Lecturer: Aram Harrow
Scribes: Sinho Chewi, William Moses, Tasha Schoenstein, Ary Swaminathan
November 9, 2018
Sampling from thermal states was one of the first and (initially) most important uses of computers. In this blog post, we will discuss both classical and quantum Gibbs distributions, also known as thermal equilibrium states. We will then discuss Markov chains that have Gibbs distributions as stationary distributions. This leads into a discussion of the equivalence of mixing in time (i.e. the Markov chain quickly equilibrates over time) and mixing in space (i.e. sites that are far apart have small correlation). For the classical case, this equivalence is known. After discussing what is known classically, we will discuss difficulties that arise in the quantum case, including (approximate) Quantum Markov states and the equivalence of mixing in the quantum case.