The problem, which the article somehow manages to avoid mentioning: > In this work, we study the problem of finding local minima in quantum systems under therm

The problem, which the article somehow manages to avoid mentioning: > In this work, we study the problem of finding local minima in quantum systems under thermal perturbations. While local minima are much easier to find than ground states, we show that finding a local minimum is computationally hard for classical computers, even when the task is to output a single-qubit observable at any local minimum. In contrast, we prove that a quantum computer can always find a local minimum efficiently using a thermal gradient descent algorithm that mimics the cooling process in Nature. (I have no idea what most of that means)