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With the development of experimental quantum technology, quantum control hasattracted increasing attention due to the realization of controllableartificial quantum systems. However, because quantum-mechanical systems areoften too difficult to analytically deal with, heuristic strategies andnumerical algorithms which search for proper control protocols are adopted,and, deep learning, especially deep reinforcement learning (RL), is a promisinggeneric candidate solution for the control problems. Although there have been afew successful applications of deep RL to quantum control problems, most of theexisting RL algorithms suffer from instabilities and unsatisfactoryreproducibility, and require a large amount of fine-tuning and a largecomputational budget, both of which limit their applicability. To resolve theissue of instabilities, in this dissertation, we investigate thenon-convergence issue of Q-learning. Then, we investigate the weakness ofexisting convergent approaches that have been proposed, and we develop a newconvergent Q-learning algorithm, which we call the convergent deep Q network(C-DQN) algorithm, as an alternative to the conventional deep Q network (DQN)algorithm. We prove the convergence of C-DQN and apply it to the Atari 2600benchmark. We show that when DQN fail, C-DQN still learns successfully. Then,we apply the algorithm to the measurement-feedback cooling problems of aquantum quartic oscillator and a trapped quantum rigid body. We establish thephysical models and analyse their properties, and we show that although bothC-DQN and DQN can learn to cool the systems, C-DQN tends to behave more stably,and when DQN suffers from instabilities, C-DQN can achieve a betterperformance. As the performance of DQN can have a large variance and lackconsistency, C-DQN can be a better choice for researches on complicated controlproblems.

Control of Continuous Quantum Systems with Many Degrees of Freedom based on Convergent Reinforcement Learning