Quantum thermal state preparation for near-term quantum processors

Preparation of quantum thermal states of many-body systems is a key computational challenge for quantum processors, with applications in physics, chemistry, and classical optimization. We provide a simple and efficient algorithm for thermal state preparation, combining engineered bath resetting and modulated system-bath coupling to derive a quantum channel approximately satisfying quantum detailed balance relations. We show that the fixed point $\hat\sigma$ of the channel approximates the Gibbs state as $\|\hat\sigma -\hat\sigma_\beta\|\sim \theta^2$, where $\theta$ is the system-bath coupling and $\hat\sigma_\beta \propto e^{-\beta \hat H_S}$. We provide extensive numerics, for the example of the 2D Quantum Ising model, confirming that the protocol successfully prepares the thermal state throughout the finite-temperature phase diagram, including near the quantum phase transition. Simulations for free-fermion systems provide further evidence for the accuracy of the protocol for large system sizes in the weak-coupling limit. Our algorithm provides a path to efficient quantum simulation of quantum-correlated states at finite temperature with current and near-term quantum processors.