Reverse engineering of one-qubit filter functions with dynamical invariants

Abstract

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.

10 pages, 4 figures

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• Designing dynamically corrected gates robust to multiple noise sources using geometric space curves
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• Nonadiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition
• Accessing the Full Capabilities of Filter Functions: A Tool for Detailed Noise and Control Susceptibility Analysis
• Robust implicit quantum control of interacting spin chains
• An automated geometric space curve approach for designing dynamically corrected gates