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Bulletin of the American Physical Society

Dynamical Decoupling with Imperfect Pulses in P Doped Silicon

Zhihao Wang, W. Zhang, V. V. Dobrovitski, Alexei M. Tyryshkin, S. A. Lyon, Joel W. Ager

Published Mar 17, 2010• 0 citations
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Dynamical decoupling (DD) is an efficient tool for preserving quantum coherence in solid-state spin systems. However, the imperfections of real pulses can ruin the performance of long DD sequences. We investigate the accumulation and compensation of different pulse errors in DD using the electron spins of phosphorus donors in silicon as a test system. We study periodic DD sequences based on spin rotations about two perpendicular axes, and their concatenated and symmetrized versions. We show that pulse errors may quickly destroy some spin states, but maintain other states with high fidelity over long times. Pulse sequences based on spin rotations about xxx and yyy axes outperform those based on xxx and zzz axes due to the accumulation of pulse errors. Concatenation provides an efficient way to suppress the impact of pulse errors, and can maintain high fidelity for all spin components: pulse errors do not accumulate (to first order) as the concatenation level increases, despite the exponential increase in the number of pulses. A symmetrized DD sequence cancels the first-order pulse errors. Our theoretical model gives a clear qualitative picture of the error accumulation and produces results in quantitative agreement with the experiments.
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.
Dynamical decoupling is widely used in many quantum computing systems to combat decoherence. In a practical superconducting quantum system, imperfections can plague decoupling performance. In this work, imperfections in a superconducting qubit and its control system are modeled via modified Hamiltonian and collapse operator. A master equation simulation is carried out on the qubit under 1/f environment noise spectrum. The average dephasing rate of qubit is extracted to characterize the impact of different imperfections on the decoupling from dephasing. We find that the precision of pulse position, on–off ratio, and filtering effect are most critical. Bounded pulses have weaker impact, while variation in pulse width and qubit relaxation are insignificant. Consequently, alternative decoupling protocols, jitter mitigation, cascaded mixers, and pulse shaping can be conducive to the performance of decoupling. This work may assist the analysis and optimization of dynamical decoupling on noisy superconducting quantum systems.