Quantum Algorithms based on the Block-Encoding Framework for Matrix Functions by Contour Integrals

• URL: http://arxiv.org/abs/2106.08076v2
• Date: Wed, 16 Jun 2021 02:06:41 GMT
• Title: Quantum Algorithms based on the Block-Encoding Framework for Matrix Functions by Contour Integrals
• Authors: Souichi Takahira, Asuka Ohashi, Tomohiro Sogabe and Tsuyoshi Sasaki Usuda
• Abstract summary: We show a framework to implement the linear combination of the inverses on quantum computers. We propose a quantum algorithm for matrix functions based on the framework.
• Score: 1.5293427903448018
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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