Coherence dynamics in quantum algorithm for linear systems of equations

Abstract

Quantum coherence is a fundamental issue in quantum mechanics and quantum information processing. We explore the coherence dynamics of the evolved states in the HHL quantum algorithm for solving the linear system of equation $A\overrightarrow{x}=\overrightarrow{b}$. By using the Tsallis relative $\alpha$ 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 $\beta_{i}$ obtained by decomposing $|b\rangle$ in the eigenbasis of $A$. We prove that the operator coherence of the inverse phase estimation $\widetilde{P}$ relies on the coefficients $\beta_{i}$, eigenvalues of $A$ and the success probability $P_{s}$, and it decreases with the increase of the probability when $\alpha\in(1,2]$. 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.

Suppressing the degeneration of quantum resources through coupling auxiliary qubits

“…Recently, the QC has been used to reveal the nonclassical characteristics of various systems. Involving superinductors [36], two-level molecular system [37], polariton condensates [38], critical unstable two-level systems [39], quantum dot systems [40], cavity magnomechanical systems [41], quantum batteries [42], neutrino [43], linear systems of equations [44], dipolar interacting magnetic system [45], Heisenberg model [46], noninertial frame [47], and spacetime expansion [48]. Besides, reservoir system is significant for quantum information [49], and the transformation between coherence and entanglement of reservoir system was revealed by Hu et al [50].…”