Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently learn to predict important properties of a quantum many-body system. In particular, ML can provably predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. Our proof technique combines signal processing with quantum many-body physics and also builds upon the recently developed framework of classical shadows. I will try to convey the ideas and also present numerical experiments that confirm our theoretical findings.
This talk is based on joint work with Hsin-Yuan (Robert) Huang, Giacomo Torlai, Victor Albert and John Preskill, see [Huang et al., Provably efficient machine learning for quantum many-body problems, Science 2022] and subsequent follow up works.