Aperiodic dynamical decoupling sequences in presence of pulse errors

TL;DR

This paper analyzes how pulse errors affect the performance of aperiodic dynamical decoupling sequences, specifically UDD and QDD, in preserving qubit states, with implications for quantum control in spin systems.

Contribution

It provides a theoretical and numerical investigation of pulse error accumulation in UDD and QDD sequences, highlighting ways to improve their robustness against errors.

Findings

Pulse errors cause initial fidelity drops and long-term saturation.

Applying control pulses along different directions improves QDD performance.

Results inform future implementations of aperiodic decoupling protocols.

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 errors accumulation for two aperiodic DD sequences, the Uhrig's DD UDD) protocol [G. S. Uhrig, Phys. Rev. Lett. {\bf 98}, 100504 (2007)], and the Quadratic DD (QDD) protocol [J. R. West, B. H. Fong and D. A. Lidar, Phys. Rev. Lett {\bf 104}, 130501 (2010)]. 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 of 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.