2021/06/15 by Souichi Takahira, Takahira, Souichi, Asuka Ohashi +5 · 5 citations
Computer Science · #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2106.08076
openalex publication_date 2021/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to implement the linear combination of the inverses on quantum computers and propose a quantum algorithm for matrix functions based on the framework. Compared with the previous study [S. Takahira, A. Ohashi, T. Sogabe, and T.S. Usuda, Quant. Inf. Comput., 20, 1&2, 14--36, (Feb. 2020)] that proposed a quantum algorithm to compute a quantum state for the matrix function based on the circular contour centered at the origin, the quantum algorithm in the present paper can be applied to a more general contour. Moreover, the algorithm is described by the block-encoding framework. Similarly to the previous study, the algorithm can be applied even if the input matrix is not a Hermitian or normal matrix.