Constructions of quasi-twisted quantum codes
- PDF / 430,741 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 42 Downloads / 308 Views
Constructions of quasi-twisted quantum codes Jingjie Lv1 · Ruihu Li1
· Junli Wang1
Received: 12 December 2019 / Accepted: 2 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese remainder theorem. Then, we utilize these self-orthogonal QT codes to provide quantum codes via the famous Hermitian construction. Moreover, we present a new construction method of q-ary quantum codes, which can be viewed as an effective generalization of the Hermitian construction. General QT codes that are not self-orthogonal are also employed to construct quantum codes. As the computational results, some binary, ternary and quaternary quantum codes are constructed and their parameters are determined, which all cannot be deduced by the quantum Gilbert–Varshamov bound. In the binary case, a small number of quantum codes are derived with strictly improved parameters compared with the current records. In the ternary and quaternary cases, our codes fill some gaps or have better performances than the current results. Keywords Quantum codes · Quasi-twisted codes · A new construction method
1 Introduction Recently, the process of quantum information, especially quantum computing, is accelerating with several companies building quantum computers [5]. In this process, we need mechanisms to reduce or control the effects of operational noises and environmental changes (decoherence). Reducing or controlling the decoherence to a certain
B
Ruihu Li [email protected] Jingjie Lv [email protected] Junli Wang [email protected]
1
Department of Basic Sciences, Air Force Engineering University, Xi’an 710051, People’s Republic of China 0123456789().: V,-vol
123
274
Page 2 of 25
J. Lv et al.
level is a central problem that must be solved by researchers [24]. Fortunately, it is possible to relieve the detrimental influence of decoherence by applying quantum error-correcting codes (or just quantum codes). Therefore, the research of quantum codes has been of great concerns for both physicists and coding theorists. In recent years, there are many quantum codes constructed from classical error-correcting codes such as cyclic codes, constacyclic codes and matrix-product codes over finite fields or finite rings [1,6,17,18,26,28,29,32–34,36,38]. It is generally known that quasi-cyclic (QC) and quasi-twisted (QT) codes are important families of linear codes, which can be regarded as valid generalizations of cyclic and constacyclic codes. In [7,22], it has been revealed that QC and QT codes are asymptotically good meeting a modified Gilbert–Varshamov (GV) bound. Naturally, QC and QT codes also can be applied to construct quantum codes. Hagiwara et al. [19] researched QC LDPC constructions of long quantum codes with a probabilistic approach. Galindo et al. [12] originally utilized QC codes of short length
Data Loading...
