  Finding optimal controls for open quantum systems needs to take into account
effects from unwanted environmental noise. Since actual realizations or states
of the noise are typically unknown, the usual treatment for the quantum
system's decoherence dynamics is via the Lindblad master equation, which in
essence describes an average evolution (mean path) of the system's state
affected by the unknown noise. We here consider an alternative view of a
noise-affected open quantum system, where the average dynamics can be
unravelled into hypothetical noisy quantum trajectories, and propose a new
control strategy for the state-preparation problem based on the likelihood of
noise occurrence. We adopt the most-likely path technique for quantum
state-preparation, constructing a stochastic path integral for noise variables
and finding control functions associated with the most-likely noise to achieve
target states. As a proof of concept, we apply the method to a qubit-state
preparation under a dephasing noise and analytically solve for controlled Rabi
drives for arbitrary target states. Since the method is constructed based on
the probability of noise, we also introduce a fidelity success rate as a new
measure of the state preparation and benchmark our most-likely path controls
against the existing mean-path approaches.
