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Physical Review A

Optimal ultrarobust quantum gates by inverse optimization

Ghassen Dridi, Xavier Laforgue, Mohamed Mejatty, S. Guérin

Published Jun 20, 2024• 6 citations
Publisher

Abstract

We propose a systematic method to construct robust optimal quantum control at high orders by inverse optimization and apply it for the generation of ultrarobust optimal quantum gates. We derive explicit integrals that characterize robustness up to seventh order against pulse amplitude for time or energy minimization. At fifth order, time optimization is achieved for a flat pulse and a detuning featuring a dual-frequency oscillation. We analyze its performance and compare it to composite pulse techniques: Ultrarobust inverse optimization is considerably faster (in the range 16%--40% depending on the considered gate) than the best composite pulses with similar performance.

DOI
10.1103/physreva.109.062613

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We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields. We determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a not quantum gate robust with respect to the pulse inhomogeneities. The method is versatile and can be applied to numerous quantum control problems, e.g., other gates, other types of imperfections, Raman processes, or dynamical decoupling of undesirable effects.
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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.
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.