Optimal preparation of graph states

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.042314· OSTI ID:21544581

Cabello, Adan; Lopez-Tarrida, Antonio J ^[1]; Danielsen, Lars Eirik ^[2]; Portillo, Jose R ^[3]

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1. Departamento de Fisica Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain)
2. Department of Informatics, University of Bergen, P.O. Box 7803, Bergen N-5020 (Norway)
3. Departamento de Matematica Aplicada I, Universidad de Sevilla, E-41012 Sevilla (Spain)

We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.

• OSTI ID: 21544581
• Journal Information: Physical Review. A, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevA.83.042314; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLIFFORD ALGEBRA
GRAPH THEORY
QUANTUM ENTANGLEMENT
QUBITS
INFORMATION
MATHEMATICS
QUANTUM INFORMATION