Quantum Information Processing

, Volume 11, Issue 5, pp 1301–1309 | Cite as

Efficiency of open quantum walk implementation of dissipative quantum computing algorithms

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Abstract

An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on the open quantum walk formalism are more efficient than the canonical dissipative quantum computing approach. In particular, the open quantum walks can be designed to converge faster to the desired steady state and to increase the probability of detection of the outcome of the computation.

Keywords

Open quantum walk Dissipative quantum computing Quantum Fourier transform 
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References

  1. 1.
    Breuer H.-P., Petruccione F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)MATHGoogle Scholar
  2. 2.
    Diehl S., Micheli A., Kantian A., Kraus B., Büchler H.P., Zoller P.: Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008)CrossRefGoogle Scholar
  3. 3.
    Vacanti G., Beige A.: Cooling atoms into entangled states. New J. Phys. 11, 083008 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    Kraus B., Büchler H.P., Diehl S., Kantian A., Micheli A., Zoller P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    Kastoryano M.J., Reiter F., Sørensen A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    Sinaysky I., Petruccione F., Burgarth D.: Dynamics of nonequilibrium thermal entanglement. Phys. Rev. A 78, 062301 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Pumulo N., Sinayskiy I., Petruccione F.: Non-equilibrium thermal entanglement for a three spin chain. Phys. Lett. A V375(36), 3157–3166 (2011)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Verstraete F., Wolf M.M., Cirac J.I.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009)CrossRefGoogle Scholar
  9. 9.
    Aharonov Y., Davidovich L., Zagury N.: Quantum random walks. Phys. Rev. A 48, 1687–1690 (1993)ADSCrossRefGoogle Scholar
  10. 10.
    Kempe J.: Quantum random walks: an introductory overview. Contemp. Phys. 44(4), 307–327 (2003)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    Childs A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Lovett N.B., Cooper S., Everitt M., Trevers M., Kendon V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81, 042330 (2010)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Kendon V.: Decoherence in quantum walks-a review. Math. Struct. Comput. Sci. V17(6), 1169–1220 (2007)MathSciNetGoogle Scholar
  14. 14.
    Kendon V., Tregenna B.: Decoherence can be useful in quantum walks. Phys. Rev. A 67, 042315 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    Attal, S., Petruccione, F., Sabot, C., Sinayskiy, I.: Open Quantum Random Walks. E-print: http://hal.archives-ouvertes.fr/hal-00581553/fr/ (2011)
  16. 16.
    Whitfield J.D., Rodríguez-Rosario C.A., Aspuru-Guzik A.: Quantum stochastic walks: a generalization of classical random walks and quantum walks. Phys. Rev. A 81, 022323 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Sinayskiy, I., Petruccione, F.: Microscopic derivation of open quantum walks (in preparation)Google Scholar
  18. 18.
    Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. CUP, Cambridge (2000)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.NITheP and School of Chemistry and PhysicsUniversity of KwaZulu-NatalDurbanSouth Africa

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