Skip to main content
SpringerLink
Log in

Robust preparation of four-qubit decoherence-free states for superconducting quantum interference devices against collective amplitude damping

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Based on the quantum Zeno dynamics, we present an approach for deterministic preparation of arbitrary four-qubit decoherence-free state of superconducting quantum interference devices with respective to collective amplitude damping in a decoherence-free way, namely, not only the form of the target state is free of decoherence, but also the whole process for preparation. The operation is fast and convenient since we only need to manipulate three weak laser pulses sequentially. Other decoherence effects such as cavity decay and the spontaneous emission of qubits are also taken into account in virtue of master equation, and the strictly numerical simulation signifies the final fidelity is high corresponding to the current experimental technology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Shor, P.W.: Polynomial-time algorithms for prime factorization, discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)

    Article  ADS  Google Scholar 

  3. Guo, G.P., Li, C.F., Li, J., Guo, G.C.: Scheme for the preparation of multiparticle entanglement in cavity QED. Phys. Rev. A 65, 042102 (2002)

    Article  ADS  Google Scholar 

  4. Wang, H.F., Zhang, S.: Linear optical generation of multipartite entanglement with conventional photon detectors. Phys. Rev. A 79, 042336 (2009)

    Article  ADS  Google Scholar 

  5. Wang, H.F., Zhang, S.: Scheme for linear optical preparation of a type of four-photon entangled state with conventional photon detectors. Eur. Phys. J. D 53, 359–363 (2009)

    Article  ADS  Google Scholar 

  6. Yang, C.P., Su, Q.P., Zheng, S.B., Han, S.: Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit. Phys. Rev. A 87, 022320 (2013)

    Article  ADS  Google Scholar 

  7. Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Steane, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)

    Article  ADS  Google Scholar 

  9. Knill, E., Laflamme, R.: Theory of quantum error-correcting codes. Phys. Rev. A 55, 900–911 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  10. Reed, M.D., DiCarlo, L., Nigg, S.E., Sun, L., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012)

    Article  ADS  Google Scholar 

  11. Choi, R.H., Fortescue, B., Gour, G., Sanders, B.C.: Entanglement sharing protocol via quantum error-correcting codes. Phys. Rev. A 87, 032319 (2013)

    Article  ADS  Google Scholar 

  12. Lidar, D.A., Chuang, I.L., Whaley, K.B.: Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998)

    Article  ADS  Google Scholar 

  13. Beige, A., Braun, D., Tregenna, B., Knight, P.L.: Quantum computing using dissipation to remain in a decoherence-free subspace. Phys. Rev. Lett. 85, 1762–1765 (2000)

    Article  ADS  Google Scholar 

  14. Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science 290, 498–501 (2000)

    Article  ADS  Google Scholar 

  15. Feng, X.L., Wu, C., Sun, H., Oh, C.H.: Geometric entangling gates in decoherence-free subspaces with minimal requirements. Phys. Rev. Lett. 103, 200501 (2009)

    Article  ADS  Google Scholar 

  16. Viola, L., Knill, E., Lloyd, S.: Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417–2421 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. Khodjasteh, K., Lidar, D.A.: Fault-tolerant quantum dynamical decoupling. Phys. Rev. Lett. 95, 180501 (2005)

    Article  ADS  Google Scholar 

  18. Biercuk, M.J., Uys, H., VanDevender, A.P., Shiga, N., Itano, W.M., Bollinger, J.J.: Optimized dynamical decoupling in a model quantum memory. Nature 458, 996–1000 (2009)

    Article  ADS  Google Scholar 

  19. Zanardi, P., Rasetti, M.: Noiseless quantum codes. Phys. Rev. Lett. 79, 33063309 (1997)

    Article  Google Scholar 

  20. Duan, L.M., Guo, G.C.: Optimal quantum codes for preventing collective amplitude damping. Phys. Rev. A 58, 3491–3495 (1998)

    Article  ADS  Google Scholar 

  21. Bourennane, M., Eibl, M., Gaertner, S., Kurtsiefer, C., Cabello, A., Weinfurter, H.: Decoherence-freequantum information processing with four-photon entangled states. Phys. Rev. Lett. 92, 107901 (2004)

    Article  ADS  Google Scholar 

  22. Zou, X.B., Shu, J., Guo, G.C.: Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions. Phys. Rev. A 73, 054301 (2006)

    Article  ADS  Google Scholar 

  23. Gong, Y.X., Zou, X.B., Niu, X.L., Li, J., Huang, Y.F., Guo, G.C.: Generation of arbitrary four-photon polarization-entangled decoherence-free states. Phys. Rev. A 77, 042317 (2008)

    Article  ADS  Google Scholar 

  24. Xia, Y., Song, J., Song, H.S., Zhang, S.: Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors. J. Opt. Soc. Am. B 26, 129–132 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  25. Xia, Y., Lu, M., Song, J., Lu, P.M., Song, H.S.: Effective protocol for preparation of four-photon polarization-entangled decoherence-free states with cross-Kerr nonlinearity. J. Opt. Soc. Am. B 30, 421–427 (2013)

    Article  ADS  Google Scholar 

  26. Wang, H.F., Zhang, S., Zhu, A.D., Yi, X.X., Yeon, K.H.: Local conversion of four Einstein–Podolsky–Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors. Opt. Express 19, 25433–25440 (2011)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  28. Facchi, P., Pascazio, S.: Quantum Zeno dynamics: mathematical, physical aspects. J. Phys. A: Math. Theor. 41, 493001 (2008)

    Article  MathSciNet  Google Scholar 

  29. Shao, X.Q., Chen, L., Zhang, S., Zhao, Y.F., Yeon, K.H.: Deterministic generation of arbitrary multi-atom symmetric Dicke states by a combination of quantum Zeno dynamics and adiabatic passage. Europhys. Lett. 90, 50003 (2010)

    Google Scholar 

  30. Shao, X.Q., Wang, H.F., Chen, L., Zhang, S., Zhao, Y.F., Yeon, K.H.: Converting two-atom singlet state into three-atom singlet state via quantum Zeno dynamics. New J. Phys. 12, 023040 (2010)

    Article  ADS  Google Scholar 

  31. Li, W.A., Wei, L.F.: Controllable entanglement preparations between atoms in spatially-separated cavities via quantum Zeno dynamics. Opt. Express 20, 13440–13450 (2012)

    Article  ADS  Google Scholar 

  32. Yang, C.P., Chu, S.I., Han, S.: Quantum information transfer, entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter. Phys. Rev. Lett. 92, 117902 (2004)

    Google Scholar 

  33. Yang, C.P., Han, S.: Preparation of Greenberger–Horne–Zeilinger entangled states with multiple superconducting quantum-interference device qubits or atoms in cavity QED. Phys. Rev. A 70, 062323 (2004)

    Article  ADS  Google Scholar 

  34. Yang, C.P., Chu, S.I., Han, S.: Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED. Phys. Rev. A 67, 042311 (2003)

    Article  ADS  Google Scholar 

  35. Zhu, S.L., Wang, Z.D., Zanardi, P.: Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity. Phys. Rev. Lett. 94, 100502 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  36. Nielsen, M.A., Chuang, I.L.: Quantum Computation, Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  37. Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  38. Carvalho, A.R.R., Hope, J.J.: Stabilizing entanglement by quantum-jump-based feedback. Phys. Rev. A 76, 010301(R) (2007)

    Article  MathSciNet  ADS  Google Scholar 

  39. Chiorescu, I., Nakamura, Y., Harmans, C.J.P.M., Mooij, J.E.: Coherent quantum dynamics of a superconducting flux qubit. Science 299, 1869–1871 (2003)

    Article  ADS  Google Scholar 

  40. Day, P.K., LeDuc, H.G., Mazin, B., Vayonakis, A., Zmuidzinas, J.: A broadband superconducting detector suitable for use in large arrays. Nature (London) 425, 817–821 (2003)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The authors thank the anonymous reviewers for constructive comments that helped in improving the quality of this manuscript. This work is supported by “the Fundamental Research Funds for the Central Universities” under Grant Nos. 11QNJJ009 and 12SSXM001, and the National Natural Science Foundation of China under Grant Nos. 11204028 and 11175044. X.Q. Shao was also supported in part by the Government of China through CSC.

Author information

Authors and Affiliations

  1. School of Physics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Xiao-Qiang Shao & Tai-Yu Zheng

  2. Department of Physics, College of Science, Yanbian University, Yanji, 133002, Jilin, People’s Republic of China

    Shou Zhang

Authors
  1. Xiao-Qiang Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tai-Yu Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shou Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-Qiang Shao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shao, XQ., Zheng, TY. & Zhang, S. Robust preparation of four-qubit decoherence-free states for superconducting quantum interference devices against collective amplitude damping. Quantum Inf Process 12, 3383–3393 (2013). https://doi.org/10.1007/s11128-013-0604-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-013-0604-y

Keywords

Search

Navigation