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A090899
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Number of nonisomorphic indecomposable self-dual quantum codes on n qubits.
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7
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1, 1, 1, 2, 4, 11, 26, 101, 440, 3132, 40457, 1274068
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OFFSET
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1,4
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COMMENTS
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Also number of nonisomorphic indecomposable self-dual codes of Type 4^H+ and length n.
Each self-dual (additive) quantum code of length n stabilizes an essentially unique quantum state on n qubits, the 2^n coefficients of which can be assumed to take values in {0,1,-1}. It also corresponds to a "quantum" set of n lines in PG(n-1,2): the Grassmannian coordinates of these lines sum to zero. A related sequence is the number of nonisomorphic (possibly decomposable) self-dual quantum codes on n qubits, A094927.
Also the number of equivalence classes of connected graphs on n nodes up to sequences of local complement ation (or vertex neighborhood complementation) and isomorphism.
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REFERENCES
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David G. Glynn and Johannes G. Maks, The classification of self-dual quantum codes of length <= 9, preprint.
D. M. Schlingemann, Stabilizer codes can be represented as graph codes, Quant. Inf. Comp. 2, 307.
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LINKS
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EXAMPLE
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For four qubits there are two nonisomorphic self-dual quantum codes corresponding to the complete graph and the circuit on four vertices.
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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David G Glynn (dglynn(AT)mac.com), Feb 26 2004
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EXTENSIONS
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a(10)-a(12) from Lars Eirik Danielsen (larsed(AT)ii.uib.no) and Matthew G. Parker (matthew(AT)ii.uib.no), Jun 17 2004
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STATUS
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approved
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