Multirobust Control Pulses Designed by Iterative Quantum Kolmogorov-Arnold-Moser Algorithm

Abstract

We introduce a multi-robust quantum control strategy designed to suppress multilevel leakage outside the computational qubit space while simultaneously ensuring robustness against unknown inhomogeneities in control parameters. It is based on a reformulation of the Derivative Removal by Adiabatic Gate (DRAG) technique which allows for the full incorporation of control pulses originally designed for two-level models by using the iterative quantum Kolmogorov-Arnold-Moser (KAM) algorithm. We apply it for optimal robust control designed by inverse optimization (RIO), referred to as RDK pulses. We analyze the performance of RDK pulses on various durations, iterations, and robustness types. We show that the two-level robustness is restored after only a few iterations with an asymptotic exponential approximation (i.e. as a superasymptotic series), even for relatively short pulse durations and that the resulting pulses are near optimal in terms of energy compared to the optimal RIO pulses defined in the qubit subspace. Such pulses are well suited for superconducting transmons as well as other forms of qubits embedded in a multi-level structure. By effectively reproducing a two-level dynamics within a multi-level system, this approach is versatile thanks to its compatibility with two-level control strategies under conditions (smoothness, duration) that are analyzed.