Normal Factor Graph Representations of Stabilizer Quantum Codes with Applications
Abstract
We develop normal factor graph (NFG) representations of stabilizer quantum error-correcting codes and entanglement-assisted quantum error-correcting codes. We introduce two complementary representations. Quantum-code NFGs describe stabilizer and normalizer label codes and provide a graphical framework for establishing self-orthogonality, constructing codes from component codes, and identifying encoding and decoding circuits. Quantum-probability NFGs represent the quantum-mechanical probabilities associated with encoding, noise, and measurement. We also introduce a doubleedge formulation that makes the relationship between these two representations explicit. We apply the framework to convolutional and tail-biting convolutional stabilizer codes, as well as to two classes of low-density parity-check stabilizer codes. Finally, we extend the quantum-probability representation to entanglementassisted codes.
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BibTeX
@misc{li2026normal,
title = {{Normal Factor Graph Representations of Stabilizer Quantum Codes with Applications}},
author = {July X. Li and Pascal O. Vontobel},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00985},
eprint = {2611.00985},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00985},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Normal Factor Graph Representations of Stabilizer Quantum Codes with Applications
AU - July X. Li
AU - Pascal O. Vontobel
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00985
UR - https://arxiv.org/abs/2611.00985
AB - We develop normal factor graph (NFG) representations of stabilizer quantum error-correcting codes and entanglement-assisted quantum error-correcting codes. We introduce two complementary representations. Quantum-code NFGs describe stabilizer and normalizer label codes and provide a graphical framework for establishing self-orthogonality, constructing codes from component codes, and identifying encoding and decoding circuits. Quantum-probability NFGs represent the quantum-mechanical probabilities associated with encoding, noise, and measurement. We also introduce a doubleedge formulation that makes the relationship between these two representations explicit. We apply the framework to convolutional and tail-biting convolutional stabilizer codes, as well as to two classes of low-density parity-check stabilizer codes. Finally, we extend the quantum-probability representation to entanglementassisted codes.
ER -