Stabilizer codes can be realized as graph codes

Quantum Information and Computation

Volumn 2, Issue 4, 2002, Pages 307-323

  Schlingemann, D ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; INFORMATION SYSTEMS;

AS GRAPH; GRAPH CODES; NEW CONSTRUCTIONS; QUANTUM ERROR CORRECTING CODES; STABILIZER CODES;

QUANTUM NOISE;

EID: 0242634028     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

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11. Concerning the additive structure in double-struck F, the corresponding dual group double-struck F∧ is isomorphic to double-struck F itself. We may choose one group isomorphism i : double-struck F → double-struck F∧ which is symmetric i(a)(a′) = i(a′)(a). Making use of the multiplicative unit 1 in double-struck F, we obtain an injective group homomorphism from F into U(1) by ε := i(1) ε double-struck F∧.
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15. Let V, W be two linear spaces over a field double-struck F. For an operator F: V → W the dual map F*: W* → V* is determined by 〈F* ŵ, v〉 := (ŵ, Fv) with ŵ ∈ W* and v ∈ V.
16. For an abelian C*-algebra A, we denote by A∧ the collection of all irreducible *-representations (characters) of A. This set is a compact Hausdorff space, called the spectrum of A, and A can be identified with the continuous functions on A∧.
17. For a linear spaces K ⊂ G, the orthogonal complement is the subspace K⊥ consisting of those vectors ĝ ∈ G* in the dual space of G for which (ĝ, k) = 0 for each k ∈ K.
18. Schlingemann, D.: Logical network implementation for cluster states and graph codes. quantph/0202007