  In quantum information, it is of high importance to efficiently detect
entanglement. Generally, it needs quantum tomography to obtain state density
matrix. However, it would consumes a lot of measurement resources, and the key
is how to reduce the consumption. In this paper, we discovered the relationship
between convolutional layer of artificial neural network and the average value
of an observable operator in quantum mechanics. Then we devise a branching
convolutional neural network which can be applied to detect entanglement in
2-qubit quantum system. Here, we detect the entanglement of Werner state,
generalized Werner state and general 2-qubit states, and observable operators
which are appropriate for detection can be automatically found. Beside,
compared with privious works, our method can achieve higher accuracy with fewer
measurements for quantum states with specific form. The results show that the
convolutional neural network is very useful for efficiently detecting quantum
entanglement.
