Authors: Laura Lewis, Hsin-Yuan Huang, Viet T. Tran, Sebastian Lehner, Richard Kueng, John Preskill
Published: 2024-01-30
DOI: 10.1038/s41467-024-45014-7
Source: Full article
AbstractFinding 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 ann-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(nc)data for a large constantc. Furthermore, the training and prediction time of the proposed ML model scale as$${{{{{{{\mathcal{O}}}}}}}}(n\log n)$$O(nlogn)in the number of qubitsn. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.