arXiv subjects

Kazue Kudo

Publications and source records attributed to Kazue Kudo.

At least 19 recordsLinked to original sources

arXiv2026

Solving Differential Equations Using Continuous-Variable Quantum Annealing

Most existing quantum annealing approaches are formulated for qubit-based architectures. Consequently, applying them to continuous-variable optimization problems requires discretizing the variables, which can incur substantial qubit overhead. Continuous-variable quantum annealing based on bosonic systems has recently been proposed as an alternative framework, in which each optimization variable is directly encoded in a bosonic mode, such as a cavity mode. In this work, we develop a continuous-variable quantum annealing formulation for solving linear differential equations. By recasting the determination of the solution as a continuous-variable optimization problem, the differential equation can be mapped onto an objective function compatible with bosonic quantum annealing. Numerical simulations of second-order linear differential equations demonstrate that, under the conditions considered, the proposed formulation reproduces the corresponding analytical solutions. These results establish a potential route toward solving differential equations without the discretization overhead inherent in qubit-based implementations.

quant-ph↗

arXiv2026

Annealing-based approach to solving partial differential equations

Solving partial differential equations (PDEs) using an annealing-based approach involves solving generalized eigenvalue problems. Discretizing a PDE yields a system of linear equations (SLE). Solving an SLE can be formulated as a general eigenvalue problem, which can be transformed into an optimization problem with an objective function given by a generalized Rayleigh quotient. The proposed algorithm requires iterative computations. However, it enables efficient annealing-based computation of eigenvectors to arbitrary precision without increasing the number of variables. Investigations using simulated annealing demonstrate how the number of iterations scales with system size and annealing time. Computational performance depends on system size, annealing time, and problem characteristics.

math.NA↗

arXiv2025

Performance of the Extended Ising Machine for the Quadratic Knapsack Problem

The extended Ising machine (EIM) enhances conventional Ising models, which handle only binary quadratic forms by allowing constraints through real-valued dependent variables. We address the quadratic knapsack problem (QKP), hard to solve using Ising machines when formulated as a quadratic unconstrained binary optimization (QUBO). We demonstrated the EIM's superiority by comparing it with the conventional Ising model-based approach, a commercial exact solver, and a state-of-the-art heuristic solver for QKP.

cond-mat.stat-mech↗

arXiv2025

Collaborative filtering based on nonnegative/binary matrix factorization

Collaborative filtering generates recommendations by exploiting user-item similarities based on rating data, which often contains numerous unrated items. To predict scores for unrated items, matrix factorization techniques such as nonnegative matrix factorization (NMF) are often employed. Nonnegative/binary matrix factorization (NBMF), which is an extension of NMF, approximates a nonnegative matrix as the product of nonnegative and binary matrices. While previous studies have applied NBMF primarily to dense data such as images, this paper proposes a modified NBMF algorithm tailored for collaborative filtering with sparse data. In the modified method, unrated entries in the rating matrix are masked, enhancing prediction accuracy. Furthermore, utilizing a low-latency Ising machine in NBMF is advantageous in terms of the computation time, making the proposed method beneficial.

cond-mat.stat-mech↗

arXiv2025

Quantum autoencoders for image classification

Classical machine learning often struggles with complex, high-dimensional data. Quantum machine learning offers a potential solution, promising more efficient processing. The quantum convolutional neural network (QCNN), a hybrid algorithm, fits current noisy intermediate-scale quantum hardware. However, its training depends largely on classical computation. Future gate-based quantum computers may realize full quantum advantages. In contrast to QCNNs, quantum autoencoders (QAEs) leverage classical optimization solely for parameter tuning. Data compression and reconstruction are handled entirely within quantum circuits, enabling purely quantum-based feature extraction. This study introduces a novel image-classification approach using QAEs, achieving classification without requiring additional qubits compared with conventional QAE implementations. The quantum circuit structure significantly impacts classification accuracy. Unlike hybrid methods such as QCNN, QAE-based classification emphasizes quantum computation. Our experiments demonstrate high accuracy in a four-class classification task, evaluating various quantum-gate configurations to understand the impact of different parameterized quantum circuit structures on classification performance. Specifically, noise-free conditions are considered, and simulations are performed using a statevector simulator to model the quantum system with full amplitude precision. Our results reveal that specific ansatz structures achieve superior accuracy. Moreover, the proposed approach achieves performance comparable to that of conventional machine-learning methods while significantly reducing the number of parameters requiring optimization. These findings indicate that QAEs can serve as efficient classification models with fewer parameters and highlight the potential of utilizing quantum circuits for complete end-to-end learning.

quant-ph↗

arXiv2024

Procedure to Reveal the Mechanism of Pattern Formation Process by Topological Data Analysis

Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics does not agree one-to-one, and the physical interpretation of the TDA features needs to be set appropriately according to the phenomenon to be analyzed. In this study, we propose an analytical procedure to physically interpret pattern dynamics through TDA and machine learning techniques. The proposed procedure was applied to the process of magnetic domain pattern formation to quantify non-trivial domain pattern classifications and reveal the nature of the underlying dynamics. On the basis of these findings, we also propose a candidate reduction model to understand the nature of magnetic domain formation.

nlin.PS↗

arXiv2024

Observation of Localization Using a Noisy Quantum Computer

Quantum dynamics in a strongly disordered quantum many-body system show localization properties. The initial state memory is maintained owing to slow relaxation when the system is in the localized regime. This work demonstrates how localization can be observed using a noisy quantum computer by evaluating the magnetization and twist overlap in a quantum spin chain after short-time evolution. The quantities obtained from quantum-circuit simulation and real-device computation show their apparent dependence on disorder strength, although real-device computation suffers from noise-induced errors significantly. Using the exact diagonalization of the Hamiltonian, we analyze how noise-induced errors affect those quantities. The analysis also suggests how the twist overlap can reflect the information on the eigenstates of the Hamiltonian.

quant-ph↗

arXiv2023

Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute. Demonstrating the benefits of this integration now becomes essential. With the advance of quantum computing, several machine-learning techniques have been proposed that use quantum annealing. In this study, we implement a matrix factorization method using quantum annealing for image classification and compare the performance with traditional machine-learning methods. Nonnegative/binary matrix factorization (NBMF) was originally introduced as a generative model, and we propose a multiclass classification model as an application. We extract the features of handwritten digit images using NBMF and apply them to solve the classification problem. Our findings show that when the amount of data, features, and epochs is small, the accuracy of models trained by NBMF is superior to classical machine-learning methods, such as neural networks. Moreover, we found that training models using a quantum annealing solver significantly reduces computation time. Under certain conditions, there is a benefit to using quantum annealing technology with machine learning.

quant-ph↗

arXiv2022

Localization detection based on quantum dynamics

Detecting many-body localization (MBL) typically requires the calculation of high-energy eigenstates using numerical approaches. This study investigates methods that assume the use of a quantum device to detect disorder-induced localization. Numerical simulations for small systems demonstrate how the magnetization and twist overlap, which can be easily obtained from the measurement of qubits in a quantum device, change from the thermal phase to the localized phase. The twist overlap evaluated using the wave function at the end of the time evolution behaves similarly to the one evaluated with eigenstates in the middle of the energy spectrum under a specific condition. The twist overlap evaluated using the wave function after time evolution for many disorder realizations is a promising probe for detecting MBL in quantum computing approaches.

cond-mat.dis-nn↗

arXiv2021

Pattern Formation Simulated by an Ising Machine

In a ferromagnetic Ising system, domain pattern formation, i.e., phase-ordering, occurs after a sudden quench. We propose the method to simulate the pattern formation dynamics by an Ising machine. We demonstrate that the method reproduces domain patterns similar to those simulated by the Monte Carlo method. Moreover, the same domain growth law is observed in the proposed method and the Monte Carlo method.

cond-mat.stat-mech↗

arXiv2020

Image Analysis Based on Nonnegative/Binary Matrix Factorization

Using nonnegative/binary matrix factorization (NBMF), a matrix can be decomposed into a nonnegative matrix and a binary matrix. Our analysis of facial images, based on NBMF and using the Fujitsu Digital Annealer, leads to successful image reconstruction and image classification. The NBMF algorithm converges in fewer iterations than those required for the convergence of nonnegative matrix factorization (NMF), although both techniques perform comparably in image classification.

cs.CV↗

arXiv2020

Localization in the constrained quantum annealing of graph coloring

Constrained quantum annealing (CQA) is a quantum annealing approach that is designed so that constraints are satisfied without penalty terms. There is an analogy between the model for the CQA of graph coloring and a set of disordered spin chains. In the model for the CQA of graph coloring, disorder corresponds to the fluctuation of effective local fields that increase in a CQA process. Numerical simulations of effective fields and entanglement demonstrate how localization appears in the CQA. Some notable features appear in the concurrence, which is a measure of entanglement, plotted as a function of the fluctuation of effective fields.

quant-ph↗

arXiv2020

Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalance

We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, and uncover that random walk of droplet for the minor component plays a fundamental role in the relaxation process. Our numerical simulations based on the binary Gross-Pitaevskii model reveal the emergence of the dynamical scaling during the relaxation, which is a hallmark of scale-invariant dynamics, in a correlation function for the minor condensate. Tracking exponents characterizing the dynamical scaling in time, we find out a crossover phenomenon that features the change in power exponents of the correlation length. To understand the fundamental mechanism inherent in the scale-invariant relaxation dynamics, we construct a random walk model for droplets. Employing the model, we analytically derive the $1/3$ and $1/2$ power laws and predict the crossover of the scaling. These exponents are in reasonable agreement with the values obtained in the numerical calculations. We also discuss a possible experimental setup for observing the scale-invariant dynamics.

cond-mat.quant-gas↗

arXiv2018

Constrained quantum annealing of graph coloring

We investigate a quantum annealing approach based on real-time quantum dynamics for graph coloring. In this approach, a driving Hamiltonian is chosen so that constraints are naturally satisfied without penalty terms, and the dimension of the Hilbert space is considerably reduced. The total Hamiltonian, which consists of driving and problem Hamiltonians, resembles a disordered quantum spin chain. The ground state of the problem Hamiltonian for graph coloring is degenerate. This degeneracy is advantageous and is characteristic of this approach. Real-time quantum simulations in a small system demonstrate interesting results and provide some insight into quantum annealing.

quant-ph↗

arXiv2018

Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition

We present a finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 XXZ spin chain with a random field by studying level statistics. We show how the dynamical transition from the thermal to MBL phase depends on interaction together with disorder by evaluating the ratio of adjacent level spacings, and thus, extend previous studies in which interaction coupling is fixed. We introduce an extra critical exponent in order to describe the nontrivial interaction dependence of the MBL transition. It is characterized by the ratio of the disorder strength to the power of the interaction coupling with respect to the extra critical exponent and not by the simple ratio between them.

cond-mat.dis-nn↗

arXiv2017

Emergence of wrinkles during the curing of coatings

Wrinkles often emerge on a paint layer when a second coat of paint is applied on an already-coated substrate. Wrinkle formation occurs when the first layer absorbs organic solvent from the second layer. We set up experiments to mimic the double-coating process, focusing on the interaction between a paint layer and an organic solvent. In the experiments, we investigated the characteristic wavelengths of the wrinkles and the time of wrinkle emergence. We propose a simple model to explain (1) the buckling induced by swelling of the layer due to absorption of the organic solvent and (2) delamination of the layer from the substrate. A linear stability analysis of the model provides a relationship between the wavelengths and the characteristic timescale that agrees reasonably well with the data obtained from our experiments. Our results indicate that compression of the layer due to swelling and delamination are both important factors in the formation of wrinkles.

cond-mat.soft↗

arXiv2017

Spread of infectious diseases: Effects of the treatment of population

In a metapopulation network, infectious diseases spread widely because of the travel of individuals. In the present study, we consider a modified metapopulation Susceptible-Infected-Removed (SIR) model with a latent period, which we call the SHIR model. In the SHIR model, an infectious period is divided into two stages. In the first stage, which corresponds to the latent period, infectious individuals can travel. However, in the second stage, the same individuals cannot travel since they are seriously ill. Final size distributions of the metapopulation SIR and SHIR models are simulated with two different methods and compared. In Monte Carlo simulations, in which the population is treated as an integer, the distributions show similar behavior. However, in reaction-diffusion systems, in which the population is treated as a real number, the final size distribution of the SHIR model has a discontinuous jump, and that of the SIR model shows a continuous transition. The discontinuous jump is found to be an artifact that occurs owing to an inappropriate termination condition.

physics.soc-ph↗

arXiv2017

Academic Meeting Scheduling Using an Antiferromagnetic Potts Model

Scheduling parallel sessions of an academic meeting is a complicated task. If each presentation is assigned to an appropriate session, an antiferromagnetic Potts model can be used for semi-automatic timetabling. The timetabling method proposed here is based on graph coloring and includes additional constraints to be considered in a practical situation. We examine the feasibility of semi-automatic timetabling in some practical examples.

physics.soc-ph↗