Cluster state

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In quantum information and quantum computing, a cluster state[1] is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement (via projective measurements) in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.[2]

Formally, cluster states are states which obey the set eigenvalue equations:

where are the correlation operators

with and being Pauli matrices, denoting the neighbourhood of and being a set of binary parameters specifying the particular instance of a cluster state.

Cluster states have been realized experimentally. They have been obtained in photonic experiments using parametric downconversion [3] .[4] They have been created also in optical lattices of cold atoms .[5]

See also[edit]

References[edit]

  1. ^ H. J. Briegel; R. Raussendorf (2001). "Persistent Entanglement in arrays of Interacting Particles". Physical Review Letters. 86 (5): 910–3. Bibcode:2001PhRvL..86..910B. PMID 11177971. arXiv:quant-ph/0004051Freely accessible. doi:10.1103/PhysRevLett.86.910. 
  2. ^ Briegel, Hans J. "Cluster States". In Greenberger, Daniel; Hentschel, Klaus & Weinert, Friedel. Compendium of Quantum Physics - Concepts, Experiments, History and Philosophy. Springer. pp. 96–105. ISBN 978-3-540-70622-9. 
  3. ^ P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer and A. Zeilinger (2005). "Experimental one-way quantum computing". Nature. 434 (7030): 169–76. Bibcode:2005Natur.434..169W. PMID 15758991. arXiv:quant-ph/0503126Freely accessible. doi:10.1038/nature03347. 
  4. ^ N. Kiesel; C. Schmid; U. Weber; G. Tóth; O. Gühne; R. Ursin; H. Weinfurter (2005). "Experimental Analysis of a 4-Qubit Cluster State". Phys. Rev. Lett. 95: 210502. Bibcode:2005PhRvL..95u0502K. PMID 16384122. arXiv:quant-ph/0508128Freely accessible. doi:10.1103/PhysRevLett.95.210502. 
  5. ^ O. Mandel; M. Greiner; A. Widera; T. Rom; T. W. Hänsch; I. Bloch (2003). "Controlled collisions for multi-particle entanglement of optically trapped atoms". Nature. 425: 937–940. Bibcode:2003Natur.425..937M. PMID 14586463. arXiv:quant-ph/0308080Freely accessible. doi:10.1038/nature02008.