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Quantum Gibbs sampling algorithms are promising candidates for simulating properties of quantum systems that are beyond the capabilities of classical computation. In recent years, several elegant quantum Gibbs sampling algorithms have been introduced. This review will cover the mathematical foundations required to understand and analyze these modern Gibbs samplingalgorithms. The review begins with a brief review of classical Gibbs sampling, including the critical concept of detailed balance. It then explores the non-commutative generalizations of detailed balance and how they relate to models of thermalization using Linbladians, including the Davies generator.Finally, the review demonstrates how one of these generalizations - Kubo-Martin-Schwinger detailed balance - can be used to derive and analyze nearly optimal Gibbs sampling algorithms. The approach will be pedagogical and will unify the existing algorithms into a single framework. Teams: Join the meeting now Meeting ID: 299 122 077 218 5 Passcode: HE2SJ6Cu Host: Luis Pedro Garcia-Pintos (T-4) |