Construction of minimal trellises for quantum stabilizer codes

The size of vertex set of quantum trellises affects the efficiency of decoding algorithms, which can be improved by reducing the number of vertices. Based on the standard check matrix of stabilizer codes, an algorithm to construct trellis-oriented generators for quantum stabilizer codes is presented. By using this algorithm, the trellises with minimal vertex set can be constructed. In addition, an algorithm to construct trellises iteratively for quantum stabilizer codes is also introduced. The algorithm proposed in this paper is more efficient and less complex than the one proposed by Olliver, and so is more suitable for the applications of larger scale and stricter timeliness.