© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Japan Society of Civil Engineers Ser C (Geosphere Engineering)

A STUDY ON OPTIMAL DESIGN OF GEOTECHNICAL STRUCTURES USING QUANTUM ANNEALING

Takayuki Shuku, Shinya YAMAMOTO

Published Jan 1, 2022• 0 citations

Abstract

本研究では，地盤工学における最適設計問題を統一的に解くための方法として量子アニーリング（quantum annealing，QA）に着目し，その適用性について検証している．本論文では，量子アニーリングの実装に必要なquadratic unconstrained binary optimization（QUBO）による最適化問題の具体的な定式化方法を示すとともに，杭の最適配置を対象とした数値実験を通して，既存の方法と比較した量子アニーリングの優位性，および最適化ソルバーとしての特性を明らかにした．さらに，数値実験で明らかとなった量子アニーリングの特性に基づき，量子アニーリングを利用したモンテカルロ法を地盤構造物の最適設計に応用することを提案し，地盤パラメータのばらつきを考慮した杭の最適設計問題への適用例を示した．

DOI: 10.2208/jscejge.78.2_116

Related papers

Quantum classical hybrid algorithm for solving partial differential equations based on the finite element method

Le Li, Mengyuan Cao, Yongle Li +2 more

摘要偏微分方程（partial differential equations, PDEs）在科学与工程领域应用广泛, 但传统数值方法在求解高维或大规模问题时面临维数灾难. 量子计算的发展为解决这一难题提供了新思路, 然而现有量子算法存在一些局限，如对硬件要求高, 量子电路的表达能力有限等. 针对以上问题, 本文对Helmholtz方程提出了一种融合量子退火(quantum annealing, QA)与高斯-赛德尔(gauss-seidel, GS)迭代的混合计算方法. 首先, 通过有限元方法离散该方程转化为线性方程组, 进而构造出二次无约束二进制优化（quadratic unconstrained binary optimization, QUBO）问题. 然后, 用量子退火求得该方程组全局最优的初始解, 并在此过程中引入了残差补偿机制. 最后, 通过高斯-赛德尔迭代来提升解的精度. 结果表明该算法不仅得到的数值解收敛到比较理想的精度, 而且迭代效率也得到了很好的提高. 另外, 该混合算法对量子硬件的要求低, 在含噪声中等规模量子(noisy intermediate-scale quantum, NISQ) 时代为高维、大规模偏微分方程求解提供了兼具效率与精度的新路径, 也可以用于其他偏微分方程的求解, 有利于推动量子经典混合计算在科学工程领域的应用.

Chinese Science Bulletin (Chinese Version)•Nov 20, 2025•0 citations

USING QUANTUM ANNEALING FOR ROUTING AND WAVELENGTH ALLOCATION OPTIMIZATION IN OPTICAL NETWORKS

Victor Virag

This work benchmarks Quantum Annealing (QA), Hybrid Annealing (HA), and Simulated Annealing (SA) for solving Wavelength Allocation (WA) and Routing and Wavelength Allocation (RWA) problems in static Wavelength Division Multiplexing (WDM) optical networks. We introduce a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation for the static RWA problem, designed to minimize link utilization, distinguishing it from existing dynamic formulations.

•Aug 20, 2024•0 citations

Study of Optimization Problems by Quantum Annealing(量子アニーリングによる最適化問題の研究)

門脇正史

•Jan 1, 1999•0 citations

Performance of quantum annealing in solving optimization problems: A review

Sei Suzuki

The European Physical Journal Special Topics•Feb 1, 2015•8 citations

CUBO-to-QUBO Conversion: Reducing Cubic Formulations to Quadratic Formulations

Shunsuke Tsukiyama, Xiaotian Li, Koji Nakano +5 more

Quadratic Unconstrained Binary Optimization (QUBO) models are defined by quadratic expressions composed of binary variables, each taking a value of either 0 or 1. The objective of the QUBO problem is to find an optimal assignment of these binary variables that minimizes the value of the QUBO model. The QUBO problem has attracted significant research interest due to its versatility in reformulating various NP-complete problems and its potential for efficiently finding heuristic solutions through quantum annealing. This paper focuses on converting Cubic Unconstrained Binary Optimization (CUBO) problems, defined by cubic expressions, into equivalent QUBO models. Through this conversion, CUBO problems can be solved using quantum annealing. Since the important NP-hard problem 3-SAT can be straightforwardly represented as a CUBO problem, investigating the conversion from CUBO to QUBO models is a meaningful endeavor.

IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum•Jun 3, 2025•1 citation

Learning Quadratic Unconstrained Binary Optimization Models for Quantum Annealing

Florian Richoux, Jean-François Baffier, Philippe Codognet

•Jan 1, 2025•0 citations

本研究では，地盤工学における最適設計問題を統一的に解くための方法として量子アニーリング（quantum annealing，QA）に着目し，その適用性について検証している．本論文では，量子アニーリングの実装に必要なquadratic unconstrained binary optimization（QUBO）による最適化問題の具体的な定式化方法を示すとともに，杭の最適配置を対象とした数値実験を通して，既存の方法と比較した量子アニーリングの優位性，および最適化ソルバーとしての特性を明らかにした．さらに，数値実験で明らかとなった量子アニーリングの特性に基づき，量子アニーリングを利用したモンテカルロ法を地盤構造物の最適設計に応用することを提案し，地盤パラメータのばらつきを考慮した杭の最適設計問題への適用例を示した．

摘要偏微分方程（partial differential equations, PDEs）在科学与工程领域应用广泛, 但传统数值方法在求解高维或大规模问题时面临维数灾难. 量子计算的发展为解决这一难题提供了新思路, 然而现有量子算法存在一些局限，如对硬件要求高, 量子电路的表达能力有限等. 针对以上问题, 本文对Helmholtz方程提出了一种融合量子退火(quantum annealing, QA)与高斯-赛德尔(gauss-seidel, GS)迭代的混合计算方法. 首先, 通过有限元方法离散该方程转化为线性方程组, 进而构造出二次无约束二进制优化（quadratic unconstrained binary optimization, QUBO）问题. 然后, 用量子退火求得该方程组全局最优的初始解, 并在此过程中引入了残差补偿机制. 最后, 通过高斯-赛德尔迭代来提升解的精度. 结果表明该算法不仅得到的数值解收敛到比较理想的精度, 而且迭代效率也得到了很好的提高. 另外, 该混合算法对量子硬件的要求低, 在含噪声中等规模量子(noisy intermediate-scale quantum, NISQ) 时代为高维、大规模偏微分方程求解提供了兼具效率与精度的新路径, 也可以用于其他偏微分方程的求解, 有利于推动量子经典混合计算在科学工程领域的应用.

Quadratic Unconstrained Binary Optimization (QUBO) models are defined by quadratic expressions composed of binary variables, each taking a value of either 0 or 1. The objective of the QUBO problem is to find an optimal assignment of these binary variables that minimizes the value of the QUBO model. The QUBO problem has attracted significant research interest due to its versatility in reformulating various NP-complete problems and its potential for efficiently finding heuristic solutions through quantum annealing. This paper focuses on converting Cubic Unconstrained Binary Optimization (CUBO) problems, defined by cubic expressions, into equivalent QUBO models. Through this conversion, CUBO problems can be solved using quantum annealing. Since the important NP-hard problem 3-SAT can be straightforwardly represented as a CUBO problem, investigating the conversion from CUBO to QUBO models is a meaningful endeavor.