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2 single photons, each in a different input mode of the polarising beam splitter, will go to the same output mode if they have the opposite polarization. |
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===Nielsen protocol===
In 2004, Nielsen proposed a protocol to create cluster states,<ref>{{cite journal | last=Nielsen | first=Michael A. | title=Optical Quantum Computation Using Cluster States | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=93 | issue=4 | date=2004-07-21 | issn=0031-9007 | doi=10.1103/physrevlett.93.040503 | page=040503| pmid=15323741 |arxiv=quant-ph/0402005| bibcode=2004PhRvL..93d0503N | s2cid=7720448 }}</ref> borrowing techniques from the [[KLM protocol|Knill-Laflamme-Milburn protocol]] (KLM protocol) to probabilistically create controlled-Z connections between qubits which, when performed on a pair of <math>|+\rangle=|0\rangle+|1\rangle</math> states (normalization being ignored), forms the basis for cluster states. While the KLM protocol requires error correction and a fairly large number of modes in order to get very high probability two-qubit gate,
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. Because of this, Nielsen's protocol doesn't rely on every individual connection being successful, just enough of them that the connections between photons allow a grid.
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