Improved machine learning algorithm for predicting ground state properties

Creators: Lewis, Laura; Huang, Hsin-Yuan; Tran, Viet T.; Lehner, Sebastian; Kueng, Richard; Preskill, John¹

1. California Institute of Technology

Abstract

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 data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require 𝒪 data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as 𝒪 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.

Copyright and License

© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Acknowledgement

The 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.

Contributions

H.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.

Data Availability

Source 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.

Code Availability

Source code for an efficient implementation of the proposed procedure is available at https://github.com/lllewis234/improved-ml-algorithm⁸³.

Conflict of Interest

The authors declare no competing interests.

Errata

Name	Size	Download all
41467_2024_45014_MOESM1_ESM.pdf md5:754fe6d3100341f0de9f15261a51a918	3.5 MB	Preview Download
s41467-024-45014-7.pdf md5:3d75933ef266f67ef26a0284056ea641	1.0 MB	Preview Download

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes