Cluster state

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 $|\phi _{\{\kappa \}}\rangle _{C}$ are states which obey the set eigenvalue equations:

K^{(a)}{\left|\phi _{\{\kappa \}}\right\rangle _{C}}=(-1)^{\kappa _{a}}{\left|\phi _{\{\kappa \}}\right\rangle _{C}}

where $K^{(a)}$ are the correlation operators

K^{(a)}=\sigma _{x}^{(a)}\bigotimes _{b\in \mathrm {N} (a)}\sigma _{z}^{(b)}

with $\sigma _{x}$ and $\sigma _{z}$ being Pauli matrices, $N(a)$ denoting the neighbourhood of $a$ and $\{\kappa _{a}\in \{0,1\}|a\in C\}$ being a set of binary parameters specifying the particular instance of a cluster state.

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

References

↑ H. J. Briegel; R. Raussendorf (2001). "Persistent Entanglement in arrays of Interacting Particles". Physical Review Letters. 86 (5): 910–3. arXiv:quant-ph/0004051. Bibcode:2001PhRvL..86..910B. doi:10.1103/PhysRevLett.86.910. PMID 11177971.
↑ 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.
↑ 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. arXiv:quant-ph/0503126. Bibcode:2005Natur.434..169W. doi:10.1038/nature03347. PMID 15758991.
↑ 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. arXiv:quant-ph/0508128. Bibcode:2005PhRvL..95u0502K. doi:10.1103/PhysRevLett.95.210502. PMID 16384122.
↑ 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. arXiv:quant-ph/0308080. Bibcode:2003Natur.425..937M. doi:10.1038/nature02008. PMID 14586463.

Quantum information science

General

Quantum communication

Quantum algorithms

Quantum complexity theory

Quantum computing models

Decoherence prevention

Physical implementations

Quantum optics	Cavity QED Circuit QED Linear optical quantum computing

Ultracold atoms	Trapped ion quantum computer Optical lattice

Spin-based	Nuclear magnetic resonance QC Kane QC Loss–DiVincenzo QC Nitrogen-vacancy center

Superconducting quantum computing	Charge qubit Flux qubit Phase qubit

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Cluster state

See also

References