arXiv subjects

Shunta Arai

Publications and source records attributed to Shunta Arai.

11 recordsLinked to original sources

arXiv2026

Slack-Free Deep-Unfolded Combinatorial Optimization Solver for Inequality Constraints

Quantum annealing (QA) is used to solve combinatorial optimization problems (COPs). When COPs are implemented on quantum annealers, they are typically encoded as quadratic unconstrained binary optimization (QUBO) problems, but constraint encodings often increase the number of qubits and the embedding overhead. This issue is particularly important for COPs with inequality constraints, where standard slack-variable formulations introduce additional binary variables. Unbalanced penalization (UP) avoids slack variables, but the original UP formulation requires tuning two penalty coefficients and contains a squared residual term that can increase the number of quadratic couplings. In this paper, we propose the unbalanced penalization Ohzeki method (UPOM), which combines UP with the Ohzeki method for inequality-constrained COPs. UPOM replaces the two static penalty coefficients of original UP with an auxiliary-variable update and removes the squared residual term from the Hamiltonian used for sampling. We further propose the deep-unfolded unbalanced penalization Ohzeki method (DU-UPOM), which learns the step-size schedule of the UPOM update from training instances. Numerical experiments on random knapsack problems show that UPOM improves over original UP and that DU-UPOM reaches optimal solutions in fewer iterations than fixed-step UPOM and other baseline. These results demonstrate that the proposed framework reduces the tuning and embedding burdens of UP while making the Ohzeki method trainable for inequality constraints.

quant-ph↗

arXiv2026

Physics-Aware Linearized ADMM and Its Unrolling

Recently, partial differential equations (PDEs) have been used to directly model the measurement process in signal processing, although their evaluation is costly. In this paper, we propose a novel alternating direction method of multipliers (ADMM)-based algorithm called physics-aware linearized ADMM (PA-LADMM) for inverse problems from PDE-based measurement processes. The key idea is the linearization of the subproblem with PDEs, leading to a cost-efficient update rule that calls only a PDE solver and its gradient evaluation per iteration. The algorithm has a theoretical convergence guarantee under certain conditions. In addition, we combine it with deep unfolding to unroll the PA-LADMM and train its internal parameters using supervised data. Two distinct experiments, compressed sensing with optical fiber communication and image restoration from noisy anisotropic diffusion, demonstrated the effectiveness of the proposed algorithms.

eess.SP↗

arXiv2026

Refined Gradient-Based Temperature Optimization for the Replica-Exchange Monte-Carlo Method

The replica-exchange Monte-Carlo (RXMC) method is a powerful Markov-chain Monte-Carlo algorithm for sampling from multi-modal distributions, which are challenging for conventional methods. The sampling efficiency of the RXMC method depends highly on the selection of the temperatures, and finding optimal temperatures remains a challenge. In this study, we propose a refined online temperature selection method by extending the gradient-based optimization framework proposed previously. Building upon the existing temperature update approach, we introduce a reparameterization technique to strictly enforce physical constraints, such as the monotonic ordering of inverse temperatures, which were not explicitly addressed in the original formulation. The proposed method defines the variance of acceptance rates between adjacent replicas as a loss function, estimates its gradient using differential information from the sampling process, and optimizes the temperatures via gradient descent. We demonstrate the effectiveness of our method through experiments on benchmark spin systems, including the two-dimensional ferromagnetic Ising model, the two-dimensional ferromagnetic XY model, and the three-dimensional Edwards-Anderson model. Our results show that the method successfully achieves uniform acceptance rates and reduces round-trip times across the temperature space. Furthermore, our proposed method offers a significant advantage over recently proposed policy gradient method that require careful hyperparameter tuning, while simultaneously preventing the constraint violations that destabilize optimization.

physics.comp-ph↗

arXiv2025

Quantum Annealing Enhanced Markov-Chain Monte Carlo

In this study, we propose quantum annealing-enhanced Markov Chain Monte Carlo (QAEMCMC), where QA is integrated into the MCMC subroutine. QA efficiently explores low-energy configurations and overcomes local minima, enabling the generation of proposal states with a high acceptance probability. We benchmark QAEMCMC for the Sherrington-Kirkpatrick model and demonstrate its superior performance over the classical MCMC method. Our results reveal larger spectral gaps, faster convergence of energy observables, and reduced total variation distance between the empirical and target distributions. QAEMCMC accelerates MCMC and provides an efficient method for complex systems, paving the way for scalable quantum-assisted sampling strategies.

quant-ph↗

arXiv2025

Transfer Learning for Deep-Unfolded Combinatorial Optimization Solver with Quantum Annealer

Quantum annealing (QA) has attracted research interest as a sampler and combinatorial optimization problem (COP) solver. A recently proposed sampling-based solver for QA significantly reduces the required number of qubits, being capable of large COPs. In relation to this, a trainable sampling-based COP solver has been proposed that optimizes its internal parameters from a dataset by using a deep learning technique called deep unfolding. Although learning the internal parameters accelerates the convergence speed, the sampler in the trainable solver is restricted to using a classical sampler owing to the training cost. In this study, to utilize QA in the trainable solver, we propose classical-quantum transfer learning, where parameters are trained classically, and the trained parameters are used in the solver with QA. The results of numerical experiments demonstrate that the trainable quantum COP solver using classical-quantum transfer learning improves convergence speed and execution time over the original solver.

quant-ph↗

arXiv2024

Deep Unfolded Local Quantum Annealing

Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective function. In the original LQA, the classical Hamiltonian is minimized via gradient descent. The performance of LQA depends on the choice of the parameters. Owing to the non-convex nature of the original cost function, LQA often becomes trapped in local minima, limiting its effectiveness. To address this challenge, we combine LQA with a deep unfolding scheme, which enables us to tune the parameters from the training data via back-propagation. {As a demonstration, we apply the deep unfolded LQA to the Sherrington-Kirkpatrick model, which is a fundamental {model} in statistical physics.} Our findings exhibit that deep unfolded LQA outperforms the original LQA, exhibiting remarkable convergence speed and performance improvement. As the trained parameters can be generalized to unknown instances and different system sizes, our results have significant practical implications and provide valuable insights for real-world applications.

quant-ph↗

arXiv2023

Effectiveness of quantum annealing for continuous-variable optimization

The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next, we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the TEBD (time-evolving block decimation) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations.

quant-ph↗

arXiv2021

Teacher-student learning for a binary perceptron with quantum fluctuations

We analysed the generalisation performance of a binary perceptron with quantum fluctuations using the replica method. An exponential number of local minima dominate the energy landscape of the binary perceptron. Local search algorithms often fail to identify the ground state of a binary perceptron. In this study, we considered the teacher-student learning method and computed the generalisation error of a binary perceptron with quantum fluctuations. Due to the quantum fluctuations, we can efficiently find robust solutions that have better generalisation performance than the classical model. We validated our theoretical results through quantum Monte Carlo simulations. We adopted the replica symmetry (RS) ansatz assumption and static approximation. The RS solutions are consistent with our simulation results, except for the relatively low strength of the transverse field and high pattern ratio. These deviations are caused by the violation of ergodicity and static approximation. After accounting for the deviation between the RS solutions and numerical results, the enhancement of generalisation performance with quantum fluctuations holds.

cond-mat.dis-nn↗

arXiv2020

Mean field analysis of reverse annealing for code-division multiple-access multiuser detection

We evaluate the typical ARA performance of the CDMA multiuser detection by means of statistical mechanics using the replica method. At first, we consider the oracle cases where the initial candidate solution is randomly generated with a fixed fraction of the original signal in the initial state. In the oracle cases, the first-order phase transition can be avoided or mitigated by ARA if we prepare for the proper initial candidate solution. We validate our theoretical analysis with quantum Monte Carlo simulations. The theoretical results to avoid the first-order phase transition are consistent with the numerical results. Next, we consider the practical cases where we prepare for the initial candidate solution obtained by commonly used algorithms. We show that the practical algorithms can exceed the threshold to avoid the first-order phase transition. Finally, we test the performance of ARA with the initial candidate solution obtained by the practical algorithm. In this case, the ARA can not avoid the first-order phase transition even if the initial candidate solution exceeds the threshold to avoid the first-order phase transition.

cond-mat.dis-nn↗

arXiv2019

Dynamics of Order Parameters of Non-stoquastic Hamiltonians in the Adaptive Quantum Monte Carlo Method

We derive macroscopically deterministic flow equations with regard to the order parameters of the ferromagnetic $p$-spin model with infinite-range interactions. The $p$-spin model has a first-order phase transition for $p>2$. In the case of $p\geq5$ ,the $p$-spin model with anti-ferromagnetic XX interaction has a second-order phase transition in a certain region. In this case, however, the model becomes a non-stoqustic Hamiltonian, resulting in a negative sign problem. To simulate the $p$-spin model with anti-ferromagnetic XX interaction, we utilize the adaptive quantum Monte Carlo method. By using this method, we can regard the effect of the anti-ferromagnetic XX interaction as fluctuations of the transverse magnetic field. A previous study derived deterministic flow equations of the order parameters in the quantum Monte Carlo method. In this study, we derive macroscopically deterministic flow equations for the magnetization and transverse magnetization from the master equation in the adaptive quantum Monte Carlo method. Under the Suzuki-Trotter decomposition, we consider the Glauber-type stochastic process. We solve these differential equations by using the Runge-Kutta method and verify that these results are consistent with the saddle-point solution of mean-field theory. Finally, we analyze the stability of the equilibrium solutions obtained by the differential equations.

cond-mat.stat-mech↗

arXiv2017

Deep Neural Network Detects Quantum Phase Transition

We detect the quantum phase transition of a quantum many-body system by mapping the observed results of the quantum state onto a neural network. In the present study, we utilized the simplest case of a quantum many-body system, namely a one-dimensional chain of Ising spins with the transverse Ising model. We prepared several spin configurations, which were obtained using repeated observations of the model for a particular strength of the transverse field, as input data for the neural network. Although the proposed method can be employed using experimental observations of quantum many-body systems, we tested our technique with spin configurations generated by a quantum Monte Carlo simulation without initial relaxation. The neural network successfully classified the strength of transverse field only from the spin configurations, leading to consistent estimations of the critical point of our model $Γ_c =J$.

cond-mat.stat-mech↗