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Bulletin of the American Physical Society

Optimized Single Qubit Gates via Filter Function Design

Yasuo Oda, Dennis G. Lucarelli, Kevin Schultz, David Clader, Greg Quiroz

Published Mar 15, 2021• 0 citations
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Noise-Aware Error Rate Reduction of Single-Qubit Gates

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Bulletin of the American Physical Society•Mar 15, 2021•0 citations
We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single-qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and, in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high-fidelity single-qubit logic operations in a wide variety of complex noise environments.
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost functional which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.