Submicrosecond entangling gate between trapped ions via Rydberg interaction

Abstract

Generating quantum entanglement in large systems on timescales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems1 with low-error entanglement gates operated within tens of microseconds using the vibrational motion of few-ion crystals2,3. To exceed the level of complexity tractable by classical computers the main challenge is to realize fast entanglement operations in crystals made up of many ions (large ion crystals)4. The strong dipole–dipole interactions in polar molecule5 and Rydberg atom6,7 systems allow much faster entangling gates, yet stable state-independent confinement comparable with trapped ions needs to be demonstrated in these systems8. Here we combine the benefits of these approaches: we report a two-ion entangling gate with 700-nanosecond gate time that uses the strong dipolar interaction between trapped Rydberg ions, which we use to produce a Bell state with 78 per cent fidelity. The sources of gate error are identified and a total error of less than 0.2 per cent is predicted for experimentally achievable parameters. Furthermore, we predict that residual coupling to motional modes contributes an approximate gate error of 10−4 in a large ion crystal of 100 ions. This provides a way to speed up and scale up trapped-ion quantum computers and simulators substantially.

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Fig. 1: Level scheme of 88Sr+ and the rotating dipole moment of a microwave-dressed Rydberg state.
Fig. 2: Tunable interaction between Rydberg ions.
Fig. 3: Experimental sequence of the Rydberg-interaction gate.
Fig. 4: Analysis of the two-ion state after the entangling gate operation.

Data availability

The datasets generated during and analysed during the current study are available from the corresponding authors on reasonable request.

References

  1. 1.

    Wineland, D. J. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998).

    CAS  Article  Google Scholar 

  2. 2.

    Ballance, C. J. et al. High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117, 060504 (2016).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Gaebler, J. P. et al. High-fidelity universal gate set for 9Be+ ion qubits. Phys. Rev. Lett. 117, 060505 (2016).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Hempel, C. et al. Quantum chemistry calculations on a trapped-ion quantum simulator. Phys. Rev. X 8, 031022 (2018).

    CAS  Google Scholar 

  5. 5.

    Anderegg, L. et al. Laser cooling of optically trapped molecules. Nat. Phys. 14, 890–893 (2018).

    CAS  Article  Google Scholar 

  6. 6.

    Wilk, T. et al. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104, 010502 (2010).

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Isenhower, L. et al. Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104, 010503 (2010).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Saffman, M. Quantum computing with atomic qubits and Rydberg interactions: progress and challenges. J. Phys. B 49, 202001 (2016).

    ADS  Article  Google Scholar 

  9. 9.

    Wang, Y. et al. Single-qubit quantum memory exceeding ten-minute coherence time. Nat. Photon. 11, 646–650 (2017).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602–605 (2004).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Wong-Campos, J. D. et al. Demonstration of two-atom entanglement with ultrafast optical pulses. Phys. Rev. Lett. 119, 230501 (2017).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Schäfer, V. M. et al. Fast quantum logic gates with trapped-ion qubits. Nature 555, 75–78 (2018).

    ADS  Article  Google Scholar 

  14. 14.

    Levine, H. et al. Parallel implementation of high-fidelity multiqubit gates with neutral atoms. Phys. Rev. Lett. 123, 170503 (2019).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Graham, T. M. et al. Rydberg mediated entanglement in a two-dimensional neutral atom qubit array. Phys. Rev. Lett. 123, 230501 (2019).

    ADS  CAS  Article  Google Scholar 

  16. 16.

    Zhang, S., Robicheaux, F. & Saffman, M. Magic-wavelength optical traps for Rydberg atoms. Phys. Rev. A 84, 043408 (2011).

    ADS  Article  Google Scholar 

  17. 17.

    Savard, T. A., O’Hara, K. M. & Thomas, J. E. Laser-noise-induced heating in far-off resonance optical traps. Phys. Rev. A 56, R1095 (1997).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Belyansky, R. et al. Nondestructive cooling of an atomic quantum register via state-insensitive Rydberg interactions. Phys. Rev. Lett. 123, 213603 (2019).

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

    ADS  CAS  Article  Google Scholar 

  20. 20.

    Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Müller, M. et al. Trapped Rydberg ions: from spin chains to fast quantum gates. New J. Phys. 10, 093009 (2008).

    ADS  Article  Google Scholar 

  22. 22.

    Feldker, T. et al. Rydberg excitation of a single trapped ion. Phys. Rev. Lett. 115, 173001 (2015).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    Higgins, G. et al. Single strontium Rydberg ion confined in a Paul trap. Phys. Rev. X 7, 021038 (2017).

    Google Scholar 

  24. 24.

    Higgins, G. et al. Coherent control of a single trapped Rydberg ion. Phys. Rev. Lett. 119, 220501 (2017).

    ADS  Article  Google Scholar 

  25. 25.

    Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313 (2010).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    Li, W. & Lesanovsky, I. Entangling quantum gate in trapped ions via Rydberg blockade. Appl. Phys. B 114, 37–44 (2014).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Urban, E. et al. Observation of Rydberg blockade between two atoms. Nat. Phys. 5, 110–114 (2009).

    CAS  Article  Google Scholar 

  28. 28.

    Gaëtan, A. et al. Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nat. Phys. 5, 115–118 (2009).

    Article  Google Scholar 

  29. 29.

    Rao, D. D. B. & Mølmer, K. Robust Rydberg-interaction gates with adiabatic passage. Phys. Rev. A 89, 030301 (2014).

    ADS  Article  Google Scholar 

  30. 30.

    Leibfried, D. et al. Creation of a six-atom ‘Schrödinger cat’ state. Nature 438, 639–642 (2005).

    ADS  CAS  Article  Google Scholar 

  31. 31.

    Higgins, G., Pokorny, F., Zhang, C. & Hennrich, M. Highly polarizable Rydberg ion in a Paul trap. Phys. Rev. Lett. 123, 153602 (2019).

    ADS  CAS  Article  Google Scholar 

  32. 32.

    Barrett, M. D. et al. Sympathetic cooling of 9Ba+ and 24Mg+ for quantum logic. Phys. Rev. A 68, 042302 (2003).

    ADS  Article  Google Scholar 

  33. 33.

    Tan, T. R. et al. Multi-element logic gates for trapped-ion qubits. Nature 528, 380–383 (2015).

    ADS  CAS  Article  Google Scholar 

  34. 34.

    Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709 (2002).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    Gambetta, F. M., Li, W., Schmidt-Kaler, F. & Lesanovsky, I. Engineering non-binary Rydberg interactions via electron-phonon coupling. Phys. Rev. Lett. 124, 043402 (2020).

    ADS  CAS  Article  Google Scholar 

  36. 36.

    Wüster, S. & Rost, J.-M. Rydberg aggregates. J. Phys. B 51, 032001 (2018).

    ADS  Article  Google Scholar 

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Acknowledgements

We thank K. Mølmer for discussions and suggestions for the gate scheme. We thank all members of the ERyQSenS consortium for discussions. This work was supported by the European Research Council under the European Unions Seventh Framework Programme/ERC grant agreement number 279508, the Swedish Research Council (Trapped Rydberg Ion Quantum Simulator), the QuantERA ERA-NET Cofund in Quantum Technologies (ERyQSenS), and the Knut & Alice Wallenberg Foundation (Photonic Quantum Information). I.L. and W.L. acknowledge support from the EPSRC through grant number EP/M014266/1 and grant number EP/R04340X/1 via the QuantERA project ERyQSenS. I.L. also gratefully acknowledges funding through the Royal Society Wolfson Research Merit Award.

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G.H., F.P. and M.H. built the experimental system. C.Z. and F.P. set up the microwave dressing and improved the ultraviolet laser system. A.P. set up ablation loading of ions and the camera software. C.Z. had the idea of combining microwave dressing and STIRAP excitation. C.Z. and G.H. carried out the measurements. C.Z. analysed the data. C.Z. and W.L. simulated the results. M.H. designed and administered the experiment, W.L. and I.L. calculated properties of atomic Rydberg states. W.L., I.L. and C.Z. analysed the scaling of the gate error. All authors contributed to discussions and the writing of the manuscript.

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Correspondence to Chi Zhang or Markus Hennrich.

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The authors declare no competing interests.

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Peer review information Nature thanks Kihwan Kim, Peter Maunz and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

This file contains Supplementary Sections 1-5, including Supplementary Figures 1-3, Supplementary Table 1 and Supplementary References.

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Zhang, C., Pokorny, F., Li, W. et al. Submicrosecond entangling gate between trapped ions via Rydberg interaction. Nature 580, 345–349 (2020). https://doi.org/10.1038/s41586-020-2152-9

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