Converting a real quantum bath to an effective classical noise

TL;DR

This paper introduces a cluster expansion method to approximate quantum spin-bath dynamics with a classical Gaussian noise model, enabling efficient analysis of decoherence and control strategies.

Contribution

The authors develop a novel cluster expansion approach that maps quantum bath dynamics to an effective classical noise process, simplifying decoherence modeling.

Findings

The classical approximation agrees with quantum results in many cases.

The method allows efficient optimization of pulse sequences for decoherence mitigation.

It reduces computational complexity in analyzing quantum control strategies.

Abstract

We present a cluster expansion method for approximating quantum spin-bath dynamics in terms of a classical Gaussian stochastic process. The cluster expansion produces the two-point correlation function of the approximate classical bath, permitting rapid evaluation of noise-mitigating quantum control strategies without resorting to computationally intensive dynamical decoupling models. Our approximation is valid for the wide class of models possessing negligible back-action and nearly-Gaussian noise. We study several instances of the central spin decoherence problem in which the central spin and randomly-located bath spins are alike and dipolarly coupled. For various pulse sequences, we compare the coherence echo decay computed explicitly quantum mechanically versus those computed using our approximate classical model, and obtain agreement in most, but not all, cases. We demonstrate the utility of these classical noise models by efficiently searching for the 4-pulse sequences that maximally mitigate decoherence in each of these cases, a computationally expensive task in the explicit quantum model.