Resource Estimates for Lindbladian-Based Gibbs State Preparation on Fault-Tolerant Quantum Computers

The simulation of physical systems is a promising use case for fault-tolerant quantum computers, but the accuracy of the simulation depends heavily on the accuracy of the initially prepared state. For finite-temperature systems, 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. Many problems of interest lie at intermediate temperatures, such as the warm dense matter regime, and detailed cost analysis is necessary to assess feasibility of preparing Gibbs states on quantum computers. We investigate the cost of Gibbs state preparation through a recent Lindbladian-based algorithm by Chen et al. [arxiv:2303.18224] on example systems. Starting from a simple, free fermion system as a prototype and working towards more realistic models like hydrogen plasmas, we combine Lindbladian block encoding costs with mixing time information from classical simulations to get logical resource estimates for Gibbs state preparation. We compare this approach to imaginary time evolution using quantum signal processing to identify the most efficient algorithm in different thermodynamic regimes.

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