Improved machine learning algorithm for predicting ground state properties - Lewis, Laura; Huang, Hsin-Yuan; Tran, Viet T.; Lehner, Sebastian; Kueng, Richard; Preskill, John (Nature communications, 2024)
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 ( n c ) data for a large constant c . Furthermore, the training and prediction time of the proposed ML model scale as 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. Recent work proposed a machine learning algorithm for predicting ground state properties of quantum many-body systems that outperforms any non-learning classical algorithm but requires extensive training data. Lewis et al. present an improved algorithm with exponentially reduced training data requirements.