Universality of Uhrig Dynamical Decoupling for Suppressing Qubit Pure Dephasing and Relaxation

The optimal N-pulse dynamical decoupling discovered by Uhrig for a spin-boson model [Phys. Rev. Lett. 98, 100504 (2007)] is proved to be universal in suppressing to O(TN+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. For suppressing the longitudinal relaxation, a Uhrig pi-pulse sequence can be generalized to be a superposition of the ideal Uhrig pi-pulse sequence as the core and an arbitrarily shaped pulse sequence satisfying certain symmetry requirements. The generalized Uhrig dynamical decoupling offers the possibility of manipulating the qubit while simultaneously combating the longitudinal relaxation.