Research on qubit mapping completion and dynamic optimization methods with nearest-neighbor coupling constraints

摘要：

为改善多数量子算法受限于量子比特最近邻约束而无法直接在嘈杂中规模量子(NISQ)设备上执行，且动态重映射引人的交换(SWAP)门将降低算法保真度的问题，提出了一种高效的量子比特映射方法。首先，该方法基于图形同构性原理与映射补全策略完成初始映射分配，在满足量子比特连接性需求的同时，减少后续映射变换的SWAP门插入数量；其次，在映射变换过程中改进启发式成本函数，结合模拟退火算法的快速收敛特性与自适应能力，为量子电路动态选择最优前瞻深度与衰减因子，实现最优成本值动态计算.实验结果表明，相较于现有方法，该方法可显著减少SWAP门插入数量，有效提升NISQ设备上量子算法的执行效率与保真度。

To address the issue that most quantum algorithms cannot be diretly executed on Noisy Intermediate-Scale Quantum(NISQ) devices due to limited qubit nearest-neighbor restriction, and that the introduction of SWAP gates through dynamic remapping reduces algorithm fidelity, an efficient qubit mapping method is proposed. First, the method performs the initial mapping allocation based on the principle of graph isomorphism and a mapping completion strategy. This step aims to satisfy the qubit connectivity requirements while reducing the number of SWAP gate insertions required for subsequent mapping transformations. Second, we enhance the heuristic cost function used during mapping transformation. By harnessing the fast convergence and adaptive nature of the simulated annealing algorithm, our method dynamically determnines the optimal look-a-head depth and decay factor for the quantum circuit, enabling the dynamic computation of the optimal cost. Experimental results show the superior performance of the proposed method over existing ones, achieving a substantial reduction in SWAP gate insertions. This reduction directly leads to improved execution efficiency and higher fidelity for quantum algorithms onNISQ devices.

作者: 

刘慧，杨晗笑，李文泽，赵博，聂凯，张冰洁

Liu Hui, Yang Hanxiao, Li Wenze, Zhao Bo, Nie Kai, Zhang Bingjie

机构地区：

河南师范大学计算机与信息工程学院(人工智能学院)；河南省教育人工智能与个性化学习重点实验室；中国人民解放军战略支援部队信息工程大学网络安全学院；郑州大学国家超级计算郑州中心

引用本文：

刘慧，杨晗笑，李文泽等。近邻耦合受限的量子比特映射补全与动态优化方法研究[J].河南师范大学学报(自然科学版),2026,54(2):143-149.(Liu Hui, Yang Hanxiao, Li Wenze,et al.Research on qubit mapping completion and dynamic optimization methods with nearest-neighbor coupling constraints [J].Journal of Henan Normal University(Natural Science Edition) .2026.54(2):143-149.DOI:10.16366/j.cnki.1000-2367.2025.02.27.0001.)

基金：

国家重点研发计划高性能计算专项；河南省科技攻关项目；河南省重大科技专项

关键词：

最近邻约束；比特映射；映射补全；模拟退火

nearest-neighbor restriction; qubit mapping; mapping completion; simulated annealing

分类号：

Q413

近邻耦合受限的量子比特映射补全与动态优化方法研究.pdf