Symmetry-Enhanced Performance of Dynamical Decoupling

TL;DR

This paper demonstrates that the effectiveness of quadratic dynamical decoupling (QDD) in preserving qubit coherence can be significantly improved by the initial symmetry and state of the bath, especially under SU(2) invariant conditions.

Contribution

It reveals how bath symmetry and initial conditions can enhance QDD performance, providing both numerical and analytical evidence.

Findings

Bath symmetry can double QDD efficiency

Performance scales with sequence duration as predicted

Initial bath state influences decoherence suppression

Abstract

We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of the bath on the performance of the sequence. The overall performance is quantified by a distance norm $d$. It is expected that $d$ scales with $T$, the total duration of the sequence, as $T^{\min \{N_x,N_z\}+1}$, where $N_x$ and $N_z$ are the number of pulses of the outer and of the inner sequence, respectively. We show both numerically and analytically that the state of the bath can boost the performance of QDD under certain conditions: The scaling of QDD for a given number of pulses can be enhanced by a factor of 2 if the bath is prepared in a highly symmetric state and if the system Hamiltonian is SU(2) invariant.