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- W3213201524 abstract "The matrix logarithm is one of the important matrix functions. Recently, a quantum algorithm that computes the state $|frangle$ corresponding to matrix-vector product $f(A)b$ is proposed in [Takahira, et al. Quantum algorithm for matrix functions by Cauchy's integral formula, QIC, Vol.20, No.1&2, pp.14-36, 2020]. However, it can not be applied to matrix logarithm. In this paper, we propose a quantum algorithm, which uses LCU method and block-encoding technique as subroutines, to compute the state $|frangle = log(A)|brangle / |log(A)|brangle|$ corresponding to $log(A)b$ via the integral representation of $log(A)$ and the Gauss-Legendre quadrature rule." @default.
- W3213201524 created "2021-11-22" @default.
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- W3213201524 date "2021-11-17" @default.
- W3213201524 modified "2023-09-24" @default.
- W3213201524 title "Quantum Algorithm for Matrix Logarithm by Integral Formula" @default.
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- W3213201524 doi "https://doi.org/10.48550/arxiv.2111.08914" @default.
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