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Improved machine learning algorithm for predicting ground state properties
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DOI：10.1038/s41467-024-45014-7.png)
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Abstract
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Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only O(log(n))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{O}}}}}}}}(\log (n))$$\end{document} data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require O(nc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{O}}}}}}}}({n}<^>{c})$$\end{document} data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as O(nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{O}}}}}}}}(n\log n)$$\end{document} in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset. Recent work proposed a machine learning algorithm for predicting ground state properties of quantum many-body systems that outperforms any non-learning classical algorithm but requires extensive training data. Lewis et al. present an improved algorithm with exponentially reduced training data requirements.
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