Learning-Based Quantum Control for Optimal Pure State Manipulation

In this letter, we propose an adaptive critic learning approach for two classes of optimal pure state transition problems for closed quantum systems: i) when the target state is an eigenstate, and ii) when the target state is a superposition pure state. First, we describe a finite-dimensional quantum system based on the Schrodinger equation with the action of control fields. Then, we consider the target state to be i) an eigenstate of the internal Hamiltonian and ii) an arbitrary pure state via a unitary transformation. Meanwhile, the quantum state manipulation is formulated as an optimal control problem for solving the complex partial differential Hamilton-Jacobi-Bellman (HJB) equation, of which the control solution is found using continuous-time Q-learning of an adaptive critic. Finally, numerical simulation for a spin-1/2 particle system demonstrates the effectiveness of the proposed approach.