Fast mixing of weakly interacting fermionic systems at any temperature

TL;DR

This paper demonstrates that weakly interacting fermionic systems can be efficiently prepared in Gibbs states at any temperature using a Lindbladian with a system-size-independent spectral gap, enabling linear-time mixing.

Contribution

It proves a constant lower bound on the spectral gap for a Lindbladian in weakly interacting fermionic systems, ensuring efficient Gibbs state preparation.

Findings

Spectral gap is independent of system size for weak interactions.

Mixing time scales linearly with system size.

Gibbs states can be prepared efficiently on quantum computers.

Abstract

We study the mixing time of a recently proposed efficiently implementable Lindbladian designed to prepare the Gibbs states in the setting of weakly interacting fermionic systems. We show that at any temperature, the Lindbladian spectral gap for even parity observables is lower bounded by a constant that is independent of the system size, when the interaction strength (e.g., the on-site interaction strength for the Fermi-Hubbard model) is below a constant threshold, which is also independent of the system size. This leads to a mixing time estimate that is at most linear in the system size, thus showing that the corresponding Gibbs states can be prepared efficiently on quantum computers.