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===Nielsen protocol===
In 2004, Nielsen proposed a protocol to create cluster states,<ref>Nielsen, M., [https://arxiv.org/pdf/quant-ph/0402005 "Optical quantum computation using cluster states"], ''Rev. Mod. Phys.'', July, 2004.</ref> borrowing techniques from the [[KLM protocol|Knill-Laflamme-Milburn protocol]] (KLM protocol) to probabilistically create controlled-Z connections between qubits. While the KLM protocol requires error correction and a fairly large number of modes in order to get very high probability two-qubit gate, Neilsen's protocol only requires a success probability per gate of greater than one half. To see how Nielsen brought about this improvement, consider the photons being generated for qubits as vertices on a two dimensional grid, and the controlled-Z operations being probabilistically added edges between nearest neighbors. Using results from [[percolation theory]], it can be shown that as long as the probability of adding edges is above a certain threshold, there will exist a complete grid as a sub-graph with near unit probability.
In order to generate these controlled-Z connections between photons, the protocol makes use of resource states of the form
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