Optimal preparation of graph states

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.

REVTeX4-1, 8 pages, 5 figures, 336 MB of data, 1 computer program

References in corpus (9)

• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Multi-party entanglement in graph states
• Quantum error-correcting codes associated with graphs
• Graphical description of the action of local Clifford transformations on graph states
• Universal resources for measurement-based quantum computation
• Parallelizing Quantum Circuits
• Entanglement in eight-qubit graph states
• Finite set of invariants to characterize local Clifford equivalence of stabilizer states
• Compact set of invariants characterizing graph states of up to eight qubits

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