  Experimental multi-objective Quantum Control is an emerging topic within the
broad physics and chemistry applications domain of controlling quantum
phenomena. This realm offers cutting edge ultrafast laser laboratory
applications, which pose multiple objectives, noise, and possibly constraints
on the high-dimensional search. In this study we introduce the topic of
Multi-Observable Quantum Control (MOQC), and consider specific systems to be
Pareto optimized subject to uncertainty, either experimentally or by means of
simulated systems. The latter include a family of mathematical test-functions
with a practical link to MOQC experiments, which are introduced here for the
first time. We investigate the behavior of the multi-objective version of the
Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES) and assess its
performance on computer simulations as well as on laboratory closed-loop
experiments. Overall, we propose a comprehensive study on experimental
evolutionary Pareto optimization in high-dimensional continuous domains, draw
some practical conclusions concerning the impact of fitness disturbance on
algorithmic behavior, and raise several theoretical issues in the broad
evolutionary multi-objective context.
