arXiv subjects

Naoki Maruyama

Publications and source records attributed to Naoki Maruyama.

7 recordsLinked to original sources

arXiv2026

Interpretation of Unfair Sampling in Quantum Annealing by Node Centrality

In applications where multiple optimal solutions are needed, transverse-field quantum annealing (QA) is known to sample degenerate ground states in a strongly biased manner. Despite extensive empirical observations, it remains unclear which features of degenerate ground states are preferentially sampled and why by QA. Here we analyze the final states using degenerate perturbation theory to characterize the preference among them. In this analysis, the adjacency matrix of the graph composed by the ground states naturally emerges, and we can predict the eigenvector centralities (one of the node centralities) are related to the probabilities of these states. We verify this prediction on toy models where degeneracy is lifted at first and second order, and we show that second-order weights encode local barrier information, relating sampling fairness to the flatness of the local energy landscape. Finally, this perspective suggests two practical routes toward fair sampling -- promoting connectivity of the graph and reducing heterogeneity of centralities -- and we illustrate consistency with higher-order drivers and minor-embedding transformations.

quant-ph↗

arXiv2025

Quantum-classical hybrid algorithm using quantum annealing for multi-objective job shop scheduling

Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.

quant-ph↗

arXiv2025

Uniformity Bias in Ground-State Sampling Induced by Replica Alignment in Quantum Monte Carlo for Quantum Annealing

Quantum annealing (QA) with a transverse field often fails to sample degenerate ground states fairly, limiting applicability to problems requiring diverse optimal solutions. Although Quantum Monte Carlo (QMC) is widely used to simulate QA, its ability to reproduce such unfair ground-state sampling remains unclear because stochastic and coherent quantum dynamics differ fundamentally. We quantitatively evaluate how accurately QMC reproduces the sampling bias in QA by comparing the final ground-state distributions from the QMC master equation and the Schrödinger equation. We find QMC tends to produce uniform ground-state probabilities, unlike QA's biased distribution, and that this uniformity bias strengthens as annealing proceeds. Our analysis reveals that this bias originates from replica alignment -- the dominance of configurations in which all Trotter replicas coincide -- caused by the energetic suppression and entropic reduction of kink configurations (replica mismatches). These findings clarify a fundamental limitation of discrete-time QMC in faithfully simulating QA dynamics, highlighting the importance of replica correlations and transition rules in achieving realistic ground-state sampling.

quant-ph↗

arXiv2025

Efficient Construction of Feasible Solutions in Column Generation using Quantum Annealing

Column generation (CG) has been used to solve constrained 0-1 quadratic programming problems. The pricing problem, which is iteratively solved in CG, can be reduced to an unconstrained 0-1 quadratic programming problem, allowing for the efficient application of quantum annealing (QA). The solutions obtained by CG are continuous relaxations, which cannot be practically used as feasible 0-1 solutions. In this paper, we propose a postprocessing method for constructing feasible 0-1 solutions from the continuous relaxations obtained through CG. The proposed technique consists of two phases: (i) mapping the continuous CG solution to a feasible 0-1 solution and (ii) applying a constraint-aware local search to improve that solution's quality. Numerical experiments on randomly generated problems demonstrate that CG with the proposed postprocessing yields solutions comparable to commercial solvers with significantly reduced computation time. Consequently, the postprocessing enables CG with QA to obtain high-quality approximate solutions faster.

quant-ph↗

arXiv2022

Eigenvalue Fluctuations of 1-dimensional random Schrödinger operators

As an extension to the paper by Breuer, Grinshpon, and White \cite{B}, we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential with order ${\cal O}(x^{-α})$ ($α>0$) at infinity. We first prove similar statements as in \cite{B} for the trace of $f(H)$, where $f$ belongs to a class of analytic functions : there exists a critical exponent $α_c$ such that the fluctuation of the trace of $f(H)$ converges in probability for $α> α_c$, and satisfies a CLT statement for $α\le α_c$, where $α_c$ differs depending on $f$. Furthermore we study the asymptotic behavior of its expectation value.

math-ph↗

arXiv2021

Graph minor embedding can affect sampling degenerate ground states using quantum annealing

Quantum annealing, as currently implemented in hardware, cannot fairly sample all ground states. Graph minor embedding, which maps a problem to the hardware graph of quantum annealers, affects sampling all states. In this study, we demonstrate the influence of graph minor embedding on fair sampling of degenerate ground states. For two embedded models that introduce auxiliary variables, numerical simulations of Schr\"odinger evolution revealed that fairness varies significantly depending on the embedding, and the chain strength is related to ground-state fairness. Using perturbation theory, we found that chain strength determines the energy landscape around ground states, with flatter landscapes having higher probabilities of being obtained.

quant-ph↗

arXiv2020

Tetragonality of Fe-C martensite -- a pattern matching electron backscatter diffraction analysis compared to X-ray diffraction

Measurements of the local tetragonality in Fe-C martensite at microstructural length-scale through pattern matching of electron backscatter diffraction patterns (EBSPs) and careful calibration of detector geometry are presented. It is found that the local tetragonality varies within the complex microstructure by several per cent at largest and that the scatter in the axial ratio is increased at higher nominal carbon content. At some analysis points the local crystal structure can be regarded as lower symmetry than simple body centred tetragonal. A linear relation between the nominal carbon content and averaged local tetragonality measured by EBSD is also obtained, although the averaged axial ratio is slightly below that obtained from more classical X-ray diffraction measurements.

cond-mat.mtrl-sci↗