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Quantum algorithms for matrix operations and linear systems of equations

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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.

matrix operationsystems of linear equations'sender-receiver'quantum computation modelquantum algorithm

Wentao Qi、Alexandr I Zenchuk、Asutosh Kumar、Junde Wu

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School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China

Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS,Chemogolovka,Russia

P.G.Department of Physics,Gaya College,Magadh University,Rampur,Gaya 823001,India

Harish-Chandra Research Institute,HBNI,Chhatnag Road,Jhunsi,Prayagraj 211019,India

Vaidic and Modem Physics Research Centre,Bhagal Bhim,Bhinmal,Jalore 343029,India

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国家自然科学基金国家自然科学基金国家自然科学基金Fundamental Research Foundation for the Central UniversitiesZhejiang University Global Partnership Fundstate task of Russian Fundamental Investigations

120310041227147461877054K20210337188170+194452119/003FFSG-2024-0002

2024

10.1088/1572-9494/ad2366

理论物理通讯(英文版)
中国科学院理论物理研究所 中国物理学会

理论物理通讯(英文版)

CSTPCD
影响因子：0.333
ISSN：0253-6102
年,卷(期)：2024.76(3)
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