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Fast Implementation of Quantum Phase Gates and Creation of Cluster States via Transitionless Quantum Driving

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Abstract

In this paper, combining transitionless quantum driving and quantum Zeno dynamics, we propose an efficient scheme to fast implement a two-qubit quantum phase gate which can be used to generate cluster state of atoms trapped in distant cavities. The influence of various of various error sources including spontaneous emission and photon loss on the fidelity is analyzed via numerical simulation. The results show that this scheme not only takes less time than adiabatic scheme but also is not sensitive to both error sources. Additionally, a creation of N-atom cluster states is put forward as a typical example of the applications of the phase gates.

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References

  1. Dridi, G., Guérin, S., Hakobyan, V., Jauslin, H.R., Eleuch, H.: Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses. Phys. Rev. A 80, 043408 (2009)

    Article  ADS  Google Scholar 

  2. Vasilev, G.S., Kuhn, A., Vitanov, N.V.: Optimum pulse shapes for stimulated Raman adiabatic passage. Phys. Rev. A 80(1), 013417 (2009)

    Article  ADS  Google Scholar 

  3. Chen, X., Torrontegui, E., Muga, J.G.: Lewis-Riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)

    Article  ADS  Google Scholar 

  4. Lewis, H.R., Riesenfeld, W.B.: An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. J. Math. Phys. 10, 1458 (1969)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Campo, A.D.: Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)

    Article  Google Scholar 

  6. Baksic, A., Ribeiro, H., Clerk, A.A.: Speeding up adiabatic quantum state transfer by using dressed States. Phys. Rev. Lett. 116, 230503 (2016)

    Article  ADS  Google Scholar 

  7. Chen, Y.H., Xia, Y., Wu, Q.C., Huang, B.H., Song, J.: Method for constructing shortcuts to adiabaticity by a substitute of counterdiabatic driving terms. Phys. Rev. A 93, 052109 (2016)

    Article  ADS  Google Scholar 

  8. Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics. Phys. Rev. A 93, 052324 (2016)

    Article  ADS  Google Scholar 

  9. Kang, Y.H., Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y, Song, J.: Reverse engineering of a Hamiltonian by designing the evolution operators. Sci. Rep. 6, 30151 (2016)

    Article  ADS  Google Scholar 

  10. Kang, Y.H., Huang, B.H., Lu, P.M., Xia, Y.: Reverse engineering of a Hamiltonian for a three-level system via the Rodrigues rotation formula. Laser Phys Lett. 14, 025201 (2017)

    Article  ADS  Google Scholar 

  11. Kang, Y.H., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Fast preparation of W states with superconducting quantum interference devices by using dressed states. Phys. Rev. A 94, 052311 (2016)

    Article  ADS  Google Scholar 

  12. Wu, J.L., Ji, X., Zhang, S.: Fast adiabatic quantum state transfer and entanglement generation between two atoms via dressed states. Sci. Rep. 7, 46255 (2017)

    Article  ADS  Google Scholar 

  13. Kang, Y.H., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm. Phys. Rev. A 96, 022304 (2017)

    Article  ADS  Google Scholar 

  14. Huang, B.H., Chen, Y.H., Wu, Q.C., Song, J., Xia, Y.: Fast generating GreenbergerCHorneCZeilinger state via iterative interaction pictures. Laser Phys. Lett. 13, 052311 (2016)

    Google Scholar 

  15. Berry, M.V.: Transitionless quantum driving. J. Phys. A 42, 365303 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Demirplak, M., Rice, S.A.: Adiabatic population transfer with control fields. J. Phys. Chem. A 107, 9937 (2003)

    Article  Google Scholar 

  17. Demirplak, M., Rice, S.A.: On the consistency, extremal, and global properties of counterdiabatic fields. J. Chem. Phys. 129, 154111 (2008)

    Article  ADS  Google Scholar 

  18. Chen, Y., Xia, Y., Song, J., Chen, Q.Q.: Shortcuts to adiabatic passage for fast generation of GreenbergerHorne-Zeilinger states by transitionless quantum driving. Sci. Rep. 5, 15616 (2015)

    Article  ADS  Google Scholar 

  19. Wu, J.L., Ji, X., Zhang, S.: Fast generations of tree-type threedimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving. Sci. Rep. 6, 33669 (2016)

    Article  ADS  Google Scholar 

  20. Huang, X.B., Zhong, Z.R., Chen, Y.H.: Generation of multi-atom entangled states in coupled cavities via transitionless quantum driving. Quantum Inf. Process. 14, 4475C4492 (2016)

    MathSciNet  Google Scholar 

  21. Dür, W., Briegel, H.J.: Stability of Macroscopic Entanglement under Decoherence. Phys. Rev. Lett. 92, 180403 (2004)

    Article  Google Scholar 

  22. Raussendorf, R., Briegel, H.J.: A One-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  23. Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  24. Walther, P., Resch, K.J., Rudolph, T., Schenk, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., Zeilinger, A.: Exprimental one-way quantum computing. Nature(London) 434, 169 (2005)

    Article  ADS  Google Scholar 

  25. Kiesel, N., Schmid, C., Weber, U., Tóth, G., Gühne, O., Ursin, R., Weinfurter, H.: Experimental analysis of a four-qubit photon cluster state. Phys. Rev. Lett. 95, 210502 (2005)

    Article  ADS  Google Scholar 

  26. Vallone, G., Pomarico, E., Mataloni, P., De, M.F., Berardi, V.: Realization and characterization of a two-photon four-qubit linear cluster state. Phys. Rev. Lett. 98, 180502 (2007)

    Article  ADS  Google Scholar 

  27. Lu, C.Y., Zhou, X.Q., Gühne, O., Gao, W.B., Zhang, J., Yuan, Z.S., Goebel, A., Yang, T., Pan, J.W.: Experimental entanglement of six photons in graph states. Nat. Phys. 3, 91 (2007)

    Article  Google Scholar 

  28. You, J.Q., Wang, X.B., Tanamoto, T., Nori, F.: Efficient one-step generation of large cluster states with solid-state circuits. Phys. Rev. A 75, 052319 (2007)

    Article  ADS  Google Scholar 

  29. Xue, Z.Y., Wang, Z.D.: Simple unconventional geometric scenario of one-way quantum computation with superconducting qubits inside a cavity. Phys. Rev. A 75, 064303 (2007)

    Article  ADS  Google Scholar 

  30. Chen, G., Chen, Z.D., Yu, L.X., Liang, J.Q.: One-step generation of cluster states in superconducting charge qubits coupled with a nanomechanical resonator. Phys. Rev. A 76, 024301 (2007)

    Article  ADS  Google Scholar 

  31. Lin, Z.R., Guo, G.P., Tu, T., Zhu, F.Y., Guo, G.C.: Generation of quantum-dot cluster states with a superconducting transmission line resonator. Phys. Rev. Lett. 101, 230501 (2008)

    Article  ADS  Google Scholar 

  32. Li, J.Q., Chen, G., Liang, J.Q.: One-step generation of cluster states in microwave cavity QED. Phys. Rev. A 77, 014304 (2008)

    Article  ADS  Google Scholar 

  33. Misra, B., Sudarshan, E.C.G.: The Zenos paradox in quantum theory. J. Math. Phys. 18, 756 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  34. Wilkinson, S.R., Bharucha, C.F., Fischer, M.C., Madison, K.W., et al.: Experimental evidence for non-exponential decay in quantum tunneling. Nature(London) 387(6633), 575 (1997)

    Article  ADS  Google Scholar 

  35. Fischer, M.C., Gutiérrez-Medina, B., Raizen, M.G.: Observation of the quantum zeno and anti-zeno effects in an unstable system. Phys. Rev. Lett. 87(4), 040402 (2001)

    Article  ADS  Google Scholar 

  36. Facchi, P., Gorini, V., Marmo, G., Pascazio, S.: Quantum Zeno dynamics. Phys. Lett. A 275, 12 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Serafini, A., Mancini, S., Bose, S.: Distributed quantum computation via optical fibers. Phys. Rev. Lett. 96, 010503(4) (2006)

    ADS  Google Scholar 

  39. Chen, L.B., Ye, M.Y., Lin, G.W., Du, Q.H., Lin, X.M.: Generation of entanglement via adiabatic passage. Phys. Rev. A 76, 62304 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  40. Spillane, S.M., Kippenberg, T.J., Vahala, K.J., Goh, K.W., Wilcut, E., Kimble, H.J.: Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)

    Article  ADS  Google Scholar 

  41. Buck, J.R., Kimble, H.J.: Optimal sizes of dielectric microspheres for cavity QED with strong coupling. Phys. Rev. A 67, 033806 (2003)

    Article  ADS  Google Scholar 

  42. Hartmann, M.J., Brandao, F.G.S.L., Plenio, M.B.: Strongly correlated polaritons in a two-dimensional array of cavities. Nat. Phys. 2, 849 (2006)

    Article  Google Scholar 

  43. Gordon, K.J., Fernandez, V., Townsend, P.D., Buller, G.S.: A short wavelength gigahertz clocked fiber-optic quantum key distribution system. IEEE J. Quantum Electron. 40, 900 (2004)

    Article  ADS  Google Scholar 

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Acknowledgments

This work was financially supported by the funding (funding number: JB14220) from the Fujian Education Department.

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  1. Information Engineering College, Yango University, Fuzhou, 350015, China

    Chun-Ling Zhang & Wen-Wu Liu

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  1. Chun-Ling Zhang
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Correspondence to Chun-Ling Zhang.

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Zhang, CL., Liu, WW. Fast Implementation of Quantum Phase Gates and Creation of Cluster States via Transitionless Quantum Driving. Int J Theor Phys 57, 2373–2387 (2018). https://doi.org/10.1007/s10773-018-3760-0

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