The relationship between quantum and classical coding is introduced, and an efficient polynomial is provided to describe the stabilizer codes. Its standard is calculated to generate quantum convolutional codes. Then the method based on classic quantum coding is applied to the realm of convolutional codes. It is converted into a pearl-necklace structure according to the optimization criterion of quantum circuit. The circuit of the structure is easy to implement, which can avoid the catastrophicerror propagation, and simplify the calculation of quantum coding minimum storage.