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\n\nThe authors thank Chi-Fang Chen, Sitan Chen, Johannes Jakob Meyer, and Spiros Michalakis for valuable input and inspiring discussions. We thank Emilio Onorati, Cambyse Rouzé, Daniel Stilck França, and James D. Watson for sharing a draft of their new results on efficiently predicting properties of states in thermal phases of matter with exponential decay of correlation and in quantum phases of matter with local topological quantum order82. LL is supported by Caltech Summer Undergraduate Research Fellowship (SURF), Barry M. Goldwater Scholarship, and Mellon Mays Undergraduate Fellowship. HH is supported by a Google PhD fellowship and a MediaTek Research Young Scholarship. JP acknowledges support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.
\nH.H. and J.P. conceived the project. L.L. and H.H. developed the mathematical aspects of this work. L.L., H.H., S.L., and V.T. conducted the numerical experiments and wrote the open-source code. L.L., H.H., R.K., and J.P. wrote the paper.
\n\nSource data are available for this paper. All data can be found or generated using the source code at https://github.com/lllewis234/improved-ml-algorithm83.
\n\nSource code for an efficient implementation of the proposed procedure is available at https://github.com/lllewis234/improved-ml-algorithm83.
\n\nThe authors declare no competing interests.
\nCorrection to: Nature Communications https://doi.org/10.1038/s41467-024-45014-7, published online 30 January 2024
\nThe original version of this Article incorrectly acknowledged Laura Lewis as a corresponding author instead of Hsin-Yuan Huang. This has now been corrected in both the PDF and HTML versions of the Article.
\nFinding 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 \ud835\udcaa(log\u2061(n)) data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require \ud835\udcaa(n\u1d9c) data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as \ud835\udcaa(n log n) 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.
", "date": "2024-02-26", "date_type": "published", "publication": "Nature Communications", "volume": "15", "publisher": "Nature Publishing Group", "pagerange": "1740", "issn": "2041-1723", "official_url": "https://authors.library.caltech.edu/records/ynhzn-84626", "funders": { "items": [ { "grant_number": "Summer Undergraduate Research Fellowship" }, { "grant_number": "Barry M. Goldwater Scholarship" }, { "grant_number": "Mellon Mays Undergraduate Fellowship" }, {}, {}, { "grant_number": "DE-NA0003525" }, { "grant_number": "DE-SC0020290" }, { "grant_number": "PHY-1733907" } ] }, "local_group": { "items": [ { "id": "AWS-Center-for-Quantum-Computing" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "IQIM" } ] }, "doi": "10.1038/s41467-024-46164-4", "primary_object": { "basename": "s41467-024-46164-4.pdf", "url": "https://authors.library.caltech.edu/records/ynhzn-84626/files/s41467-024-46164-4.pdf" }, "pub_year": "2024", "author_list": "Lewis, Laura; Huang, Hsin-Yuan; et al." } ]