Constructing Noise-Robust Quantum Gates via Pontryagin's Maximum Principle

Abstract: Reliable quantum information technologies depend on precise actuation and techniques to mitigate the effects of undesired disturbances such as environmental noise and imperfect calibration. In this work, we present a general framework based in geometric optimal control theory to synthesize smooth control pulses for implementing arbitrary noise-robust quantum gates. The methodology applies to generic unitary quantum dynamics with any number of qubits or energy levels, any number of control fields, and any number of disturbances, extending existing dynamical decoupling approaches that are only applicable for limited gate sets or small systems affected by one or two disturbances. The noise-suppressing controls are computed via indirect trajectory optimization based on Pontryagin's maximum principle, eliminating the need to make heuristic structural assumptions on parameterized pulse envelopes.