Towards Efficient Quantum Thermal State Preparation via Local Driving: Lindbladian Simulation with Provable Guarantees

Abstract

Preparing the thermal density matrix $\ddot{I}{}_{\hat{I}}^2\propto e^{-{\hat{I}}^{2}H}$ corresponding to a given Hamiltonian $H$ is a task of central interest across quantum many-body physics, and is particularly salient when attempting to study it with quantum computers. Although solved in principle by recent constructions of efficiently simulable Lindblad master equations -- that provably have $\ddot{I}{}_{\hat{I}}^2$ as a steady state [C.-F.~Chen \emph{et al.}, Nature \textbf{646}, pp.~561--566 (2025)] -- the implementation of these ``exact Gibbs samplers'' requires large-scale quantum computational resources and is hence challenging \emph{in practice} on current or even near-term quantum devices. Here, we propose a scheme for approximately simulating an exact Gibbs sampler that only requires the repeated implementation of three readily available ingredients: (a) analog simulation of $H$; (b) strictly local but time-dependent couplings to ancilla qubits; and (c) reset of the ancillas. We give rigorous guarantees on the difference between the fixed point reached by our protocol and the exact thermal state, which only depend on parameters of the protocol and its \emph{mixing time}. The procedure is efficiently implementable on near-term devices if $H$ is local, and the mixing time scales mildly with both system size and protocol parameters. While guaranteeing the latter for Hamiltonians of interest remains an important problem for future work, here we lay the groundwork for developing fully efficient thermal state preparation protocols on quantum simulators.

31 pages, 4 Figures