Aperiodic dynamical decoupling sequences in the presence of pulse errors

Abstract

Dynamical decoupling (DD) is a promising tool for preserving the quantum states of qubits. However, small imperfections in the control pulses can seriously affect the fidelity of decoupling, and qualitatively change the evolution of the controlled system at long times. Using both analytical and numerical tools, we theoretically investigate the effect of the pulse error accumulation for two aperiodic DD sequences, Uhrig's DD (UDD) protocol (Uhrig 2007 Phys. Rev. Lett. 98 100504), and the quadratic DD (QDD) protocol (West et al 2010 Phys. Rev. Lett. 104 130501). We consider the implementation of these sequences using the electron spins of phosphorus donors in silicon, where DD sequences are applied to suppress dephasing of the donor spins. The dependence of the decoupling fidelity on different initial states of the spins is the focus of our study. We investigate in detail the initial drop in the DD fidelity, and its long-term saturation. We also demonstrate that by applying the control pulses along different directions, the performance of QDD protocols can be noticeably improved, and explain the reason for such an improvement. Our results can be useful for future implementations of the aperiodic decoupling protocols, and for better understanding of the impact of errors on quantum control of spins.