Robust Quantum Control: Analysis & Synthesis via Averaging — Part 2: Experiment

Useful quantum information processors require their control to be robust to the inherent noise and system uncertainties. We propose an approach to design robust quantum operations via a two-stage algorithm. We first improve the control fidelities close to optimality before optimizing for robustness in system uncertainties. The two-stage approach leverages the control landscape topology to enable a computationally efficient method. The algorithm aims to maintain high control fidelities while increasing the robustness. To verify the utility and efficacy of the theoretically and numerically developed approach, we test it on a multi-quit NMR system. We experimentally extract the maximally possible fidelity of single- and multi-qubit gates designed by the algorithm. The algorithm designs the control instances using incomplete knowledge of the quantum system and upper bounds of the system uncertainties, such as the coupling to environmental two-level systems. The algorithm successfully compensates for unknown system couplings and outperforms standard optimal control algorithms. The numerically and experimentally implemented algorithm enables the design of quantum logic gates under realistic circumstances in which only limited knowledge of the accurate and complete system Hamiltonian is available. The proposed robustness approach eases the experimental effort to characterize the quantum system meticulously and enables efficient and high-fidelity quantum logic gate design under these uncertainties.