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Systems & Control Letters

Dynamical decoupling in quantum control: A system theoretic approach

Francesco Ticozzi, Augusto Ferrante

Published Mar 7, 2006• 11 citations
Publisher
DOI
10.1016/j.sysconle.2006.01.003

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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.

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Constructing high-fidelity control pulses that are robust to control and system/environment fluctuations is a crucial objective for quantum information processing (QIP). We combine dynamical decoupling (DD) with optimal control (OC) to identify control pulses that achieve this objective numerically. Previous DD work has shown that general errors up to (but not including) third order can be removed from {pi}- and {pi}/2-pulses without concatenation. By systematically integrating DD and OC, we are able to increase pulse fidelity beyond this limit. Our hybrid method of quantum control incorporates a newly-developed algorithm for robust OC, providing a nested DD-OC approach to generate robust controls. Motivated by solid-state QIP, we also incorporate relevant experimental constraints into this DD-OC formalism. To demonstrate the advantage of our approach, the resulting quantum controls are compared to previous DD results in open and uncertain model systems.

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We describe experimental and theoretical studies of open-loop quantum control techniques known as dynamical decoupling (DD) for the suppression of decoherence-induced errors in quantum systems. Our experiments on trapped atomic ion qubits demonstrate that it is possible to optimize the construction of DD sequences for a given noise power spectral density. Studies of novel sequences derived analytically or through numerical optimization – while maintaining fixed control resources – demonstrate large gains in our ability to preserve quantum coherence in arbitrary noise environments.

Conference on Lasers and Electro-Optics•Jan 1, 2010•0 citations
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.
Constructing high-fidelity control pulses that are robust to control and system/environment fluctuations is a crucial objective for quantum information processing (QIP). We combine dynamical decoupling (DD) with optimal control (OC) to identify control pulses that achieve this objective numerically. Previous DD work has shown that general errors up to (but not including) third order can be removed from {pi}- and {pi}/2-pulses without concatenation. By systematically integrating DD and OC, we are able to increase pulse fidelity beyond this limit. Our hybrid method of quantum control incorporates a newly-developed algorithm for robust OC, providing a nested DD-OC approach to generate robust controls. Motivated by solid-state QIP, we also incorporate relevant experimental constraints into this DD-OC formalism. To demonstrate the advantage of our approach, the resulting quantum controls are compared to previous DD results in open and uncertain model systems.
We describe experimental and theoretical studies of open-loop quantum control techniques known as dynamical decoupling (DD) for the suppression of decoherence-induced errors in quantum systems. Our experiments on trapped atomic ion qubits demonstrate that it is possible to optimize the construction of DD sequences for a given noise power spectral density. Studies of novel sequences derived analytically or through numerical optimization – while maintaining fixed control resources – demonstrate large gains in our ability to preserve quantum coherence in arbitrary noise environments.