  A promising avenue for the preparation of Gibbs states on a quantum computer
is to simulate the physical thermalization process. The Davies generator
describes the dynamics of an open quantum system that is in contact with a heat
bath. Crucially, it does not require simulation of the heat bath itself, only
the system we hope to thermalize. Using the state-of-the-art techniques for
quantum simulation of the Lindblad equation, we devise a technique for the
preparation of Gibbs states via thermalization as specified by the Davies
generator.
  In doing so, we encounter a severe technical challenge: implementation of the
Davies generator demands the ability to estimate the energy of the system
unambiguously. That is, each energy of the system must be deterministically
mapped to a unique estimate. Previous work showed that this is only possible if
the system satisfies an unphysical 'rounding promise' assumption. We solve this
problem by engineering a random ensemble of rounding promises that
simultaneously solves three problems: First, each rounding promise admits
preparation of a 'promised' thermal state via a Davies generator. Second, these
Davies generators have a similar mixing time as the ideal Davies generator.
Third, the average of these promised thermal states approximates the ideal
thermal state.
