Towards an efficient variational quantum algorithm for solving linear equations  

作　　者：WenShan Xu Ri-Gui Zhou YaoChong Li XiaoXue Zhang 

机构地区：[1]College of Information Engineering,Shanghai Maritime University,Shanghai 201306,China [2]Research Center of Intelligent Information Processing and Quantum Intelligent Computing,Shanghai 201306,China

出　　处：《Communications in Theoretical Physics》2024年第11期54-65,共12页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.62172268 and 62302289;the Shanghai Science and Technology Project under Grant Nos.21JC1402800 and 23YF1416200。

摘　　要：Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.

关 键 词：quantum computing variational quantum algorithm systems of linear equations parameterized quantum circuit 

分 类 号：O241.6[理学—计算数学]