Lyapunov control of finite-dimensional quantum systems based on bi-objective quantum-behaved particle swarm optimization algorithm

Abstract

This paper presents a Lyapunov control scheme to drive finite-dimensional closed and Markovian open quantum systems into any target pure state with as high fidelity and as little time as possible. The control law is established by a Lyapunov function with an unknown Hermitian operator, where the eigenvectors of the operator are constructed based on the condition that the LaSalle invariant set contains the desired target state and a set of optimal eigenvalues of the Hermitian operator is searched by the quantum-behaved particle swarm optimization (QPSO) algorithm. In particular, for open systems, when the denominator in the control law is quite small, we propose an improved QPSO algorithm with constraints to enhance the flexibility in implementation. Finally, numerical simulations are carried out on a five-level and a three-qubit closed quantum systems, and a five-level and a ten-level open quantum systems. Simulation results demonstrate that the proposed control scheme can achieve high-fidelity transfer to desired target states for high-dimensional closed and open quantum systems.