Coherence dynamics in quantum algorithm for linear systems of equations
Linlin Ye, Zhaoqi Wu, Shao-Ming Fei · Physica Scripta · 2023
Abstract Quantum coherence is a fundamental issue in quantum mechanics and quantum information processing. We explore the coherence dynamics of the evolved states in HHL quantum algorithm for solving the linear system of equation A x → = b → . By using the Tsallis relative α entropy of coherence and the l 1,p norm of coherence, we show that the operator coherence of the phase estimation P relies on the coefficients β i obtained by decomposing ∣b〉 in the eigenbasis of A. We prove that the operator coherence of the inverse phase estimation P ̃ relies on the coefficients β i , eigenvalues of A and the success probability P s , and it decreases with the increase of the probability when α ∈ (1, 2]. Moreover, the variations of coherence deplete with the increase of the success probability and rely on the eigenvalues of A as well as the success probability.