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arxiv 2106.08076 v2 pith:RLAVN7WM submitted 2021-06-15 quant-ph

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

Souichi Takahira , Asuka Ohashi , Tomohiro Sogabe , Tsuyoshi Sasaki Usuda This is my paper
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keywords matrixquantumalgorithmframeworkcontourfunctionsappliedblock-encoding
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Faster quantum linear system solver beyond the condition number

    quant-ph 2026-07 accept novelty 7.0

    Two quantum linear system solvers are presented with query complexity independent of the condition number, scaling instead with an effective condition number or a solution-norm ratio.

  2. A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations

    quant-ph 2026-04 unverdicted novelty 7.0

    A dual Fourier-PSF and contour-PSF framework resolves the smoothness-sparsity trade-off for efficient quantum simulation of singular and holomorphic matrix functions.