Soft-Pulse Dynamical Decoupling with Markovian Decoherence

TL;DR

This paper analyzes how broadband Markovian decoherence affects dynamical decoupling sequences and demonstrates that pulse shaping can significantly improve the decoupling performance of soft pulses.

Contribution

It develops cumulant expansions for effective decoherence operators under soft pulse sequences, highlighting the impact of pulse shaping on decoupling efficiency.

Findings

Soft pulses generally perform worse than ideal delta pulses in Markovian environments.

Pulse shaping can substantially enhance the decoupling effectiveness of soft pulses.

Theoretical framework for analyzing decoherence with shaped pulses in dynamical decoupling.

Abstract

We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape, and for several sequences of $\pi$- and $\pi/2$-pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\delta$-pulses, it can be substantially improved by shaping.