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Improved machine learning algorithm for predicting ground state properties

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Peer-reviewed

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Authors

Lewis, Laura 
Tran, Viet T. 
Lehner, Sebastian 
Kueng, Richard 

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

Description

Acknowledgements: 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.

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Journal Title

Nature Communications

Conference Name

Journal ISSN

2041-1723

Volume Title

15

Publisher

Nature Publishing Group UK