Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for 1/f noise in solid-state quantum information processors. High-frequency components of the noise necessitate a small time step to avoid aliasing, whereas low-frequency components that are crucial to capture drift in such systems require long simulation times to observe. This broad range of relevant timescales results in high simulation cost. Here we present an approach for simulating Hamiltonian classical stochastic noise that performs temporal coarse-graining by effectively integrating out the high-frequency components of the noise. This is achieved by generating a realization of the stochastic process on a coarse time grid, expressing the conditioned stochastic process in terms of a bridge process, and performing the ensemble average over the bridge process. We focus on the case where the noise can be expressed as a sum of Ornstein-Uhlenbeck processes, where correlators of the bridge processes can be expressed analytically. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages that we highlight with numerical examples.