Encoding and decoding of quantum convolutional codes

The research on quantum convolutional codes is aimed at protecting a flow of information over long distance communications. The polynomial representation of a quantum state is defined. Based on the Calderbank-Shor-Steane (CSS)-type construction of quantum codes, a new method for encoding and decoding of CSS-type quantum convolutional codes is presented and corresponding networks are described. The basis state of the code is transformed into the product of an information polynomial by the generator polynomial. Then networks can be realized by operations of polynomial multiplication. Finally, inspired by classical convolutional decoding idea, a quantum Viterbi algorithm with linear complexity is put forward.