Article
Quantum Science & Technology
Guohui Wang, Chunming Tang, Weiming Wei
Summary: This paper proposes several classes of Hermitian self-orthogonal MDS codes with subcodes of arbitrary dimensions. By taking advantage of the special structure of these classic MDS codes, several new classes of optimal AQECCs are obtained. A large number of optimal AQECCs can be generated using the construction methods presented in this paper.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Quantum Science & Technology
Arun J. Moorthy, Lane G. Gunderman
Summary: Quantum computers require effective error-correcting codes and the use of qudits instead of qubits can reduce the number of particles that need to be controlled. This study demonstrates how to construct codes with specific parameters using the technique of local-dimension-invariant (LDI) codes, and further reduces the requirement for large local-dimensions by utilizing the structure of CSS codes.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Quantum Science & Technology
Clarice Dias de Albuquerque, Giuliano Gadioli La Guardia, Reginaldo Palazzo, Catia Regina de Oliveira Quilles Queiroz, Vandenberg Lopes Vieira
Summary: This paper presents constructions of asymmetric quantum error-correcting codes, including topological quantum codes and hyperbolic asymmetric codes. By investigating the structure and properties of topological quantum codes on Euclidean and hyperbolic surfaces and analyzing parameters such as encoding rates and distances, the performance of topological codes can be determined. By introducing asymmetry and different tessellations, quantum codes with different error protection characteristics can be generated.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Multidisciplinary Sciences
Renyu Wang, Leonid P. Pryadko
Summary: Generalized bicycle codes are a type of quantum error-correcting code constructed from binary circulant matrices. They have linear distance scaling and low-weight stabilizer generators, which can potentially improve performance in the presence of measurement errors.
Article
Optics
Priya J. Nadkarni, Shayan Srinivasa Garani
Summary: The use of preshared entangled states in nonbinary entanglement-assisted stabilizer codes is essential for achieving better error correction capability in quantum communication channels. A novel design architecture of the syndrome computation unit for qudit stabilizer codes has been proposed using classical additive codes and gates. The proposed quantum error correction architectures are beneficial for developing high-density coded quantum memories for archival quantum storage.
Article
Computer Science, Information Systems
Yannis Bousba, Travis Russell
Summary: The study presents a quantum analogue of the Ramsey theorem, showing that quantum channels on specific matrices have quantum graphs with certain structures. While most quantum graphs generated by channels exhibit specific structures, not all cases can be reformulated using stabilizer codes and specific channels to represent the Ramsey theorem.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Physics, Multidisciplinary
Lijuan Xing, Zhuo Li
Summary: This paper uses BCH codes to construct quantum codes, finding classical BCH codes with suitable cyclotomic cosets, constructing nonbinary quantum BCH codes, and realizing a new family of quantum BCH codes through extensions. This work expands the study of quantum error correcting codes and improves their code parameters and minimum distances.
Article
Quantum Science & Technology
Xueting Wang, Tongjiang Yan, Yuhua Sun, Tao Wang
Summary: This paper constructs good quantum stabilizer codes by using the images of cyclic codes of length q(2m) - 1 and r(q(2) - 1), respectively. The construction results in quantum stabilizer codes with larger minimum distances or better code rates than previously known ones, and also introduces quantum stabilizer codes with the new length m(q(2m) - 1).
QUANTUM INFORMATION PROCESSING
(2023)
Article
Quantum Science & Technology
Markus Grassl
Summary: We propose a new propagation rule for CSS codes that can generate a CSS code with parameters [[n - 2, k, d - 1]](q) from a CSS code [[n, k, d]](q). This is an improvement compared to the usual result of [[n - 2, k, d - 2]]q. The new rule also applies to asymmetric quantum codes from the CSS construction.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Mathematics
Hristo Kostadinov, Nikolai Manev
Summary: Memory devices based on floating-gate transistors have become the dominant technology for non-volatile storage devices. Errors observed in flash memory devices are typically of a special, asymmetric type, and integer codes have been shown to be effective in correcting them. This paper presents a new construction of integer codes capable of correcting single errors typical for flash memory devices.
Article
Physics, Multidisciplinary
Yuan Li, Jin-Yang Li
Summary: An effective method for constructing long-length quantum codes is essential in large-scale data applications. With the rapid growth of quantum computing, the construction of these codes has become a key research area in quantum information theory. By utilizing the block jacket matrix and its circulant permutation, a construction method for quantum quasi-cyclic (QC) codes using two classical codes is proposed. This method simplifies the coding process for long-length quantum error-correction codes (QECC) by employing number decomposition. The obtained codes have a code length of O(n2) if an appropriate prime number n is chosen and exhibit good performance for low density codes with four cycles in their generator matrices.
Article
Computer Science, Information Systems
Daryus Chandra, Soon Xin Ng, Lajos Hanzo
Summary: This study proposes a novel quantum Turbo short-block code design that achieves multiple quantum coding rates. The design uses multiple-rate quantum short-block codes as the outer codes and a quantum unity-rate code as the inner code. Simulation results show that the proposed design performs close to the ultimate limit of the quantum hashing bound.
Article
Quantum Science & Technology
Khaled Khalfaoui, El Hillali Kerkouche, Tahar Boudjedaa, Allaoua Chaoui
Summary: This paper presents an automatic searching approach for exploring the quantum space as a constraints satisfaction problem. It introduces a constraint based on quantum circuits equivalence to optimize the implementation. The approach is applied in automatically searching quantum error correction protocols based on code stabilizer, and the generated results and mechanisms are presented.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Telecommunications
Jiaxin Li, Zhongwen Guo, Hongyang Ma
Summary: This paper introduces a novel hybrid ARQ protocol for quantum communication system using quantum stabilizer codes. The protocol ensures information security through the quantum entangled state, improves transmission reliability through hybrid ARQ system, and corrects errors in codewords with quantum stabilizer codes.
CHINA COMMUNICATIONS
(2021)
Article
Quantum Science & Technology
Priya J. Nadkarni, Shayan Srinivasa Garani
Summary: The paper presents a coding-theoretic framework for constructing entanglement-assisted stabilizer codes over qudits of dimension p(k), utilizing pre-shared entangled states between the encoder and decoder. Various contributions such as mathematical decomposition of qudits, properties of the code, analytical expression for minimum entangled subqudits, code construction procedure, and quantum coding bounds are discussed. The error correction capability of the code is shown to be enhanced through entanglement assistance, making it useful for coded quantum computing and communication systems over p(k)-dimensional qudits.
QUANTUM INFORMATION PROCESSING
(2021)
