While quantum computing is promised to be powerful, its successful realisation requires sophisticated control of the quantum systems and the ability of mitigating errors during operations. Machine learning, a class of algorithms extracting key information from a large amount of data, provides us a new methodology for dealing with quantum control and error mitigation. In chapter I of the thesis, I introduce some fundamental concepts about quantum computing, including quantum bit(qubit), quantum gate, and measurement. Several machine learning algorithms that are used later, including Q-learning, policy gradient, and autoencoder will also be introduced. In chapter II, I apply reinforcement learning to the problem of quantum state transfer in a nearest-neighbor spin chain. I show how to determine the control sequence by transferring the state transfer to a Markov-decision process and how to find the optimal control strategy with reinforcement learning. Numerical results show that the transfer speed is closer to the quantum speed limit compared to conventional algorithms, such as the Krotov method. In chapter III, I provide a further discussion on reinforcement learning. A simple problem of quantum state preparation is considered. I study the performance of three reinforcement learning methods: Q-learning, deep Q-learning, and policy gradient, and two conventional optimization methods: stochastic gradient descent and Krotov algorithm. I provide comparisons on different aspects: the control speed, adaptivity, the ability to scaling up, etc. The advantages and challenges about reinforcement learning are discussed. In chapter IV, inspired by the classical denoising autoencoder, I propose a quantum error mitigation method based on a quantum version of autoencoder. The quantum data set is first compressed to a subspace, after which a measurement is applied to detect errors. After the measurement, the inverse operation of the compression is applied to recover the original quantum data. I demonstrate how this supervised-learning-based method has a near-optimal error mitigation power for the noisy quantum data. At the end of the thesis, I summarise my attempts of applying reinforcement learning and unsupervised learning techniques to quantum computing. The challenges and outlooks for future study about machine learning and quantum information processing are discussed.