Normal Factor Graph Representations of Stabilizer Quantum Codes with Applications

arXiv:2611.00985v1 Announce Type: new 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.