Optimized Dynamical Decoupling for Power Law Noise Spectra

TL;DR

This paper develops an optimized dynamical decoupling sequence tailored for baths with power law spectra, improving decoherence suppression in quantum systems by interpolating between known sequences based on bath properties.

Contribution

It introduces a new sequence optimization method for dynamical decoupling that adapts to the bath's spectral properties, bridging CPMG and UDD sequences.

Findings

Optimized sequence closely matches CPMG for soft cutoff baths.

Sequence approaches UDD performance as the bath cutoff becomes harder.

Analytical conditions for optimal sequence are derived and numerically solved.

Abstract

We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal $\pi$ pulses is optimized according to the power of the bath. We expand the decoherence function and separate the cancelling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill (CPMG) sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling (UDD) sequence as the cutoff becomes harder.