Quantum Learning: Complexity and Predictive Models

This lecture discusses the complexity and learnability in complex quantum systems, focusing on the emerging quantum technologies and their implications for computer science. The instructor presents quantum theory as a generalization of probability theory, introducing concepts such as qubits and their representation. The lecture highlights the challenges posed by noise in quantum circuits and explores the guiding questions regarding quantum advantages in learning and predicting other quantum systems. A holistic approach is emphasized, utilizing rigorous mathematics, numerics, and experimental designs. The discussion includes a map for quantum learning, outlining three frontiers: predicting observables, recovering Hamiltonians, and addressing randomness in quantum supremacy experiments. The instructor also covers learning Ising models and the application of quantum Monte Carlo methods to bridge classical and quantum learning. The lecture concludes with long-term goals aimed at developing practical tools for predicting properties of quantum states and addressing the challenges of learning from noisy quantum supremacy experiments.