Layer-by-layer generation of cluster states

Brown, Katherine L. and Horsman, Clare and Kendon, Viv and Munro, William J. (2012) Layer-by-layer generation of cluster states. Physical Review A - Atomic, Molecular, and Optical Physics, 85 (5). 052305. ISSN 1050-2947 (

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Cluster states can be used to perform measurement-based quantum computation. The cluster state is a useful resource, because once it has been generated only local operations and measurements are needed to perform universal quantum computation. In this paper, we explore techniques for quickly and deterministically building a cluster state. In particular, we consider generating cluster states on a qubus quantum computer, a computational architecture which uses a continuous variable ancilla to generate interactions between qubits. We explore several techniques for building the cluster, with the number of operations required depending on whether we allow the ability to destroy previously created controlled-phase links between qubits. In the case where we cannot destroy these links, we show how to create an n×m cluster using just 3nm-2n- 3m/2 +3 operations. This gives more than a factor of 2 savings over a naive method. Further savings can be obtained if we include the ability to destroy links, in which case we only need 13(8nm-4n-4m-8) operations. Unfortunately, the latter scheme is more complicated so choosing the correct order to interact the qubits is considerably more difficult. A halfway scheme, that keeps a modular generation but saves additional operations over never destroying links requires only 3nm-2n-2m+4 operations. The first scheme and the last scheme are the most practical for building a cluster state because they split up the generation into the repetition of simple sections.