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International Congress on Image and Signal Processing (CISP)

New Non-Binary Stabilizer Quantum Codes Derived from Quasi-Negacyclic Codes

Jingjie Lv, Xi Zhang, Ruihu Li

Published Oct 1, 2019• 2 citations
Publisher

Abstract

Constructions of quantum error-correcting codes with good properties utilizing classical codes is an important task for quantum computing and quantum information. In this paper, we employ a class of one-generator quasi-negacyclic codes and provide a sufficient condition for symplectic self-orthogonality. As the computational results, some good non-binary stabilizer quantum codes are constructed and their parameters are determined.

DOI
10.1109/cisp-bmei48845.2019.8965879

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Constructions of quantum error-correcting codes with good properties utilizing classical codes is an important task for quantum computing and quantum information. In this paper, we employ a class of one-generator quasi-negacyclic codes and provide a sufficient condition for symplectic self-orthogonality. As the computational results, some good non-binary stabilizer quantum codes are constructed and their parameters are determined.
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In this short letter, our main objective is to construct good quantum stabilizer codes over small fields, which have a more potential possibility to be employed in actual quantum processors. We firstly consider a suitable class of two-generators quasi-cyclic (QC) codes and determine their parameters. Then by virtue of their symplectic dual algebraic structure, we derive a sufficient condition to be symplectic dual-containing of these codes. Subsequently, an explicit construction of stabilizer codes from quasi-cyclic codes is presented. As for computational results, we provide many stabilizer codes with good parameters over binary, ternary and quaternary fields that all can not be deduced by the quantum Gilbert-Varshamov (GV) bound. In the binary case, our several codes strictly improve the lower bounds on the minimum distance in current records. In the ternary and quaternary occasions, numerous codes fill some gaps or have better parameters than the current results.
In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner product. As the computational results, five new binary quantum codes with parameters [[45,29,5]], [[63,36,7]], [[73,55,5]], [[105,71,7]], and [[105,72,7]] improving the best-known lower bounds on minimum distance in Grassl's code tables are constructed.
In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of 1-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct many new binary symplectic self-orthogonal QC codes with excellent parameters, leading to 117 record-breaking quantum error-correction codes.
Abstract The development of quantum codes and entanglement-assisted quantum codes with improved parameters through classical codes has been a critical area in both quantum communications and quantum information theory. In this paper, we introduce a novel approach using a family of one-generator quasi-twisted codes of index 3 and provide an extended version of them that maintain self-orthogonality, enabling the creation of stabilizer quantum codes. Computational findings include the construction of binary stabilizer codes with good parameters. Additionally, we propose techniques to design maximal-entanglement entanglement-assisted quantum codes based on this class of quasi-twisted codes. As a practical outcome, we find some optimal quantum codes and good maximal-entanglement entanglement-assisted quantum codes derived from these class of quasi-twisted codes and their extension.