Preparing thermal states of quantum systems by dimension reduction

TL;DR

This paper introduces an efficient quantum algorithm for preparing thermal Gibbs states of one-dimensional quantum systems, significantly reducing time complexity and memory overhead compared to existing methods.

Contribution

The authors develop a memory-efficient quantum algorithm that prepares thermal states with improved time complexity, especially in higher dimensions, advancing quantum simulation capabilities.

Findings

Time complexity dominated by N^{||h||/T}

No memory overhead in the preparation process

Improved scaling for higher-dimensional systems

Abstract

We present an algorithm that prepares thermal Gibbs states of one dimensional quantum systems on a quantum computer without any memory overhead, and in a time significantly shorter than other known alternatives. Specifically, the time complexity is dominated by the quantity $N^{\|h\|/ T}$, where $N$ is the size of the system, $\|h\|$ is a bound on the operator norm of the local terms of the Hamiltonian (coupling energy), and $T$ is the temperature. Given other results on the complexity of thermalization, this overall scaling is likely optimal. For higher dimensions, our algorithm lowers the known scaling of the time complexity with the dimension of the system by one.