On Quantum Tensor Product Codes
Jihao Fan, Yonghui Li, Min-Hsiu Hsieh, Hanwu Chen

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…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography
