On quantum tensor product codes
(pp1105-1122)
Jihao
Fan, Yonghui Li, Min-Hsiu Hsieh, and Hanwu Chen
doi:
https://doi.org/10.26421/QIC17.13-14-3
Abstracts:
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 constructed 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 flexible 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.
Key words:
Quantum error-correction codes, Tensor product codes,
Burst-errorcorrection codes, Concatenated quantum codes (CQC),
Maximal-distance-separable (MDS) codes, BCH codes |