I. Introduction
Quantum error-correction is a basic technique for transmitting quantum information reliably over a noisy quantum channel. Many explicit constructions of quantum error-correcting codes[1], [2], [3], [4] have been proposed so far. In classical coding theory, practical systems have mostly used convolutional codes[5] rather than block codes, because convolutional codes are usually superior in terms of their performance-complexity tradeoff So, people also pay attention to construct quantum convolutional codes (QCCs)[6]. These codes are aimed at protecting a flow of quantum information over long distance communication. Grassl and Beth gave a general method to construct quantum shift registers in 2000[7]. In this paper, we present a technique for encoding and decoding tailored to quantum convolutional codes. The resulting quantum circuits are based on the quantum version of polynomial multiplication. Finally, a simple error estimation algorithm inspired by their classical analogue is provided.