Effects of stochastic noise on dynamical decoupling procedures

TL;DR

This paper models the effects of stochastic noise on dynamical decoupling in quantum systems, aiming to explain discrepancies between theoretical and experimental fidelity improvements.

Contribution

It introduces a stochastic Ito differential equation model for imperfect dynamical decoupling, providing analytical and numerical insights into its impact on quantum system evolution.

Findings

The model explains the fidelity gap observed in experiments.

Analytical results for continuous control scenarios.

Numerical simulations and bounds for finite control cases.

Abstract

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.