Topic: finite temperature

Quantum Gibbs samplers generalize classical thermalization dynamics such as Glauber and Metropolis processes. This talk shows that one-dimensional, short-range quantum Hamiltonians admit samplers with an optimal spectral gap independent of system size at every finite temperature.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamic