Probabilistic pathways: New frontiers in quantum ensemble control

In this paper, we propose a novel probabilistic control framework for efficiently controlling an ensemble of quantum systems that can also compensate for the interaction of the systems with the external environment. The main challenge in this problem is to simultaneously steer an ensemble of systems with variation in their internal parameters from an initial state to a desired final state. The minimization of the discrepancy between the probabilistic description of the dynamics of a quantum ensemble and a predefined desired probabilistic description is the key step in the proposed framework. With this objective, the derived solution will not only allow the transitioning of the ensemble from one state to another, but will generally allow steering an initial distribution of the ensemble to a final distribution. Numerical results are presented, demonstrating the effectiveness of the proposed probabilistic control framework.