TY - JOUR
T1 - Learning-Based Quantum Control for Optimal Pure State Manipulation
AU - Chen, Anthony siming
AU - Herrmann, Guido
AU - Vamvoudakis, Kyriakos g.
AU - Vijayan, Jayadev
PY - 2024/6/5
Y1 - 2024/6/5
N2 - In this paper, 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.
AB - In this paper, 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.
KW - Adaptive optimal control
KW - quantum control
KW - Q-learning
KW - Schrodinger equation
U2 - 10.1109/LCSYS.2024.3409671
DO - 10.1109/LCSYS.2024.3409671
M3 - Article
SN - 2475-1456
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
ER -