Thermal State Preparation via Rounding Promises

TL;DR

This paper introduces a quantum thermalization method using Davies generators for Gibbs state preparation, overcoming previous limitations by employing a randomized rounding promise approach that ensures accurate thermal states.

Contribution

It develops a novel randomized rounding promise technique enabling efficient Gibbs state preparation via Davies generators without unphysical assumptions.

Findings

Successfully engineered a random ensemble of rounding promises.

Achieved thermal state approximation with similar mixing times to ideal Davies generators.

Demonstrated that the average of promised thermal states approximates the ideal state.

Abstract

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.