Abstract:

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 convolution codes is presented. Its corresponding networks are also described. The basis state of the code is transformed into the multiplication of an information polynomial by the generator polynomial. Then networks can be realized with operations of polynomial multiplication. The simple method possesses a highly regular structure, and the networks are easy to realize.

Key words: CSS-type quantum convolutional codes, encoding and decoding, polynomial multiplication, cyclic shifting