Improved machine learning algorithm for predicting ground state properties

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.