Improved machine learning algorithm for predicting ground state properties

Laura Lewis; Hsin-Yuan Huang; Viet T Tran; Sebastian Lehner; Richard Kueng; John Preskill

doi:10.1038/s41467-024-45014-7

Improved machine learning algorithm for predicting ground state properties

Nat Commun. 2024 Jan 30;15(1):895. doi: 10.1038/s41467-024-45014-7.

Authors

Laura Lewis^{1

2}, Hsin-Yuan Huang^{3

4

5}, Viet T Tran⁶, Sebastian Lehner⁶, Richard Kueng⁶, John Preskill^{1

7}

Affiliations

¹ California Institute of Technology, Pasadena, CA, USA.
² University of Cambridge, Cambridge, UK.
³ California Institute of Technology, Pasadena, CA, USA. hsinyuan@caltech.edu.
⁴ Massachusetts Institute of Technology, Cambridge, MA, USA. hsinyuan@caltech.edu.
⁵ Google Quantum AI, Venice, CA, USA. hsinyuan@caltech.edu.
⁶ Johannes Kepler University, Linz, Austria.
⁷ AWS Center for Quantum Computing, Pasadena, CA, USA.

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