Dynamical decoupling of a qubit with always-on control fields

TL;DR

This paper introduces a novel continuous control dynamical decoupling sequence called CAFE, derived from UDD and Chebyshev polynomials, optimized for qubit protection against dephasing noise.

Contribution

It develops a Fourier series-based method for always-on control sequences, creating the CAFE sequence and analyzing its effectiveness and robustness.

Findings

CAFE sequence achieves comparable decoupling to UDD.

The method provides a flexible framework for designing continuous control sequences.

Filter functions are derived to evaluate sequence robustness.

Abstract

We consider dynamical decoupling schemes in which the qubit is continuously manipulated by a control field at all times. Building on the theory of the Uhrig Dynamical Decoupling sequence (UDD) and its connections to Chebyshev polynomials, we derive a method of always-on control by expressing the UDD control field as a Fourier series. We then truncate this series and numerically optimize the series coefficients for decoupling, constructing the CAFE (Chebyshev and Fourier Expansion) sequence. This approach generates a bounded, continuous control field. We simulate the decoupling effectiveness of our sequence vs. a continuous version of UDD for a qubit coupled to fully-quantum and semi-classical dephasing baths and find comparable performance. We derive filter functions for continuous-control decoupling sequences, and we assess how robust such sequences are to noise on control fields. The methods we employ provide a variety of tools to analyze continuous-control dynamical decoupling sequences.