Quantum Coding via Quasi-Cyclic Block Matrix

Abstract

An effective construction method for long-length quantum code has important applications in the field based on large-scale data. With the rapid development of quantum computing, how to construct this class of quantum coding has become one of the key research fields in quantum information theory. Motivated by the block jacket matrix and its circulant permutation, we proposed a construction method for quantum quasi-cyclic (QC) codes with two classical codes. This simplifies the coding process for long-length quantum error-correction code (QECC) using number decomposition. The obtained code length N can achieve O(n2) if an appropriate prime number n is taken. Furthermore, with a suitable parameter in the construction method, the obtained codes have four cycles in their generator matrices and show good performance for low density codes.