A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation

We study a qDRIFT-type randomized method to simulate the Lindblad equations. For Lindblad dynamics generated by an ensemble of Lindbladians ₐ ∈ A, our approach implements a single randomly sampled Lindbladian Lₐ at each time step. The only assumption is that each Lₐ involves only a single jump operator with an efficient implementation available for the evolution et Lₐ. A notable application of the randomized method is for quantum Gibbs sampling, where the Lindblad dynamics is utilized to prepare a specific Gibbs state. Unlike existing deterministic methods that require numerous jump operators to ensure ergodicity, our approach simplifies the implementation by using a single randomly sampled jump operator. As an example, we demonstrate that our method ensures fast thermalization of Hamiltonian systems characterized by random Pauli strings, where the spectral density closely adheres to the semi-circle law.