Thermal State Preparation for Quantum Simulation of Degenerate Plasmas

Predicting properties of materials at extreme conditions is a promising application for fault-tolerant quantum computers, but accurate quantum simulation relies on accurate state preparation. As system temperature varies, the difficulty of preparing an initial Gibbs state varies between classically efficient at high temperatures and QMA-hard in the zero-temperature limit of finding the ground state. The warm dense matter regime lies at intermediate temperatures, where thermal state preparation with controllable accuracy can provide more accurate results than mean-field methods while potentially being feasible on fault-tolerant quantum computers. We consider the feasibility of preparing Gibbs states by providing a detailed cost analysis for two quantum algorithms applied to plasma systems, starting from a simple hydrogen plasma model. We compare imaginary time evolution by quantum signal processing and a Lindbladian algorithm by Chen et al. [arxiv:2303.18224], and we find that the Lindbladian algorithm generally offers better scaling but involves large overheads that can make quantum signal processing preferable for small systems or high temperatures.