  With the development of experimental quantum technology, quantum control has
attracted increasing attention due to the realization of controllable
artificial quantum systems. However, because quantum-mechanical systems are
often too difficult to analytically deal with, heuristic strategies and
numerical algorithms which search for proper control protocols are adopted,
and, deep learning, especially deep reinforcement learning (RL), is a promising
generic candidate solution for the control problems. Although there have been a
few successful applications of deep RL to quantum control problems, most of the
existing RL algorithms suffer from instabilities and unsatisfactory
reproducibility, and require a large amount of fine-tuning and a large
computational budget, both of which limit their applicability. To resolve the
issue of instabilities, in this dissertation, we investigate the
non-convergence issue of Q-learning. Then, we investigate the weakness of
existing convergent approaches that have been proposed, and we develop a new
convergent 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 2600
benchmark. We show that when DQN fail, C-DQN still learns successfully. Then,
we apply the algorithm to the measurement-feedback cooling problems of a
quantum quartic oscillator and a trapped quantum rigid body. We establish the
physical models and analyse their properties, and we show that although both
C-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 better
performance. As the performance of DQN can have a large variance and lack
consistency, C-DQN can be a better choice for researches on complicated control
problems.
