Abstract:
Many scientific advancements in physics and chemistry depend on our ability to learn and make predictions in a quantum-mechanical world. The talk will begin with results for understanding the power of classical machine learning (ML) algorithms in solving quantum many-body problems [1, 2]. We will prove that classical ML algorithms can efficiently predict ground-state properties in a gapped quantum phase after learning from data. In contrast, under widely accepted complexity theory assumptions, we will show that any polynomial-time classical algorithm that does not learn from data cannot achieve the same guarantee. After seeing how powerful classical ML can be, we will examine the predictive power of quantum ML in the second half of the talk [3, 4]. We will prove that, in various tasks, quantum machines could learn from exponentially fewer experiments than those required by their classical counterparts. The exponential advantage holds in predicting many properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. Experiments with up to 40 superconducting qubits and 1300 quantum gates demonstrate that the quantum advantage can be realized using today's relatively noisy quantum processors.