On the construction of stabilizer codes with an arbitrary binary matrix

Authors:
Yongsoo Hwang;Byung-Soo Choi;Moongu Jeon
Affiliations:
Department of Information and Communications, Gwangju Institute of Science and Technology, Gwangju, Republic of Korea;Electrical and Computer Engineering Department, Duke University, Durham, USA;Department of Information and Communications, Gwangju Institute of Science and Technology, Gwangju, Republic of Korea
Venue:
Quantum Information Processing
Year:
2013

Citing 10
Cited 0

Quantum computation and quantum information

Quantum computation and quantum information
Quantum Reed-Solomon Codes

AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Error Correction Coding: Mathematical Methods and Algorithms

Error Correction Coding: Mathematical Methods and Algorithms
Quantum serial turbo codes

IEEE Transactions on Information Theory
Efficient quantum stabilizer codes: LDPC and LDPC-convolutional constructions

IEEE Transactions on Information Theory
On the iterative decoding of sparse quantum codes

Quantum Information & Computation
Quantum error correction via codes over GF(4)

IEEE Transactions on Information Theory
Sparse-graph codes for quantum error correction

IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs

IEEE Transactions on Information Theory
High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper proposes a simple framework for constructing a stabilizer code with an arbitrary binary matrix. We define a relation between A 1 and A 2 of a binary check matrix A = (A 1|A 2) associated with stabilizer generators of a quantum error-correcting code. Given an arbitrary binary matrix, we can derive a pair of A 1 and A 2 by the relation. As examples, we illustrate two kinds of stabilizer codes: quantum LDPC codes and quantum convolutional codes. By the nature of the proposed framework, the stabilizer codes covered in this paper belong to general stabilizer (non-CSS) codes.