A Facile Two-Step Method to Implement \(N\sqrt {i\text {SWAP}}\) and \(N\sqrt {\text {SWAP}}\) Gates in a Circuit QED

Article
  • 8 Downloads

Abstract

We propose a way for implementing a two-step \(N\sqrt {i\text {SWAP}}\) and \(N \sqrt {\text {SWAP}}\) gates based on the qubit-qubit interaction with \(N\) superconducting qubits, by coupling them to a resonator driven by a strong microwave field. The operation times do not increase with the growth of the qubit number. Due to the virtual excitations of the resonator, the scheme is insensitive to the decay of the resonator. Numerical analysis shows that the scheme can be implemented with high fidelity. Moreover, we propose a detailed procedure and analyze the experimental feasibility. So, our proposal can be experimentally realized in the range of current circuit QED techniques.

Keywords

\(N\sqrt {i\text {SWAP}}\) gate \(N\sqrt {\text {SWAP}}\) gate Superconducting qubit Circuit QED 

References

  1. 1.
    Eleuch, H., Ben Nessib, N., Bennaceur, R.: Eur. Phys. J. D 29, 391 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    Eleuch, H.: Noise spectra of microcavity-emitting field in the linear regime. Eur. Phys. J. D 49, 391 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    Sete, E.A., Eleuch, H.: Interaction of a quantum well with squeezed light: quantum-statistical properties. Phys. Rev. A 82, 043810 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences. Cambridge University Press, Cambridge (2004)Google Scholar
  5. 5.
    Rips, S., Hartmann, M.J.: Quantum information processing with nanomechanical qubits. Phys. Rev. Lett. 110, 120503 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    Šašura, M., Buzek, V.: Multiparticle entanglement with quantum logic networks: application to cold trapped ions. Phys. Rev. A 64, 012305 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    Berrada, K., Chafik, A., Eleuch, H., Hassouni, Y.: Concurrence in the framework of coherent states. Quantum Inf. Process 9, 13 (2010)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Sete, E.A., et al.: Using quantum coherence to generate gain in the XUV and X-ray: gain-swept superradiance and lasing without inversion. IEEE J. Sel. Top. Quantum Electron. 18, 541 (2012)CrossRefGoogle Scholar
  9. 9.
    Ferrando-Soria, J., et al.: A modular design of molecular qubits to implement universal quantum gates. Nat. Commun. 7, 11377 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    Eckert, K., et al.: Quantum computing in optical microtraps based on the motional states of neutral atoms. Phys. Rev. A 66, 042317 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    Isenhower, L., Urban, E., Zhang, X., et al.: Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104, 010503 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    Kiesel, N., Schmid, C., Weber, U., et al.: Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    Monroe, C., Meekhof, D.M., King, B.E., Itano, W.M., Wineland, D.J.: Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Fushman, I., Englund, D., Faraon, A., et al.: Controlled phase shifts with a single quantum dot. Science 2008(320), 769–772 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    Jones, J.A., et al.: Implementation of a quantum search algorithm on a quantum computer. Nature (London) 393, 344 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    Hua, M., Tao, M.J., Deng, F.G.: Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED. Sci. Rep. 5, 9274 (2015)CrossRefGoogle Scholar
  17. 17.
    Tanamoto, T., Liu, Y.X., Hu, X., Nori, F.: Efficient quantum circuits for one-way quantum computing. Phys. Rev. Lett. 102(10), 100501 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    Deutsch, D., Barenco, A., Ekert, A.: Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669 (1995)ADSMathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321 (1997)ADSMathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Vatan, F., Williams, C.: Optimal quantum circuits for general two-qubit gates. Phys. Rev. A 69, 032315 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    Liu, Q., Ye, L.: Implementation of a two-atom (swap)1/2 gate in cavity QED. Chin. Phys. Lett. 24, 599 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    Song, K.H., Zhao, Y.J., Shi, Z.G., Xiang, S.H., Chen, X.W.: Simultaneous implementation of \(n\) SWAP gates using superconducting charge qubits coupled to a cavity. Opt. Commun. 10, 1016 (2010)Google Scholar
  23. 23.
    Essammouni, K., Chouikh, A., Said, T., Bennai, M.: NiSWAP and NTCP gates realized in a circuit QED system. Int. J. Geom. Meth. Mod. Phys. 14, 1750100 (2017)CrossRefMATHGoogle Scholar
  24. 24.
    Barenco, A., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)ADSCrossRefGoogle Scholar
  25. 25.
    Beth, T., Rötteler, M.: Quantum Algorithms: Applicable Algebra and Quantum Physics. Quantum Information, Ch. 4, vol. 173, p 96. Springer, Berlin (2001)Google Scholar
  26. 26.
    Braunstein, S.L. et al.: Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit. Phys. Rev. A 63, 052313 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    Gaitan, F.: Quantum Error Correction and Fault Tolerant Quantum Computing. CRC Press, Boca Raton (2008)CrossRefMATHGoogle Scholar
  28. 28.
    Blais, A., et al.: Quantum-information processing with circuit quantum electrodynamics. Phys. Rev. A 75, 032329 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    Deng, Z.J., Feng, M., Gao, K.L.: Simple scheme for the two-qubit Grover search in cavity QED. Phys. Rev. A 72, 034306 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Ye, L., Guo, G.C.: Scheme for implementing quantum dense coding in cavity QED. Phys. Rev. A 71, 034304 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    Everitt, M., Garraway, B.: Multiphoton resonances for all-optical quantum logic with multiple cavities. Phys. Rev. A 90, 012335 (2014)ADSCrossRefGoogle Scholar
  32. 32.
    Chouikh, A., Said, T., Essammouni, K., Bennai, M.: Implementation of universal two- and three-qubit quantum gates in a cavity QED. Opt. Quant. Electron. 48, 463 (2016)CrossRefGoogle Scholar
  33. 33.
    Grochol, M., Piermarocchi, C.: Multispin errors in the optical control of a spin quantum lattice. Phys. Rev. B 78, 165324 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    Barnett, S.M., et al.: Fidelity and the communication of quantum information. J. Phys. A Math. Gen. 34, 6755 (2001)ADSMathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Vion, D., et al.: Manipulating the quantum state of an electrical circuit. Science 296, 886 (2002)ADSCrossRefGoogle Scholar
  36. 36.
    Yang, C.P., Liu, Y.X., Nori, F.: Phase gate of one qubit simultaneously controlling n qubits in a cavity or coupled to a resonator. Phys. Rev. A 81, 062323 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    Gao, G.L., et al.: \(1 \rightarrow \mathrm {N}\) quantum controlled phase gate realized in a circuit QED system. Sci. China Phys. 55(8), 1422–1426 (2012)CrossRefGoogle Scholar
  38. 38.
    Kuhr, S., et al.: Ultrahigh finesse Fabry-Perot superconducting resonator. Appl. Phys. Lett. 90, 164101 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    Wallraff, A., et al.: Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Physique de la Matière Condensée, Equipe Physique Quantique et Applications, Faculté des Sciences Ben M’sikUniversité Hassan IICasablancaMorocco
  2. 2.LPHE-Modelisation et SimulationFaculté des Sciences RabatRabatMorocco

Personalised recommendations