Quantum algorithms for matrix operations and linear systems of equations  

作　　者：Wentao Qi Alexandr I Zenchuk Asutosh Kumar Junde Wu 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China [2]Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS,Chernogolovka,Russia [3]P.G.Department of Physics,Gaya College,Magadh University,Rampur,Gaya 823001,India [4]Harish-Chandra Research Institute,HBNI,Chhatnag Road,Jhunsi,Prayagraj 211019,India [5]Vaidic and Modern Physics Research Centre,Bhagal Bhim,Bhinmal,Jalore 343029,India

出　　处：《Communications in Theoretical Physics》2024年第3期100-112,共13页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12031004 and Grant No.12271474,61877054);the Fundamental Research Foundation for the Central Universities(Project No.K20210337);the Zhejiang University Global Partnership Fund,188170+194452119/003;partially funded by a state task of Russian Fundamental Investigations(State Registration No.FFSG-2024-0002)。

摘　　要：Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver’s density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations.

关 键 词：matrix operation systems of linear equations ‘sender-receiver’quantum computation model quantum algorithm 

分 类 号：O413[理学—理论物理]