Coherence dynamics in quantum algorithm for linear systems of equations

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 Aoverrightarrow{x}=overrightarrow{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 |brangle in the eigenbasis of A. We prove that the operator coherence of the inverse phase estimation widetilde{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 αin(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.