Graphs, quadratic forms, and quantum codes

Graphs, quadratic forms, and quantum codes. Grassl, M., Klappenecker, A., & Rotteler, M. In Proceedings IEEE International Symposium on Information Theory,, pages 45–, June, 2002. ZSCC: 0000092
doi abstract bibtex

We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms.

@inproceedings{grassl_graphs_2002,
	title = {Graphs, quadratic forms, and quantum codes},
	doi = {10/brmmtr},
	abstract = {We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms.},
	booktitle = {Proceedings {IEEE} {International} {Symposium} on {Information} {Theory},},
	author = {Grassl, M. and Klappenecker, A. and Rotteler, M.},
	month = jun,
	year = {2002},
	note = {ZSCC: 0000092},
	keywords = {Computer science, Contracts, Eigenvalues and eigenfunctions, Galois fields, Hamming weight, Quantum computing, Quantum mechanics, Symmetric matrices, additive group, error correction codes, error-correcting codes, finite field, graph theory, graphical quantum code, quadratic forms, quantum communication, stabilizer code, undirected graph},
	pages = {45--}
}

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