Study Of Quantum Convolutional Codes-Construction, Encoding And Decoding

Quantum computer has interested people greatly for its remarkable computation capacity. However, to make quantum computer practical, it is necessary to find the effective method to win through decoherence. Quantum error-correcting code is one of good methods to get over decoherence. Based on the classical information theory and quantum mechanics, Quantum error-correcting code is one of the newest cross-linked research fields, hence it has become a significant part in quantum information.This dissertation focuses on the study of several problems in the theory of quantum convolutional codes. By the construction principle of classical convolutional codes and the characteristic of quantum stabilizer codes, a necessary and sufficient condition to construct quantum convolutional codes from classical convolutional codes is provided. A class of quantum codes with simple block structure is also given. Two new methods for encoding and decoding of Calderbank-Shor-Steane(CSS)-type quantum convolutional codes are presented in first time. In method one, the basis state of the codes are transformed into the multiplication of an information polynomial by the generator polynomial. Then networks can be realized with operations of polynomial multiplication. In method two, the standard form of stabilizers and encoding operators are given. The traditional method of encoding and decoding of quantum block codes is expanded to the field of quantum convolutional codes. Inspired by classical convolutional decoding idea, a quantum Viterbi algorithm with linear complexity is put forward.