1,4

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.

A. Bouchet, Graphic presentations of isotropic systems, J. Combin. Theory, Ser. B, 45, (1988), 58-76.

L. E. Danielsen and M. G. Parker, On the classification of all self-dual additive codes over GF(4) of length up to 12, Preprint 2005.

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.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum Error Correction Via Codes Over GF(4), IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.

Lars Eirik Danielsen, Database of Self-Dual Quantum Codes.

L. E. Danielsen, T. A. Gulliver, M. G. Parker, Aperiodic Propagation Criteria for Boolean Functions, preprint, 2004.

David G. Glynn and Johannes G. Maks, Quantum Error Correction Project (Aotearoa), ClassSD3.pdf.

M. Hein, J. Eisert and H. J. Briegel. Multi-party entanglement in graph states, Phys. Rev. A (3) 69 (2004), no. 6, 062311, 20 pp.

For four qubits there are two nonisomorphic self-dual quantum codes corresponding to the complete graph and the circuit on four vertices.

Cf. A094927, A110302, A110306.

Sequence in context: A122121 A080009 A123432 this_sequence A123440 A071314 A123441

Adjacent sequences: A090896 A090897 A090898 this_sequence A090900 A090901 A090902

hard,nonn

David G Glynn (dglynn(AT)mac.com), Feb 26 2004

Extended from 9 to 12 terms by Lars Eirik Danielsen (larsed(AT)ii.uib.no) and Matthew G. Parker (matthew(AT)ii.uib.no), Jun 17, 2004.