Abstract
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.
基金项目
国家自然科学基金(12031004)
国家自然科学基金(12271474)
国家自然科学基金(61877054)
Fundamental Research Foundation for the Central Universities(K20210337)
Zhejiang University Global Partnership Fund(188170+194452119/003)
state task of Russian Fundamental Investigations(FFSG-2024-0002)
NETL
NSTL
万方数据