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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58676", author = "Eugene Grichuk and Margarita Kuzmina and Eduard Manykin", title = "Network of Coupled Stochastic Oscillators and One-way Quantum Computations", abstract = "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.", keywords = "network of stochastic oscillators, one-way quantumcomputations, a beam of polarized light.", volume = "4", number = "9", pages = "1272-6", }