Provably Efficient Quantum Thermal State Preparation via Local Driving (2505.22816v1)

Abstract: Preparing the thermal density matrix $\rho_{\beta}\propto e^{-\beta H}$ 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 $\rho_{\beta}$ as a steady state [C.-F. Chen {\it et al}, arXiv:2311.09207] -- their implementation requires large-scale quantum computational resources and is hence challenging {in practice} on current or even near-term quantum devices. Here, we propose a scheme for approximately preparing quantum thermal states 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 performance guarantees independent of detailed physical knowledge of $H$ beyond its locality.