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arXiv · 2604.14801

Coherence dynamics in quantum algorithm for linear systems of equations

Linlin Ye·Zhaoqi Wu·Shao-Ming Fei
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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 $A\overrightarrow{x}=\overrightarrow{b}$. 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.

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Linlin Ye, Zhaoqi Wu, Shao-Ming Fei. 2026-04-16. Coherence dynamics in quantum algorithm for linear systems of equations. https://doi.org/10.1088/1402-4896%2Fad0584

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