How to implement multi-qubit gates efficiently with high precision is essential for realizing universal fault tolerant computing. For a physical system with some external controllable parameters, it is a great challenge to control the time dependence of these parameters to achieve a target multi-qubit gate efficiently and precisely. Here we construct a dueling double deep Q-learning neural network (DDDQN) to find out the optimized time dependence of controllable parameters to implement two typical quantum gates: a single-qubit Hadamard gate and a two-qubit CNOT gate. Compared with traditional optimal control methods, this deep reinforcement learning method can realize efficient and precise gate control without requiring any gradient information during the learning process. This work attempts to pave the way to investigate more quantum control problems with deep reinforcement learning techniques. PACS numbers: 03.67.Ac, 03.67.Lx, 07.05.Mh II. BANG-BANG CONTROL MODEL TO IMPLEMENT QUANTUM GATESIn this section, we give a bang-bang control model to implement quantum gates, which explains the physical problems we solve in this paper.

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