Variational algorithms for linear algebra

作     者：Xiaosi Xu Jinzhao Sun Suguru Endo Ying Li Simon C.Benjamin Xiao Yuan 徐晓思;孙金钊;Endo Suguru;李颖;Simon C.Benjamin;袁骁

作者机构：Center on Frontiers of Computing StudiesDepartment of Computer Science.Peking UniversityBeijing 100871China Department of MaterialsUniversity of OxfordOxford 0X13PHUK Clarendon LaboratoryUniversity of OxfordOxford 0X13PUUK Graduate School of China Academy of Engineering PhysicsBeijing 100193China 

出 版 物：《Science Bulletin》 (科学通报（英文版）)

年 卷 期：2021年第66卷第21期

页      面：2181-2188,M0003页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：the Engineering and Physical Sciences Research Council National Quantum Technology Hub in Networked Quantum Information Technology(EP/M013243/1) Japan Student Services Organization(JASSO)Student Exchange Support Program(Graduate Scholarship for Degree Seeking Students) the National Natural Science Foundation of China(U1730449) the European Quantum Technology Flagship project AQTION 

主　　题：Quantum computing Quantum simulation Linear algebra Matrix multiplication Variational quantum eigensolver 

摘      要：Quantum algorithms have been developed for efficiently solving linear algebra ***,they generally require deep circuits and hence universal fault-tolerant quantum *** this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum *** show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed *** on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution *** algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation *** algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system *** evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of *** implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.