Comment on “Asymptotic quantum algorithm for the Toeplitz systems”

Abstract

In their recent paper [], Wan proposed a quantum algorithm to solve systems of linear equations Ax=b, where A is an n×n Toeplitz matrix generated by the Fourier coefficients of a continuous, 2π-periodic, and positive function f. For large enough n, they claimed that the algorithm is valid for all b. In this Comment we prove that, in general, this is not true. Published by the American Physical Society 2024