Optimal Lower Bounds for Quantum Learning via Information Theory

Explore quantum learning theory through this 21-minute conference talk presented at the 18th Theory of Quantum Computation Conference (TQC 2023). Delve into optimal lower bounds for quantum sample complexity in PAC and agnostic learning models using an information-theoretic approach. Learn how quantum learners compare to classical ones in efficiency, and discover new insights into the Quantum Coupon Collector problem. Examine the mathematical foundations behind quantum state identification, including properties of Gram matrix spectra and the distinguishability of pure state ensembles. Follow along as the speaker presents novel findings about quantum sample complexity bounds, demonstrates why certain information-theoretic approaches may not yield optimal results in specific scenarios, and explores the implications for quantum learning theory. Understand how these theoretical advances contribute to the broader field of quantum information science, with potential applications in quantum computing and machine learning.