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Detecting non-Abelian geometric phase in circuit QED

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Abstract

We propose a scheme for detecting noncommutative feature of the non-Abelian geometric phase in circuit QED, which involves three transmon qubits capacitively coupled to an one-dimensional transmission line resonator. By controlling the external magnetic flux of the transmon qubits, we can obtain an effective tripod interaction of our circuit QED setup. The noncommutative feature of the non-Abelian geometric phase is manifested that for an initial state undergo two specific loops in different order will result in different final states. Our numerical calculations show that this difference can be unambiguously detected in the proposed system.

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References

  1. Berry, M.V.: Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984)

    Article  ADS  MATH  Google Scholar 

  2. Wilczek, F., Zee, A.: Appearance of gauge structure in simple dynamical systems. Phys. Rev. Lett. 52, 2111–2114 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  3. Carollo, A., Fuentes-Guridi, I., Santos, M.F., Vedral, V.: Geometric phase in open systems. Phys. Rev. Lett. 90, 160402 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  4. De Chiara, G., Palma, G.M.: Berry phase for a spin 1/2 particle in a classical fluctuating field. Phys. Rev. Lett. 91, 090404 (2003)

    Article  Google Scholar 

  5. Carollo, A., Fuentes-Guridi, I., Santos, M.F., Vedral, V.: Spin-1/2 geometric phase driven by decohering quantum fields. Phys. Rev. Lett. 92, 020402 (2004)

    Article  ADS  Google Scholar 

  6. Solinas, P., Zanardi, P., Zanghi, N.: Robustness of non-Abelian holonomic quantum gates against parametric noise. Phys. Rev. A 70, 042316 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  7. Fuentes-Guridi, I., Girelli, F., Livine, E.: Holonomic quantum computation in the presence of decoherence. Phys. Rev. Lett. 94, 020503 (2005)

    Article  ADS  Google Scholar 

  8. Zhu, S.-L., Zanardi, P.: Geometric quantum gates that are robust against stochastic control errors. Phys. Rev. A 72, 020301(R) (2005)

    ADS  Google Scholar 

  9. Filipp, S., et al.: Experimental demonstration of the stability of Berry’s phase for a spin-1/2 particle. Phys. Rev. Lett. 102, 030404 (2009)

    Article  ADS  Google Scholar 

  10. Zanardi, P., Rasetti, M.: Holonomic quantum computation. Phys. Lett. A 264, 94–99 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Pachos, J., Zanardi, P., Rasetti, M.: Non-Abelian Berry connections for quantum computation. Phys. Rev. A 61, 010305(R) (1999)

    Article  MathSciNet  Google Scholar 

  12. Jones, J.A., Vedral, V., Ekert, A., Castagnoli, G.: Geometric quantum computation using nuclear magnetic resonance. Nature (London) 403, 869–871 (2000)

    Article  ADS  Google Scholar 

  13. Duan, L.-M., Cirac, J.I., Zoller, P.: Geometric manipulation of trapped ions for quantum computation. Science 292, 1695–1697 (2001)

    Article  ADS  Google Scholar 

  14. Zhu, S.-L., Wang, Z.D.: Unconventional geometric quantum computation. Phy. Rev. Lett. 91, 187902 (2003)

    Article  ADS  Google Scholar 

  15. 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 

  16. 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 

  17. Xue, Z.-Y., Wang, Z.D., Zhu, S.-L.: Physical implementation of topologically decoherence-protected superconducting qubits. Phys. Rev. A 77, 024301 (2008)

    Article  ADS  Google Scholar 

  18. Xue, Z.-Y.: Fast geometric gate operation of superconducting charge qubits in circuit QED. Quantum Inf. Process. 11, 1381–1388 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Tycko, R.: Adiabatic rotational splittings and Berry’s phase in nuclear quadrupole resonance. Phys. Rev. Lett. 58, 2281–2284 (1987)

    Article  ADS  Google Scholar 

  20. Anandan, J., Christian, J., Wanelik, K.: Resource Letter GPP-1: geometric phases in physics. Am. J. Phys. 65, 180–185 (1997)

    Article  ADS  Google Scholar 

  21. Leek, P.J., et al.: Observation of Berry’s phase in a solid-state qubit. Science 318, 1889 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Möttönen, M., Vartiainen, J.J., Pekola, J.P.: Experimental determination of the Berry phase in a superconducting charge pump. Phys. Rev. Lett. 100, 177201 (2008)

    Article  ADS  Google Scholar 

  23. Leibfried, D., et al.: Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature (London) 422, 412–415 (2003)

    Article  ADS  Google Scholar 

  24. Unanyan, R.G., Shore, B.W., Bergmann, K.: Laser-driven population transfer in four-level atoms: consequences of non-Abelian geometrical adiabatic phase factors. Phys. Rev. A 59, 2910–2919 (1999)

    Article  ADS  Google Scholar 

  25. Ruseckas, J., Juzeliūnas, G., Öhberg, P., Fleischhauer, M.: Non-Abelian gauge potentials for ultracold atoms with degenerate dark states. Phys. Rev. Lett. 95, 010404 (2005)

    Article  ADS  Google Scholar 

  26. Zhang, X.-D., Wang, Z.D., Hu, L.-B., Zhang, Z.-M., Zhu, S.-L.: Detecting unambiguously non-Abelian geometric phases with trapped ions. New J. Phys. 10, 043031 (2008)

    Article  ADS  Google Scholar 

  27. Du, Y.-X., Xue, Z.-Y., Zhang, X.-D., Yan, H.: Detecting non-Abelian geometric phases with three-level \(\Lambda \) systems. Phys. Rev. A 84, 034103 (2011)

    Google Scholar 

  28. Sjöqvist, E., Tong, D.M., Andersson, L.M., Hessmo, B., Johansson, M., Singh, K.: Non-adiabatic holonomic quantum computation. New J. Phys. 14, 103035 (2012)

    Article  ADS  Google Scholar 

  29. Johansson, M., Sjöqvist, E., Andersson, L.M., Ericsson, M., Hessmo, B., Singh, K., Tong, D.M.: Robustness of nonadiabatic holonomic gates. Phys. Rev. A 86, 062322 (2012)

    Article  ADS  Google Scholar 

  30. Feng, Z.-B., Zhang, Y.-M., Wang, G.-Z., Han, H.: Detecting non-Abelian geometric phases with superconducting nanocircuits. Phys. E 41, 1859–1863 (2009)

    Google Scholar 

  31. You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature 474, 589–597 (2011)

    Article  ADS  Google Scholar 

  32. You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58(11), 42–47 (2005)

    Article  Google Scholar 

  33. Buluta, I., Nori, F.: Quantum simulators. Science 326, 108–111 (2009)

    Article  ADS  Google Scholar 

  34. Buluta, I., Ashhab, S., Nori, F.: Natural and artificial atoms for quantum computation. Rep. Prog. Phys. 74, 104401 (2011)

    Article  ADS  Google Scholar 

  35. Schoelkopf, R.J., Girvin, S.M.: Wiring up quantum systems. Nature (London) 451, 664–669 (2008)

    Article  ADS  Google Scholar 

  36. Blais, A., Huang, R.S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    Article  ADS  Google Scholar 

  37. Reed, M.D., et al.: Realization of three-qubit quantum error correction with superconducting circuits. Nature (London) 482, 382–385 (2012)

    Article  ADS  Google Scholar 

  38. DiCarlo, L., et al.: Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature (London) 467, 574–578 (2010)

    Article  ADS  Google Scholar 

  39. Neeley, M., et al.: Generation of three-qubit entangled states using superconducting phase qubits. Nature (London) 467, 570–573 (2010)

    Article  ADS  Google Scholar 

  40. Kamleitner, I., Solinas, P., Müller, C., Shnirman, A., Möttönen, M.: Geometric quantum gates with superconducting qubits. Phys. Rev. B 83, 214518 (2011)

    Article  ADS  Google Scholar 

  41. Koch, J., et al.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)

    Article  ADS  Google Scholar 

  42. You, J.Q., Hu, X., Ashhab, S., Nori, F.: Low-decoherence flux qubit. Phys. Rev. B 75, 140515(R) (2007)

    ADS  Google Scholar 

  43. Day, P.K., LeDuc, H.G., Mazin, B.A., 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

This work was supported by the NFRPC (No. 2013CB921804), the NSFC (No. 11004065), the PCSIRT, the NSF of Guangdong Province, and the Program of the Education Department of Anhui Province (No. KJ2012B075).

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Authors and Affiliations

  1. Laboratory of Quantum Information Technology, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, 510006, China

    Man-Lv Peng, Jian Zhou & Zheng-Yuan Xue

  2. Anhui Xinhua University, Hefei, 230088, China

    Jian Zhou

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  1. Man-Lv Peng
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  2. Jian Zhou
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  3. Zheng-Yuan Xue
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Correspondence to Zheng-Yuan Xue.

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Peng, ML., Zhou, J. & Xue, ZY. Detecting non-Abelian geometric phase in circuit QED. Quantum Inf Process 12, 2739–2747 (2013). https://doi.org/10.1007/s11128-013-0560-6

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  • DOI: https://doi.org/10.1007/s11128-013-0560-6

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