Optimal Controls for Open Quantum Systems Using Stochastic Path Integrals

Abstract

We propose a new optimal control protocol for quantum state preparation in the presence of environmental noises based on the Most Likely Path (MLP) approach. The standard method for dealing with unknown noises in open quantum systems is via Lindblad master equation, which describes the Mean Path (MP) of noisy quantum trajectories. However, the mean path does not always faithfully represent the ensemble of trajectories, especially when the trajectory distribution is multimodal. The most likely path of quantum trajectories is extracted from stochastic path integral formulation, constructed from the joint probability of quantum statetrajectories and the noises. We study a quantum control problem of a single-qubit state preparation, controlling the qubit from an arbitrary initial state to the desired target state in the presence of a dephasing noise, where the control is the Rabi oscillation. This approach yields the analytical solution for the optimal control protocol for the Rabi drive, which is not possible using the standard MP approach. We also investigate the benefits of optimal Rabi drive by looking at the distribution of final states in the Bloch sphere; we find that the distribution of final state is concentrated around the desired target state and does not spread out over the qubit.