An Analytic Theory of Quantum Imaginary Time Evolution

Quantum Physics arXiv:2510.22481 (quant-ph) [Submitted on 26 Oct 2025] Title:An Analytic Theory of Quantum Imaginary Time Evolution Authors:Min Chen, Bingzhi Zhang, Quntao Zhuang, Junyu Liu View a PDF of the paper titled An Analytic Theory of Quantum Imaginary Time Evolution, by Min Chen and 3 other authors View PDF HTML (experimental) Abstract:Quantum imaginary time evolution (QITE) algorithm is one of the most promising variational quantum algorithms (VQAs), bridging the current era of Noisy Intermediate-Scale Quantum devices and the future of fully fault-tolerant quantum computing. Although practical demonstrations of QITE and its potential advantages over the general VQA trained with vanilla gradient descent (GD) in certain tasks have been reported, a first-principle, theoretical understanding of QITE remains limited. Here, we aim to develop an analytic theory for the dynamics of QITE. First, we show that QITE can be interpreted as a form of a general VQA trained with Quantum Natural Gradient Descent (QNGD), where the inverse quantum Fisher information matrix serves as the learning-rate tensor. This equivalence is established not only at the level of gradient update rules, but also through the action principle: the variational principle can be directly connected to the geometric geodesic distance in the quantum Fisher information metric, up to an integration constant. Second, for wide quantum neural networks, we employ the quantum neural tangent kernel framework to construct an analytic model for QITE. We prove that QITE always converges faster than GD-based VQA, though this advantage is suppressed by the exponential growth of Hilbert space dimension. This helps explain certain experimental results in quantum computational chemistry. Our theory encompasses linear, quadratic, and more general loss functions. We validate the analytic results through numerical simulations. Our findings establish a theoretical foundation for QITE dynamics and provide analytic insights for the first-principle design of variational quantum algorithms. Comments: Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2510.22481 [quant-ph] (or arXiv:2510.22481v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.22481 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Min Chen [view email] [v1] Sun, 26 Oct 2025 01:43:55 UTC (1,077 KB) Full-text links: Access Paper: View a PDF of the paper titled An Analytic Theory of Quantum Imaginary Time Evolution, by Min Chen and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: cs cs.AI cs.LG stat stat.ML References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)