A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation

Understand

We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, $\mathcal{L} = \sum_{a \in \mathcal{A}} \mathcal{L}_a$, where each $\mathcal{L}_a$ comprises a simple Hamiltonian and a single jump operator.

• Assuming an efficient quantum simulation is available for the Lindblad evolution $e^{t\mathcal{L}_a}$, we implement $e^{t\mathcal{L}_a}$ for a randomly sampled $\mathcal{L}_a$ at each time step according to a probability distribution $\mu$ over the ensemble $\{\mathcal{L}_a\}_{a \in \mathcal{A}}$.
• This randomized strategy reduces the quantum cost of simulating Lindblad dynamics, particularly in quantum many-body systems with a large or even infinite number of jump operators.
• Our contributions are two-fold.