Improved machine learning algorithm for predicting ground state properties

Laura Lewis, Hsin-Yuan Huang (), Viet T. Tran, Sebastian Lehner, Richard Kueng and John Preskill
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Laura Lewis: California Institute of Technology
Hsin-Yuan Huang: California Institute of Technology
Viet T. Tran: Johannes Kepler University
Sebastian Lehner: Johannes Kepler University
Richard Kueng: Johannes Kepler University
John Preskill: California Institute of Technology

Nature Communications, 2024, vol. 15, issue 1, 1-8

Abstract: 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 $${{{{{{{\mathcal{O}}}}}}}}(\log (n))$$ O ( log ( n ) ) data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $${{{{{{{\mathcal{O}}}}}}}}({n}^{c})$$ O ( n c ) data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as $${{{{{{{\mathcal{O}}}}}}}}(n\log n)$$ O ( 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
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DOI: 10.1038/s41467-024-45014-7

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