Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

TL;DR

This paper introduces a method for simulating classical stochastic noise in quantum systems by coarse-graining over high-frequency components, simplifying the modeling of complex noise with temporal correlations like 1/f noise.

Contribution

The authors develop a novel approach that integrates out high-frequency noise components using Ornstein-Uhlenbeck processes, enabling efficient simulation of correlated classical noise in quantum systems.

Findings

Efficient noise simulation via coarse-graining reduces computational complexity.

Analytical expressions for noise propagators facilitate precomputation.

Numerical examples demonstrate practical advantages of the method.

Abstract

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. 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. We focus on the case where the stochastic noise can be expressed as a sum of Ornstein-Uhlenbeck processes. Temporal coarse-graining is then achieved by conditioning the stochastic process on a coarse realization of the noise, expressing the conditioned stochastic process in terms of a sum of smooth, deterministic functions and bridge processes with boundaries fixed at zero, and performing the ensemble average over the bridge processes. For Ornstein-Uhlenbeck processes, the deterministic components capture all dependence on the coarse realization, and the stochastic bridge processes are not only independent but taken from the same distribution with correlators that can be expressed analytically, allowing the associated noise propagators to be precomputed once for all simulations. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages, such as a simple concatenation rule, that we highlight with numerical examples.