Network of Coupled Stochastic Oscillators and One-way Quantum Computations

A network of coupled stochastic oscillators is proposed for modeling of a cluster of entangled qubits that is exploited as a computation resource in one-way quantum computation schemes. A qubit model has been designed as a stochastic oscillator formed by a pair of coupled limit cycle oscillators with chaotically modulated limit cycle radii and frequencies. The qubit simulates the behavior of electric field of polarized light beam and adequately imitates the states of two-level quantum system. A cluster of entangled qubits can be associated with a beam of polarized light, light polarization degree being directly related to cluster entanglement degree. Oscillatory network, imitating qubit cluster, is designed, and system of equations for network dynamics has been written. The constructions of one-qubit gates are suggested. Changing of cluster entanglement degree caused by measurements can be exactly calculated.

Authors:

• Eugene Grichuk
• Margarita Kuzmina
• Eduard Manykin

Keywords:

• network of stochastic oscillators
• one-way quantumcomputations
• a beam of polarized light.

References:

[1] P.W.Shor, Young, "Polynomial time algorithms for prime factorization
and discrete algorithms on a quantum computer, SIAM J. Sci. Statist.
Comput., 1997, v.26, p. 1484.
[2] A.S.Holevo, "Probabilistic and statistical aspects of quantum theory".
Nauka, Moscow, 1980; North Holland Translation - 1982.
[3] A.S.Holevo, " Quantum probability and quantum statistics", VINITI,
1991, v.83, Moscow (in Rusian).
[4] M.A.Nielsen and I.L.Chuang, Quantum computation and quantum
information, Cambridge Univ. Press, 2000.
[5] R.Raussendorf and H.J.Breigel, "A one way quantum computer", Phys.
Rev. Lett. , 2001, V.86, p.5188.
[6] R.Raussendorf and H.J.Breigel, "Computational model underlying the
one-way quantum computer", Quant. Inf. Comp., 2002, v.6, p. 443;
quant-ph/ 0108063 (2001).
[7] R.Raussendorf and H.J.Breigel, Computational model underlying the
one-way quantum computer: concepts and summary", in: Th.Beth ans G.
Leuch, Quantum Information processing, Wiley-VCH, 2003.
[8] L.K.Grover, "A fast quantum mechanical algorithm for database search",
Proc. 28 Annual ACM Symp. on Theory of Computing, 1996, p.22.
[9] I.L.Chuang, L.M.K.Vandersypen, X.Zhou, D.W.Leung, S.Lloyd,
"Experimental realization of a quantum algorithm", Nature, 1998, v.
393, p.143.
[10] L.M.K. Vandersypen, I.L.Chuang, "NMR technique for quantum control
and computation", arXiv: quant-ph/0404064 v.2, 2004.
[11] M.G. Kuzmina, E.A. Manykin and I.I. Surina, "Oscillatory network
with self-organized dynamical connections for synchronization-based
visual image segmentation", BioSystems, 2004, vol. 76, pp. 43-53.
[12] E.S Grichuk, M.G. Kuzmina, E.A. Manykin, "Oscillatory Network for
Synchronization-based Adaptive Image Segmentation", Proc. of WCCI
2006, Vancouver, BC, Canada; Proc. of Int. Joint Conf on Neural
Networks 2006, p.4529.
[13] E.S.Grichuk, M.G.Kuzmina, E.A.Manykin, "Adaptive image processing
via synchronization in self-organizing oscillatory network",
Proceedings of European Computing Conference (ECC 2007), Athens,
Greece; Lecture Notes in Electrical Engineering, (Eds. N.Mastorakis,
V.Mladenov, V.T.Kontargyri), Berlin: Springer, 2009, v.1, p.103.
[14] R.M.A.Azzam, N.M.Bashara, "Ellipsometry and polarized light",
North-Holland Publishing Company, Amsterdam-New-York, Oxford,
1977.