西安电子科技大学学报（自然科学版）2025，Vol.52Issue(5)：72-87,16.DOI:10.19665/j.issn1001-2400.20250504
一类量子求解算法的电路设计及有效仿真
Circuitdesign and effective simulation of a class of quantum solving algorithm
摘要
Abstract
Classical simulation of quantum algorithms plays a crucial role in evaluating the algorithm performance and verifying theoretical correctness.For high-order sparse matrices,the corresponding Hamiltonians often exhibit complex structures and characteristics,leading to excessively high complexity in quantum solving,which severely constrains simulation efficiency and accuracy.To address the challenges in simulating Hamiltonians,modular decomposition techniques and function construction methods are proposed to approximate the evolution of Hamiltonians,thereby establishing a general circuit design scheme for implementing the Harrow-Hassidim-Lloyd(HHL)algorithm on classical computers.We implement multi-scale quantum circuits with 13/14 qubits(basic scale)and 20/21 qubits(extended scale)based on the Qiskit quantum computing framework,and verify the applicability of the designed circuits by testing multiple sets of 8 × 8 Hermitian matrices and column vectors.Finally,we analyze the fidelity and error under different conditions for various linear systems,as well as the time and space resources they occupy.Experimental results demonstrate that as the qubit scale expands,quantum circuits incorporating these two techniques exhibit synchronous optimization characteristics with enhanced fidelity and reduced errors when solving linear systems.Compared with other methods,both techniques demonstrate superior large-scale circuit processing capabilities,providing a scalable technical route for utilizing quantum algorithms to solve high-dimensional linear systems.关键词
线性系统/哈密顿量模拟/电路仿真/模块分解技术/构造函数技术Key words
linear systems/hamiltonians simulation/circuit simulation/module decomposition/function construction分类
信息技术与安全科学引用本文复制引用
高嘉佩,李雪莲,高军涛..一类量子求解算法的电路设计及有效仿真[J].西安电子科技大学学报（自然科学版）,2025,52(5):72-87,16.基金项目
陕西省重点研发计划(2021ZDLGY06-04) （2021ZDLGY06-04）
西安电子科技大学交叉培育项目(21103240011) （21103240011）
