Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation

TL;DR

This paper proves that Uhrig dynamical decoupling is universally effective in suppressing both pure dephasing and relaxation of a qubit in short-time evolution, with potential generalizations for finite-duration pulses.

Contribution

The paper demonstrates the universality of Uhrig dynamical decoupling for suppressing qubit decoherence and relaxation, extending its applicability to generic baths and finite-duration pulses.

Findings

Uhrig dynamical decoupling suppresses dephasing and relaxation to order T^{N+1}.

The optimal N-pulse sequence is universal for a broad class of baths.

Finite-duration pulses can be incorporated into the Uhrig sequence with symmetry conditions.

Abstract

The optimal $N$-pulse dynamical decoupling discovered by Uhrig for a spin-boson mmodel [Phys. Rev. Lett, {\bf 98}, 100504 (2007)] is proved to be universal in suppressing to $O(T^{N+1})$ the pure dephasing or the longitudinal relaxation of a qubit (or spin-1/2) coupled to a generic bath in a short-time evolution of duration $T$. It is also found that for the purpose of suppressing the longitudinal relaxation, an ideal Uhrig $\pi$-pulse sequence can be generalized to a sequence consisting of the ideal one superimposed with finite-duration pulses satisfying certain symmetry requirements.