  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.
