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Coherence dynamics in quantum algorithm for linear systems of equations

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arXiv:2604.14801v1 Announce Type: new 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 $

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Quantum Physics [Submitted on 16 Apr 2026] Coherence dynamics in quantum algorithm for linear systems of equations Linlin Ye, Zhaoqi Wu, Shao-Ming Fei 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. Comments: 24 pages, 2 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.14801 [quant-ph] (or arXiv:2604.14801v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.14801 Focus to learn more Journal reference: Phys. Scr. 98 (2023) 125104 Related DOI: https://doi.org/10.1088/1402-4896/ad0584 Focus to learn more Submission history From: Zhaoqi Wu [view email] [v1] Thu, 16 Apr 2026 09:25:22 UTC (106 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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