectral data. We formulate wavelength-region selection for sugar content estimation as a binary black-box optimization problem and propose a method based on Bayesian optimization. The proposed method constructs a sparse quadratic surrogate model and sequentially extracts interested wavelength regions by Thompson sampling. Minimizing an acquisition function is performed as a quadratic unconstrained binary optimization problem by simulated or quantum annealing. Experiments show that the proposed method improves the prediction accuracy of partial least squares regression and yields more consistent wavelength regions than genetic-algorithm-based selection and simulated annealing. Under one-bit local perturbations, the selected wavelength regions show minimal fluctuations in root mean square errors between observed and predicted values of a validation set. This local stability suggests that our method converges to a smoother error landscape and avoids isolated overfitted solutions. These results indicate that combinatorial Bayesian optimization is a useful framework for robust feature selection in spectroscopic prediction tasks.

stat.ML↗

arXiv2026

QUBO-Based Optimization of Social Indicator Configurations for Working-Age Population Growth

The decline of the working-age population is a major challenge for regional sustainability, particularly in ageing societies such as Japan. We present a methodological demonstration of a quadratic unconstrained binary optimization (QUBO)-based framework for exploring social-indicator configurations associated with working-age population growth. Using Japanese municipal data, we regressed the 2010-2020 working-age population growth rate on ten discretized social indicators. The resulting quadratic surrogate model showed reasonable predictive performance, with a test-set correlation coefficient of 0.84 and an average R-squared value of 0.76. Its coefficient matrix provides an interpretable representation of individual indicator-level contributions and pairwise associations. We converted the fitted model into a QUBO formulation with one-hot constraints and optimized it using quantum annealing, simulated annealing, and Gurobi. All three methods identified the same optimal feasible configuration, while the annealing-based samplers also generated feasible suboptimal configurations with different predicted growth rates. Municipality-level single-indicator analyses showed that changing one indicator can increase or decrease the predicted growth rate depending on the other indicators. The framework provides an interpretable and optimization-ready approach for connecting municipal social statistics, nonlinear interactions, and model-based scenario generation. It should be regarded as an exploratory tool for policy discussion rather than as a causal estimate of policy interventions.

quant-ph↗

arXiv2026

Mixed-Binary Quadratic Programming via QUBO Sampling without Continuous-Variable Binarization

Quantum annealing and related combinatorial optimization methods typically accept quadratic unconstrained binary optimization (QUBO) problems as input, whereas many practical models include constraints and continuous variables. Standard QUBO conversions discretize continuous variables, increasing the binary dimension and often making feasible low-energy states harder to sample. We develop a finite-temperature formulation for a separable class of mixed-binary quadratic programs (MBQPs) that avoids this discretization. At fixed Lagrange multipliers, the continuous sector is integrated out analytically and enters only the multiplier update, leaving a QUBO over the original binary variables. We evaluate the method on the continuous relaxation of the quadratic $p$-median problem. Compared with a penalty-based QUBO formulation, it generates feasible solutions more reliably. At an appropriate inverse temperature, its conditional relative error is comparable to that of local search for small instances and often lower for the larger tested instances. In the time-to-target experiment, it also reaches the target faster than a commercial mixed-integer optimization solver toward the upper end of the tested range.

quant-ph↗

arXiv2026

Optimization of Connection Patterns between Mobile Phones and Base Stations using Quantum Annealing

In current mobile networks, optimizing which base station a mobile phone in a particular area connects to is crucial for ensuring good communication quality for each mobile phone but presents a challenging combinatorial optimization problem. In this study, we optimize the connection patterns to base stations using quantum annealing which is a heuristic optimization algorithm using quantum fluctuations. However, since the number of qubits on a quantum annealer is limited, it is necessary to consider a formulation that efficiently utilizes qubits. By adopting a variable reduction formulation, we significantly reduce the qubit requirements compared to the naive formulation that is typically used when considering pattern-matching problems. Furthermore, experiments using quantum annealing revealed that the accuracy of the approximate solution obtained by the new formulation is superior to that of the conventional formulation. In addition, we demonstrate that the new formulation provides better solutions than the conventional formulation as the problem size increases, even when using simulated annealing, the classical counterpart of quantum annealing.

quant-ph↗

arXiv2026

Dynamical Criticality of a Machine-learning-assisted Monte Carlo algorithm for a Mean-Field Spin Glass model

We critically assess the performance of an autoregressive generative neural network model by applying it to an antiferromagnetic Ising model on a random regular graph. We train the network on equilibrium configurations in the low-temperature spin-glass phase of the model and perform Monte Carlo simulations using spin configurations generated by the network. The relaxation time of the Monte Carlo simulations drastically decreases with increasing the size of the training dataset and converges to an optimal value. The dynamical exponent characterizing the growth of the optimal relaxation time as a function of the system size is slightly reduced compared to the local Monte Carlo dynamics. However, we find that the size of the training dataset to achieve the optimal performance grows much faster with the system size than the relaxation time, implying that the total training cost eventually hinders a practical use of the method at large system sizes.

cond-mat.dis-nn↗

arXiv2026

Absence of Spin-Glass Order on Migdal--Kadanoff Hierarchical Lattices near Three Dimensions

We derive a rigorous sufficient condition for the absence of spin-glass order in the Ising spin glass with symmetric binary couplings on Migdal--Kadanoff (MK) hierarchical lattices with even branching number. The key observation is that a single exact renormalization-group step creates zero effective bonds with positive probability, thereby reducing the problem to bond percolation on the corresponding hierarchical lattice. When the induced dilution exceeds the percolation threshold, both spin-glass order and stiffness are absent at all temperatures, including zero temperature. As a consequence, our criterion gives a rigorous proof that the Ising spin glass on the square lattice does not exhibit a spin-glass phase within the MK approximation. More unexpectedly, by choosing sufficiently large scale factors and branching numbers, we construct MK hierarchical lattices whose fractal dimensions are arbitrarily close to three from below but still exhibit no spin-glass order. This sharply contrasts with numerical estimates obtained for MK hierarchical lattices with relatively small scale factors and branching numbers, which placed the lower critical dimension near $2.52$.

cond-mat.dis-nn↗

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↗