الگوریتم کلونی مورچه بر اساس صلاحیت با Q-learning سیستم کوانتومی Fidelity-Based Ant Colony Algorithm with Q-learning of Quantum System

1 Introduction There are two kinds of control strategies for the optimum designs, i.e., the open-loop control and the closed-loop control. Because there is a simple controller in the open-loop control, which is convenient to be implemented, the open-loop control strategy was initially adopted for solving the optimizing problems in quantum system [1]. It must satisfy the following constraints: i) The system Hamiltonian H0 is known to high precision. ii) The multidimensional Schro¨dinger equation i∂ψ ∂t = [H0 − με(t)]ψ may be reliably solved. iii) The resultant control field design ε(t) may be faithfully reproduced. Unfortunately, it is difficult to practically implement such an open-loop control strategy that satisfies the above-mentioned assumptions, leading to the quantum closed-loop control strategy in the literature [2]. The traditional closed-loop learning control strategy was initially proposed by Rabitz [3]. It is an effective control method for the quantum control, which can optimize the system performance through learning from experience by searching for the best control strategy. It involves three elements, i.e., i) an input initial guess, ii) the laboratory generation of the control applying to the sample and subsequently observed for its impact, and iii) a learning algorithm that considers the prior experiments and suggests the form of the next control input. Designing the appropriate quantum learning control algorithm is an important task for the closed-loop learning control strategy, which includes the gradient algorithm, the genetic algorithm, the linear mapping algorithm, the nonlinear mapping algorithm, the reinforcement learning algorithm, and so on. There is strong robustness required for the gradient algorithm [3], whereas the gradient δJ/δε(t) must be measured with the inherent errors. The genetic algorithm was widely used in quantum control, due to its strong optimization ability and powerful search ability [4]. However a potential difficulty with this algorithm is that it has to work with large numbers of control variables. The input-output relationship of controlled system can be fully considered in the linear mapping algorithm and be simplified to the linear maps. So the linear mapping algorithm can be effectively used in the closed-loop learning control. Because the quantum control systems may be highly nonlinear, the practical application of the linear mapping algorithm has been limited. Under such circumstances, the nonlinear mapping algorithm has been development [5, 6].