Optical cluster state: Difference between revisions

Revision as of 23:48, 14 December 2017

Revision as of 23:48, 14 December 2017

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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 which, when performed on a pair of <math>|plus+\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, Neilsen's protocol only requires a success probability per gate of greater than one half. Given that the success probability for a connection using <math>n</math> ancilla photons is <math>n^2/(n+1)^2</math>, relaxation of the success probability from nearly one to anything over one half presents a major advantage in resources, as well as simply reducing the number of required elements in the photonic circuit.

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.