No-go theorem and optimization of dynamical decoupling against noise with soft cutoff

TL;DR

This paper investigates the limits of dynamical decoupling in suppressing decoherence caused by soft-cutoff Gaussian noise, establishing a no-go theorem and optimizing pulse sequences for certain noise conditions.

Contribution

It provides a no-go theorem showing the impossibility of perfect decoherence suppression with dynamical decoupling under soft cutoff noise and derives optimal pulse sequences for specific noise correlation structures.

Findings

No dynamical decoupling scheme can eliminate decoherence to arbitrary order with soft cutoff noise.

The Carr-Purcell-Meiboom-Gill sequence is optimal for linear order noise correlations in the short-time limit.

The paper formulates equations for optimizing pulse sequences to minimize decoherence up to the highest possible order.

Abstract

We study the performance of dynamical decoupling in suppressing decoherence caused by soft-cutoff Gaussian noise, using short-time expansion of the noise correlations and numerical optimization. For the noise with soft cutoff at high frequencies, there exists no dynamical decoupling scheme to eliminate the decoherence to arbitrary orders of the short time, regardless of the timing or pulse shaping of the control under the population conserving condition. We formulate the equations for optimizing pulse sequences that minimizes decoherence up to the highest possible order of the short time for the noise correlations with odd power terms in the short-time expansion. In particular, we show that the Carr-Purcell-Meiboom-Gill sequence is optimal in short-time limit for the noise correlations with a linear order term in the time expansion.