On the construction of stabilizer codes with an arbitrary binary matrix

Abstract

This paper proposes a simple framework for constructing a stabilizer code with an arbitrary binary matrix. We define a relation between A (1) and A (2) of a binary check matrix A = (A (1)|A (2)) associated with stabilizer generators of a quantum error-correcting code. Given an arbitrary binary matrix, we can derive a pair of A (1) and A (2) by the relation. As examples, we illustrate two kinds of stabilizer codes: quantum LDPC codes and quantum convolutional codes. By the nature of the proposed framework, the stabilizer codes covered in this paper belong to general stabilizer (non-CSS) codes.