Optimal control for state preparation in a noisy environment via the most-likely path

One of the stepping stones to quantum technologies is the ability to actively control and prepare desired quantum states with high success rates. In open quantum systems, state preparation can be a challenging task due to the unpredictability of environmental noises. The conventional approach is to search for optimal controls based on the Lindblad master equation. The equation describes the system's average evolution over noise realizations and can be used to maximize the average fidelity to a target state in the state preparation task. However, the Lindblad evolution does not always capture the best estimate of the bona fide noisy state evolution. In this work, we propose an optimal control protocol for the state preparation based on the most-likely state evolution (path). We apply the least action principle to the stochastic path integral constructed for a noisy quantum dynamics. We then investigate the qubit state preparation under the dephasing noise, and analytically obtain the Rabi drive that maximizes the likelihood of reaching the target state. Our most-likely path approach can lead to controls with higher success rates than the conventional Lindblad approach based on the average fidelity.