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Optimal preparation of graph states

Cabello, Adán; Danielsen, Lars Eirik; López-Tarrida, Antonio J.; Portillo, José R.
Peer reviewed, Journal article
Accepted version
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URI
https://hdl.handle.net/1956/6536
Date
2011-04-12
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  • Department of Informatics [536]
Original version
Phys. Rev. A 83, 042314   https://doi.org/10.1103/physreva.83.042314
Abstract
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.
Publisher
American Physical Society
Journal
Physical Review A
Copyright
Copyright 2011 American Physical Society

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