On Quantum Tensor Product Codes

TL;DR

This paper introduces a flexible framework for constructing quantum tensor product codes (QTPCs) that can correct various quantum errors, including multiple bursts, with improved parameters over existing quantum error-correcting codes.

Contribution

The paper presents a novel general framework for QTPC construction, allowing more flexible component code selection and improved error correction capabilities compared to prior quantum codes.

Findings

Constructed QTPCs with parameters surpassing existing quantum codes.

Developed QTPCs capable of correcting multiple quantum burst errors.

Demonstrated QTPCs based on cyclic and MDS codes with enhanced performance.

Abstract

We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is con- structed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more exible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.