Quantum convolutional codes design and their encoder architectures

Abstract

In this paper, design of quantum convolutional codes and their encoder architectures have been investigated. We claim that rate-1/(n+1) quantum systematic convolutional codes can be constructed from rate-1/n classical nonsystematic convolutional codes, where n is greater than or equal to 2. The free distances (d/sub free/) of proposed rate-1/(n+1) quantum systematic convolutional codes are larger than that of original rate-1/n classical nonsystematic convolutional codes. A quantum convolutional code encoder can be implemented by using quantum linear feed-forward shift registers and quantum exclusive-OR (controlled-NOT: CNOT) gates. A quantum memory may be used as a quantum state delay element of a quantum register. It is also shown that different encoder architectures one needed for quantum nonsuperposition and superposition state inputs. For quantum superposition state input, additional Hadamard gates should be used in conjunction with a quantum convolutional code encoder for quantum nonsuperposition state input.