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Graphs, Quadratic Forms, and Quantum Codes

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arxiv quant-ph/0703112 v1 pith:3PCHPSSS submitted 2007-03-13 quant-ph cs.ITmath.IT

Graphs, Quadratic Forms, and Quantum Codes

Markus Grassl , Andreas Klappenecker , Martin Roetteler This is my paper
classification quant-ph cs.ITmath.IT
keywords codequantumcodesfieldfiniteformsgraphicalquadratic
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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. We provide some simple examples to illustrate our results.

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  1. Local Equivalences of Graph States

    quant-ph 2025-11 conditional novelty 8.0

    Graph states are LU-equivalent if and only if they are linked by r-local complementations for some integer r; LU-equivalence is decidable in quasi-polynomial time, and LU=LC holds on at most 19 qubits.