立方格上带权最大割问题的误差缓解量子退火求解方案
An error-mitigated quantum annealing solution for the weighted Max-Cut problem on a cubic lattice
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中文总结 AI 辅助
本文针对立方格带权最大割问题，提出SEMO误差缓解量子退火方法，经与多种基线求解器对比，其求解时间显著更短，有望提升量子退火效率与应用范围。
中文摘要 AI 辅助
带权最大割问题是具有应用价值的NP难问题，本文在含113个节点、边权为混合符号随机值的立方格上对其展开研究。对于固定的边权上界，已有研究表明，边权下界越负，计算难度越大。本文提出一种新型误差缓解量子退火方法，将其求解该问题的时间与标准D-Wave量子退火（QA）、BQM混合求解器及多种经典求解器进行对比。针对可嵌入量子处理单元（QPU）的混合符号边权带权最大割实例，定量验证了SEMO（优化问题自旋误差缓解）误差缓解量子退火方法相较于标准D-Wave QA、D-Wave BQM、模拟退火和禁忌搜索基线方法，实现了显著更短的求解时间。本文提出的误差缓解量子退火方法有望提升量子退火的效率与应用范围，可用于求解其他可建模为二次无约束二元优化（QUBO）或伊辛（Ising）实例的离散优化问题，其可观的求解时间优势对时间敏感的优化应用尤为重要。
英文摘要
The weighted Max-Cut problem is an NP-hard problem with application implications. It is investigated on a cubic lattice with 113 nodes and mixed-signed random edge weights. For a fixed upper bound on edge weights, it has been demonstrated that the computational difficulty increases as the lower bound on edge weights becomes more negative. The solution time for the problem using a novel error-mitigated quantum annealing approach is compared with standard D-Wave quantum annealing (QA) and BQM hybrid solvers, as well as various classical solvers. For the QPU-embeddable weighted Max-Cut instances with mixed-signed edge weights, it has been quantitatively demonstrated that the SEMO (spin-error mitigation for optimisation) error-mitigated quantum annealing achieved substantially shorter time-to solution than standard D-Wave QA, D-Wave BQM, simulated annealing and Tabu search baselines. The error-mitigated quantum annealing approach presented in this article potentially elevates the efficiency and application scope of quantum annealing and would be applicable in solving other discrete optimisation problems that can be formulated as QUBO or Ising instances. The promising solution time advantage would be particularly impactful for time-critical optimisation applications.
