  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.
