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Optical holonomic single quantum gates with a geometric spin under a zero field

Abstract

The realization of fast fault-tolerant quantum gates on a single spin is the core requirement for solid-state quantum-information processing. As polarized light shows geometric interference, spin coherence is also geometrically controlled with light via the spin–orbit interaction. Here, we show that a geometric spin in a degenerate subspace of a spin-1 electronic system under a zero field in a nitrogen vacancy centre in diamond allows implementation of optical non-adiabatic holonomic quantum gates. The geometric spin under quasi-resonant light exposure undergoes a cyclic evolution in the spin–orbit space, and acquires a geometric phase or holonomy that results in rotations about an arbitrary axis by any angle defined by the light polarization and detuning. This enables universal holonomic quantum gates with a single operation. We demonstrate a complete set of Pauli quantum gates using the geometric spin preparation and readout techniques. The new scheme opens a path to holonomic quantum computers and repeaters.

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Figure 1: Optical geometric spin rotation.
Figure 2: Experimental procedure and characterization of the NV centre.
Figure 3: Optical geometric spin rotation.
Figure 4: Simulated fidelity tolerance of the holonomic quantum gates.

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References

  1. Sekiguchi, Y. et al. Geometric spin echo under zero field. Nat. Commun. 7, 11668 (2016).

    Article  ADS  Google Scholar 

  2. Pancharatnam, S. Generalized theory of interference, and its applications. Proc. Indian Acad. Sci. 44, 247–262 (1956).

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. Anandan, J. Non-adiabatic non-Abelian geometric phase. Phys. Lett. A 133, 171–175 (1988).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  6. Wang, X.-B. & Matsumoto, K. Nonadiabatic conditional geometric phase shift with NMR. Phys. Rev. Lett. 87, 097901 (2001).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Feng, G., Xu, G. & Long, G. Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110, 190501 (2013).

    Article  ADS  Google Scholar 

  10. Abdumalikov, A. A. Jr et al. Experimental realization of non-Abelian non-adiabatic geometric gates. Nature 496, 482–485 (2013).

    Article  ADS  Google Scholar 

  11. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003).

    Article  ADS  Google Scholar 

  12. Toyoda, K., Uchida, K., Noguchi, A., Haze, S. & Urabe, S. Realization of holonomic single-qubit operations. Phys. Rev. A 87, 052307 (2013).

    Article  ADS  Google Scholar 

  13. Economou, S. E. & Reinecke, T. L. Theory of fast optical spin rotation in a quantum dot based on geometric phases and trapped states. Phys. Rev. Lett. 99, 217401 (2007).

    Article  ADS  Google Scholar 

  14. Greilich, A. et al. Ultrafast optical rotations of electron spins in quantum dots. Nat. Phys. 5, 262–266 (2009).

    Article  Google Scholar 

  15. 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).

    Article  ADS  Google Scholar 

  16. Zu, C. et al. Experimental realization of universal geometric quantum gates with solid-state spins. Nature 514, 72–75 (2014).

    Article  ADS  Google Scholar 

  17. Yale, C. G. et al. Optical manipulation of the Berry phase in a solid-state spin qubit. Nat. Photon. 10, 184–189 (2016).

    Article  ADS  Google Scholar 

  18. Sjöqvist, E. A new phase in quantum computation. Physics 1, 35 (2008).

    Article  Google Scholar 

  19. Sjöqvist, E. et al. Non-adiabatic holonomic quantum computation. New J. Phys. 14, 103035 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  20. Kosaka, H. et al. Coherent transfer of light polarization to electron spins in a semiconductor. Phys. Rev. Lett. 100, 096602 (2008).

    Article  ADS  Google Scholar 

  21. Kosaka, H. et al. Spin state tomography of optically injected electrons in a semiconductor. Nature 457, 702–705 (2009).

    Article  ADS  Google Scholar 

  22. Kosaka, H. & Niikura, N. Entangled absorption of a single photon with a single spin in diamond. Phys. Rev. Lett. 114, 053603 (2015).

    Article  ADS  Google Scholar 

  23. Yang, S. et al. High-fidelity transfer and storage of photon states in a single nuclear spin. Nat. Photon. 10, 507–511 (2016).

    Article  ADS  Google Scholar 

  24. Maze, J. R. et al. Properties of nitrogen-vacancy centers in diamond: the group theoretic approach. New J. Phys. 13, 025025 (2011).

    Article  ADS  Google Scholar 

  25. Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  27. Berezovsky, J., Mikkelsen, M. H., Stoltz, N. G., Coldren, L. A. & Awschalom, D. D. Picosecond coherent optical manipulation of a single electron spin in a quantum dot. Science 320, 349–352 (2008).

    Article  ADS  Google Scholar 

  28. Press, D., Ladd, T. D., Zhang, B. & Yamamoto, Y. Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218–221 (2008).

    Article  ADS  Google Scholar 

  29. Buckley, B. B., Fuchs, G. D., Bassett, L. C. & Awschalom, D. D. Spin-light coherence for single-spin measurement and control in diamond. Science 330, 1212–1215 (2010).

    Article  ADS  Google Scholar 

  30. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  31. Scharfenberger, B., Kosaka, H., Munro, W. J. & Nemoto, K. Absorption-based quantum communication with NV centres. New J. Phys. 17, 103012 (2015).

    Article  ADS  Google Scholar 

  32. Howard, M. et al. Quantum process tomography and Linblad estimation of a solid-state qubit. New J. Phys. 8, 33–33 (2006).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank Y. Matsuzaki, B. Scharfenberger, K. Nemoto, W. Munro, N. Mizuochi, N. Yokoshi, F. Jelezko and J. Wrachtrup for discussions and experimental help. This work was supported by the National Institute of Information and Communications Technology (NICT) Quantum Repeater Project and by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (24244044, 16H06326, 16H01052) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) ‘Exploratory Challenge on Post-K computer’ project (Frontiers of Basic Science: Challenging the Limits).

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N.N. carried out the experiment. Y.S., R.K. and H.Ka. supported the experiment. Y.S. and H.Ko. analysed the data. Y.S. and H.Ko. wrote the manuscript. H.Ko. supervised the project. All authors discussed the results and commented on the manuscript.

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Correspondence to Hideo Kosaka.

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The authors declare no competing financial interests.

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Sekiguchi, Y., Niikura, N., Kuroiwa, R. et al. Optical holonomic single quantum gates with a geometric spin under a zero field. Nature Photon 11, 309–314 (2017). https://doi.org/10.1038/nphoton.2017.40

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