Robust Control of Quantum Dynamics under Input and Parameter Uncertainty

Abstract: Despite significant progress in theoretical and laboratory quantum control, engineering quantum systems remains principally challenging due to manifestation of noise and uncertainties associated with the field and Hamiltonian parameters. In this paper, we extend and generalize the asymptotic quantum control robustness analysis method -- which provides more accurate estimates of quantum control objective moments than standard leading order techniques -- to diverse quantum observables, gates and moments thereof, and also introduce the Pontryagin Maximum Principle for quantum robust control. In addition, we present a Pareto optimization framework for achieving robust control via evolutionary open loop (model-based) and closed loop (model-free) approaches with the mechanisms of robustness and convergence described using asymptotic quantum control robustness analysis. In the open loop approach, a multiobjective genetic algorithm is used to obtain Pareto solutions in terms of the expectation and variance of the transition probability under Hamiltonian parameter uncertainty. The set of numerically determined solutions can then be used as a starting population for model-free learning control in a feedback loop. The closed loop approach utilizes real-coded genetic algorithm with adaptive exploration and exploitation operators in order to preserve solution diversity and dynamically optimize the transition probability in the presence of field noise. Together, these methods provide a foundation for high fidelity adaptive feedback control of quantum systems wherein open loop control predictions are iteratively improved based on data from closed loop experiments.