Skip to main content
Log in

Room Temperature High-fidelity Non-adiabatic Holonomic Quantum Computation on Solid-state Spins in Nitrogen-vacancy Centers

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The high-speed implementation and robustness against of non-adiabatic holonomic quantum computation provide a new idea for overcoming the difficulty of the quantum system interacting with the environment easily decoherence, which realizing large-scale quantum computer construction. Here, we show that high-fidelity quantum gates to implement non-adiabatic holonomic quantum computation under electron spin states in Nitrogen-Vacancy(NV ) centers, providing an extensible experimental platform that has the potential for room-temperature quantum computing, which has increased attention recent years. Compared with the previous method, we can implement both the one- and two-qubit gates by varying the amplitude and phase of the microwave pulse applied to control the non-Abelian geometric phase acquired by NV centers. We also found that our proposed scheme may be implemented in the current experiment to discuss the gate fidelity with the experimental parameters. Therefore, the scheme adopts a new method to achieve high-fidelity non-adiabatic holonomic quantum computation.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  1. ÓBrien, J.L.: Optical quantum computing. Science 318, 1567–1570 (2007)

    ADS  Google Scholar 

  2. Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., ÓBrien, J.L.: Quantum computers. Nature(London) 464, 45–53 (2010)

    ADS  Google Scholar 

  3. Suter, D., Lim, K.: Scalable architecture for spin-based quantum computers with a single type of gate. Phys. Rev. A 65, 052309 (2002)

    ADS  Google Scholar 

  4. Sjöqvist, E., Pati, A.K., Ekert, A., Anandan, J.S., Ericsson, M., Oi, D.K.L., Vedral, V.: Geometric phases for mixed states in interferometry. Phys. Rev. Lett. 85, 2845 (2000)

    ADS  Google Scholar 

  5. Falci, G., Fazio, R., Palma, G.M., Siewert, J., Vedral, V.: Detection of geometric phases in superconducting nanocircuits. Nature(London) 407, 355–358 (2000)

    ADS  Google Scholar 

  6. Zhu, S.L., Wang, Z.D.: Implementation of universal quantum gates based on nonadiabatic geometric phases. Phys. Rev. Lett. 89, 097902 (2002)

    ADS  Google Scholar 

  7. Zhu, S.L.: Scaling of geometric phases close to the quantum phase transition in the spin chain. Phys. Rev. Lett. 96, 077206 (2006)

    ADS  Google Scholar 

  8. Mousolou, V.A., Sjöqvist, E.: Non-Abelian geometric phases in a system of coupled quantum bits. Phys. Rev. A 89, 022117 (2014)

    ADS  Google Scholar 

  9. Simeonov, L.S., Vitanov, N.V.: Generation of non-Abelian geometric phases in degenerate atomic transitions. Phys. Rev. A 96, 032102 (2017)

    ADS  MathSciNet  Google Scholar 

  10. Abdumalikov Jr, A.A., Fink, J.M., Juliusson, K., Pechal, M., Berger, S., Wallraff, A., Filipp, S.: Experimental realization of non-Abelian non-adiabatic geometric gates. Nature(London) 496, 482–485 (2013)

    ADS  Google Scholar 

  11. Xu, G.F., Long, G.L.: Universal nonadiabatic geometric gates in two-qubit decoherence-free subspaces. Sci. Rep. 4, 6814 (2014)

    ADS  Google Scholar 

  12. Liang, Z.T., Yue, X.X., Lv, Q., Du, Y.X., Huang, W., Yan, H., Zhu, S.L.: Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers. Phys. Rev. A 93(R), 040305 (2016)

    ADS  Google Scholar 

  13. Berger, S., Pechal, M., Abdumalikov Jr, A.A., Eichler, C., Steffen, L., Fedorov, A., Wallraff, A., Filipp, S.: Exploring the effect of noise on the berry phase. Phys Rev. A 87(R), 060303 (2013)

    ADS  Google Scholar 

  14. Yale, C.G., Heremans, F.J., Zhou, B.B., Auer, A., Burkard, G., Awschalom, D.D.: Optical manipulation of the Berry phase in a solid-state spin qubit. Nat. Photon. 10, 184 (2016)

    ADS  Google Scholar 

  15. Albash, T., Lidar, D.A.: Decoherence in adiabatic quantum computation. Phys. Rev. A 91, 062320 (2015)

    ADS  Google Scholar 

  16. Sjöqvist, E.: Nonadiabatic holonomic single-qubit gates in off-resonant Λ systems. Phys. Lett. A 380, 65–67 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Duan, L.M., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Science 292, 1695–1697 (2001)

    ADS  Google Scholar 

  18. Recati, A., Calarco, T., Zanardi, P., Cirac, J.I., Zoller, P.: Holonomic quantum computation with neutral atoms. Phys. Rev. A 66, 032309 (2002)

    ADS  Google Scholar 

  19. Zhang, P., Wang, Z.D., Sun, J.D., Sun, C.P.: Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity. Phys. Rev. A 71, 042301 (2005)

    ADS  Google Scholar 

  20. Zhang, X.D., Zhang, Q., Wang, Z.D.: Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions. Phys. Rev. A 74, 34302 (2006)

    ADS  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  Google Scholar 

  23. Knill, E., Laflamme, R., Viola, L.: Theory of quantum error correction for general noise. Phys. Rev. Lett. 84, 2525 (2000)

    ADS  MathSciNet  MATH  Google Scholar 

  24. Nayak, C., Simon, S.H., Stern, A., Freedman, M., Das Sarma, S.: Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  25. 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)

    ADS  MathSciNet  Google Scholar 

  26. Zhou, J., Liu, B.J., Hong, Z.P., Xue, Z.Y.: Fast holonomic quantum computation on solid-state spins with all-optical control. Sci. China Phys. Mech. 1, 010312 (2018)

    Google Scholar 

  27. Dong, P., Yu, L.B., Zhou, J.: Holonomic quantum computation on microwave photons with all resonant interactions. Laser Phys. Lett. 13, 085201 (2016)

    ADS  Google Scholar 

  28. Herr, D., Nori, F., Devitt, S.J.: Lattice surgery translation for quantum computation. New J. Phys. 19, 013034 (2017)

    ADS  Google Scholar 

  29. Liu, J., Dong, P., Zhou, J., Cao, Z.L.: Universal non-adiabatic holonomic quantum computation in decoherence-free subspaces with quantum dots inside a cavity. Laser Phys. Lett. 14, 055202 (2017)

    ADS  Google Scholar 

  30. Zhou, J., Yu, W.C., Gao, Y.M., Xue, Z.Y.: Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers. Opt. Express 23, 14027 (2015)

    ADS  Google Scholar 

  31. Liang, Z.T., Du, Y.X., Huang, W., Xue, Z.Y., Yan, H.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions. Phys. Rev. A 89, 062312 (2014)

    ADS  Google Scholar 

  32. Xu, G.F., Liu, C.L., Zhao, P.Z., Tong, D.M.: Nonadiabatic holonomic gates realized by a single-shot implementation. Phys. Rev. A 92, 052302 (2015)

    ADS  Google Scholar 

  33. Xue, Z.Y., Zhou, J., Chu, Y.M., Hu, Y.: Nonadiabatic holonomic quantum computation with all-resonant control. Phys. Rev. A 94, 022331 (2016)

    ADS  Google Scholar 

  34. Herterich, E., Sjöqvist, E.: Single-loop multiple-pulse nonadiabatic holonomic quantum gates. Phys. Rev. A 94, 052310 (2016)

    ADS  Google Scholar 

  35. Zhao, P.Z., Xu, G.F., Tong, D.M.: Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases. Phys. Rev. A 94, 062327 (2016)

    ADS  Google Scholar 

  36. Xu, G.F., Zhao, P.Z., Xing, T.H., Sjöqvist, E., Tong, D.M.: Composite nonadiabatic holonomic quantum computation. Phys. Rev. A 95, 032311 (2017)

    ADS  Google Scholar 

  37. Liu, B.J., Huang, Z.H., Xue, Z.Y., Zhang, X.D.: Superadiabatic holonomic quantum computation in cavity QED. Phys. Rev. A 95, 062308 (2017)

    ADS  Google Scholar 

  38. Zhao, P.Z., Xu, G.F., Ding, Q.M., Sjöqvist, E., Tong, D.M.: Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces. Phys. Rev. A 95, 062310 (2017)

    ADS  Google Scholar 

  39. Xue, Z.Y., Gu, F.L., Hong, Z.P., Yang, Z.H., Zhang, D.W., Hu, Y., You, J.Q.: Nonadiabatic holonomic quantum computation with dressed-state qubits. Phys. Rev. Applied 7, 054022 (2017)

    ADS  Google Scholar 

  40. Xu, G.F., Zhang, J., Tong, D.M., Sjöqvist, E., Kwek, L.C.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces. Phys. Rev. Lett. 109, 170501 (2012)

    ADS  Google Scholar 

  41. Abdumalikov Jr, A.A., Fink, J.M., Juliusson, K., Pechal, M., Berger, S., Wallra, A., Filipp, S.: Experimental realization of non-Abelian non-adiabatic geometric gates. Nature. 7446 (2013)

  42. Zu, C., Wang, W.B., He, L., Zhang, W.G., Dai, C.Y., Wang, F., Duan, L.M.: Experimental realization of universal geometric quantum gates with solid-state spins. Nature. 7520 (2014)

  43. Zhou, B.B., Jerger, P.C., Shkolnikov, V.O., Heremans, F.J., Burkard, G., Awschalom, D.D.: Holonomic quantum control by coherent optical excitation in diamond. Phys. Rev. Lett. 14, 140503 (2017)

    Google Scholar 

  44. Arroyo-Camejo, S., Lazariev, A., Hell, S.W., Balasubramanian, G.: Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin. Nat. Commun. 5, 4870 (2014)

    ADS  Google Scholar 

  45. Sekiguchi, Y., Niikura, N., Kuroiwa, R., Kano, H., Kosaka, H: Optical holonomic single quantum gates with a geometric spin under a zero field. Nat. Photon. 11, 309–314 (2017)

    ADS  Google Scholar 

  46. Yale, C.G., Heremans, F.J., Zhou, B.B., Auer, A., Burkard, G., Awschalom, D.D.: Optical manipulation of the Berry phase in a solid-state spin qubit. Nat. Photon. 110, 184–189 (2016)

    ADS  Google Scholar 

  47. Clark, S., Parkins, A.: Entanglement and entropy engineering of atomic two-qubit states. Phys. Rev. Lett. 90, 047905 (2003)

    ADS  Google Scholar 

  48. Vernooy, D.W., Ilchenko, V.S., Mabuchi, H., Streed, E.W., Kimble, H.J.: High-q measurements of fused-silica microspheres in the near infrared. Opt. Lett. 23, 247–249 (1998)

    ADS  Google Scholar 

  49. Tittel, W., Brendel, J., Zbinden, H., Gisin, N.: Quantum cryptography using entangled photons in energy-time bell states. Phys. Rev. Lett. 84, 4737 (2000)

    ADS  Google Scholar 

Download references

Acknowledgments

This work are supported by the Project of Introduction and Cultivation for Young Innovative Talents in Colleges and Universities of Shandong Province and National Natural Science Foundation of China under Grant Nos. 11674253, 11674089, 11725524 and 61471356.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Guo-An Yan or Hua Lu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, GA., Lu, H. Room Temperature High-fidelity Non-adiabatic Holonomic Quantum Computation on Solid-state Spins in Nitrogen-vacancy Centers. Int J Theor Phys 59, 2223–2231 (2020). https://doi.org/10.1007/s10773-020-04500-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04500-6

Keywords

Navigation