Optical cluster state: Difference between revisions

Revision as of 00:17, 25 August 2022

Latest revision as of 09:33, 18 March 2025

(One intermediate revision by one other user not shown)

Line 25:

===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, NeilsenNielsen'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.

Line 97:

===Polarization encoding===

Polarization entangled photon pairs have also been produced on-chip.<ref>{{cite journal | last1=Matsuda | first1=Nobuyuki | last2=Le Jeannic | first2=Hanna | last3=Fukuda | first3=Hiroshi | last4=Tsuchizawa | first4=Tai | last5=Munro | first5=William John | last6=Shimizu | first6=Kaoru | last7=Yamada | first7=Koji | last8=Tokura | first8=Yasuhiro | last9=Takesue | first9=Hiroki |display-authors=5| title=A monolithically integrated polarization entangled photon pair source on a silicon chip | journal=Scientific Reports | volume=2 | issue=1 | date=2012-11-12 | issn=2045-2322 | doi=10.1038/srep00817|pmc=3495342 | page=817| pmid=23150781 | arxiv=1211.2885 | bibcode=2012NatSR...2E2..817M |doi-access=free}}</ref> The setup involves a silicon wire waveguide that is split in half by a [[polarization rotator]]. This process, like the entanglement generation described for the dual rail encoding, makes use of the nonlinear process of spontaneous four-wave mixing, which can occur in the silicon wire on either side of the polarization rotator. However, the geometry of these wires are designed such that horizontal polarization is preferred in the conversion of laser pump photons to signal and idler photons. Thus when the photon pair is generated, both photons should have the same polarization, i.e.

::<math>|\psi\rangle=|H_s,H_i\rangle</math>.