Research On Dynamic Optimal Control Of Controlled Quantum Systems Based On Deep Reinforcement Learning

Heat engines have long played a crucial role in advancing human technology and improving life.There is a trade-off between the power and efficiency of a heat engine during a thermodynamic cycle.In an ideal heat engine with sufficiently slow evolution while the efficiency can reach high values,the power goes to zero.Therefore,exploring effective control schemes for quantum thermal cycles and studying finite-time quantum heat engines that balance efficiency and power are important research topics in the field of quantum control.Moreover,the preparation of quantum states is a central task in quantum information processing.The preparation of finite-time,high-fidelity quantum states is a prerequisite and basis for tasks such as quantum computation and quantum communication.Exploring efficient quantum state preparation schemes that can be easily manipulated experimentally is also a hot research topic in dynamical control of quantum systems.Machine learning,as a powerful tool for dealing with optimization and control problems,has been widely used in various fields such as information processing and system dynamics control.More recently,machine learning algorithms have also found applications in quantum physics,providing a potential means to solve complex problems.Currently,the study of optimizing the dynamics of controlled quantum systems using machine learning algorithms is just beginning.In this paper,we explore the optimization of quantum thermal cycle performance and quantum state preparation using machine learning algorithms.The main research contents include:(1)Using a single spin qubit system as the working medium and combining a policybased deep reinforcement learning algorithm,we investigated the optimal driving strategy(optimized distribution of driving field strength)with an additional driving field during the expansion and compression processes.We compared and analyzed the performance of the optimized driving control strategy with respect to the quantum Otto cycle under free evolution conditions,including output power,power and efficiency.It is shown that the overall performance of the optimized driving control policy is significantly better than that under free evolution,demonstrating the effectiveness of deep reinforcement learning in assisting in improving the performance of the quantum Otto cycle.(2)Using the deep deterministic policy gradient(DDPG)algorithm,we studied the preparation of quantum states for both single and double qubit systems and analyzed the optimal distribution of external driving fields during the process of preparing them from arbitrary initial states to specified target states.Compared with the deep Q-network(DQN)algorithm in recent literature,quantum state preparation under the DDPG algorithm has significant advantages.On the one hand,the average fidelity and noise resistance of quantum state preparation have been significantly improved.On the other hand,the DDPG algorithm uses an optimization process to obtain the optimal action sequence from the continuous action(Driving Field)space,making it more controllable in practical experimental operations than the DQN algorithm,which searches for the optimal sequence in a specified discrete action space.