Evolutionary multi-objective quantum control experiments with the covariance matrix adaptation

Experimental multi-objective Quantum Control is an emerging topic within the broad physics and chemistry application 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-Objective Quantum Control (MOQC), and consider specific systems to be Pareto optimized subject to uncertainty (noise), either experimentally or by means of simulated systems. Unlike the vast majority of other reported systems, the current modeling of noise considers additive Gaussian noise on the input (decision) parameters, which propagates in an unknown manner to the observable (fitness) values. We employ the multi-objective version of the CMA-ES (MO-CMA), which, to the best of our knowledge, is applied here for the first time to a real-world experimental problem, and assess its performance on the investigated systems. In particular, we study its empirical behavior on the MOQC noisy systems, as well as on the Multi-Sphere model landscape, in light of previous theoretical studies on single-objective single-parent Evolution Strategies, and draw some practical conclusions concerning the projection of fitness disturbance on the perceived Pareto front and the need for parental fitness reevaluation in elitist strategies. We show that elitism diminishes the value of the archived Pareto set, even when the perceived Pareto front is well approximated to the true front.