Control design of two-level quantum systems with reinforcement learning

In recent years, some experimental studies and simulations show that reinforcement learning (RL) is an effective learning control approach for solving certain quantum control problems. In this paper, Q-learning with different exploration strategies (e.g., ε-greedy and Softmax), probabilistic Q-learning (PQL) and quantum reinforcement learning (QRL) are applied to solve the state transition problem of two-level quantum systems (e.g., spin-1/2 systems), respectively. These reinforcement learning algorithms are introduced and analyzed regarding the learning control problem of the spin-1/2 system. According to the constraints of the control fields, two typical kinds of controllers, i.e., three-switch controller and Bang-Bang controller, are designed using reinforcement learning. The learning performance of the above RL algorithms for both of the three-switch control and Bang-Bang control of two-level quantum systems are demonstrated and analyzed.