Learning in the Quantum Universe

Citation

Huang, Hsin-Yuan (2024) Learning in the Quantum Universe. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/fgpv-3112. https://resolver.caltech.edu/CaltechTHESIS:05032024-044352582

Abstract

In this thesis, I will present our progress in building a rigorous theory to understand how scientists, machines, and future quantum computers could learn models of our quantum universe. The thesis begins with an experimentally feasible procedure for converting a quantum many-body system into a succinct classical description of the system, its classical shadow. Classical shadows can be applied to efficiently predict many properties of interest, including expectation values of local observables and few-body correlation functions. I will then build on the classical shadow formalism to answer two fundamental questions at the intersection of machine learning and quantum physics: Can classical machines learn to solve challenging problems in quantum physics? And can quantum machines learn exponentially faster and predict more accurately than classical machines? The thesis answers both questions positively through mathematical analysis and experimental demonstrations.

Thesis Files