Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Fast quantum logic gates with trapped-ion qubits


Quantum bits (qubits) based on individual trapped atomic ions are a promising technology for building a quantum computer1. The elementary operations necessary to do so have been achieved with the required precision for some error-correction schemes2,3,4. However, the essential two-qubit logic gate that is used to generate quantum entanglement has hitherto always been performed in an adiabatic regime (in which the gate is slow compared with the characteristic motional frequencies of the ions in the trap3,4,5,6,7), resulting in logic speeds of the order of 10 kilohertz. There have been numerous proposals of methods for performing gates faster than this natural ‘speed limit’ of the trap8,9,10,11,12. Here we implement one such method11, which uses amplitude-shaped laser pulses to drive the motion of the ions along trajectories designed so that the gate operation is insensitive to the optical phase of the pulses. This enables fast (megahertz-rate) quantum logic that is robust to fluctuations in the optical phase, which would otherwise be an important source of experimental error. We demonstrate entanglement generation for gate times as short as 480 nanoseconds—less than a single oscillation period of an ion in the trap and eight orders of magnitude shorter than the memory coherence time measured in similar calcium-43 hyperfine qubits. The power of the method is most evident at intermediate timescales, at which it yields a gate error more than ten times lower than can be attained using conventional techniques; for example, we achieve a 1.6-microsecond-duration gate with a fidelity of 99.8 per cent. Faster and higher-fidelity gates are possible at the cost of greater laser intensity. The method requires only a single amplitude-shaped pulse and one pair of beams derived from a continuous-wave laser. It offers the prospect of combining the unrivalled coherence properties2,13, operation fidelities2,3,4 and optical connectivity14 of trapped-ion qubits with the submicrosecond logic speeds that are usually associated with solid-state devices15,16.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Qubit states and Raman beam geometry.
Figure 2: Optical beat notes and motional trajectories of the ions for two initial optical phases (ϕ0 = 0 and ϕ0 = π/2).
Figure 3: Theoretical and experimental two-qubit gate errors.

Similar content being viewed by others


  1. Wineland, D. J. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl Inst. Stand. Technol. 103, 259–328 (1998)

    Article  CAS  Google Scholar 

  2. Harty, T. P. et al. High-fidelity preparation, gates, memory, and readout of a trapped-ion quantum bit. Phys. Rev. Lett. 113, 220501 (2014)

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  5. Turchette, Q. A. et al. Deterministic entanglement of two trapped ions. Phys. Rev. Lett. 81, 3631–3634 (1998)

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  7. Benhelm, J. et al. Towards fault-tolerant quantum computing with trapped ions. Nat. Phys. 4, 463–466 (2008)

    Article  CAS  Google Scholar 

  8. García-Ripoll, J. J., Zoller, P. & Cirac, J. I. Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. Phys. Rev. Lett. 91, 157901 (2003)

    Article  ADS  Google Scholar 

  9. Duan, L.-M. Scaling ion trap quantum computation through fast quantum gates. Phys. Rev. Lett. 93, 100502 (2004)

    Article  ADS  Google Scholar 

  10. García-Ripoll, J. J., Zoller, P. & Cirac, J. I. Coherent control of trapped ions using off-resonant lasers. Phys. Rev. A 71, 062309 (2005)

    Article  ADS  Google Scholar 

  11. Steane, A. M. et al. Pulsed force sequences for fast phase-insensitive quantum gates in trapped ions. New J. Phys. 16, 053049 (2014)

    Article  ADS  Google Scholar 

  12. Palmero, M. et al. Fast phase gates with trapped ions. Phys. Rev. A 95, 022328 (2017)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  14. Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007)

    Article  CAS  ADS  Google Scholar 

  15. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  17. Fowler, A. G. et al. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)

    Article  ADS  Google Scholar 

  18. Monroe, C. & Kim, J. Scaling the ion trap quantum processor. Science 339, 1164–1169 (2013)

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  20. Lin, Y. et al. Sympathetic electromagnetically-induced-transparency laser cooling of motional modes in an ion chain. Phys. Rev. Lett. 110, 153002 (2013)

    Article  CAS  ADS  Google Scholar 

  21. Bowler, R. et al. Coherent diabatic ion transport and separation in a multizone trap array. Phys. Rev. Lett. 109, 080502 (2012)

    Article  CAS  ADS  Google Scholar 

  22. Ruster, T. et al. Experimental realization of fast ion separation in segmented Paul traps. Phys. Rev. A 90, 033410 (2014)

    Article  ADS  Google Scholar 

  23. Noek, R. et al. High speed, high fidelity detection of an atomic hyperfine qubit. Opt. Lett. 38, 4735–4738 (2013)

    Article  ADS  Google Scholar 

  24. Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002)

    Article  CAS  ADS  Google Scholar 

  25. Turchette, Q. A. et al. Heating of trapped ions from the quantum ground state. Phys. Rev. A 61, 063418 (2000)

    Article  ADS  Google Scholar 

  26. Ruster, T. et al. A long-lived Zeeman trapped-ion qubit. Appl. Phys. B 122, 254 (2016)

    Article  ADS  Google Scholar 

  27. Wong-Campos, J. D., Moses, S. A., Johnson, K. G. & Monroe, C. Demonstration of two-atom entanglement with ultrafast optical pulses. Phys. Rev. Lett. 119, 230501 (2017)

    Article  CAS  ADS  Google Scholar 

  28. Ozeri, R. et al. Errors in trapped-ion quantum gates due to spontaneous photon scattering. Phys. Rev. A 75, 042329 (2007)

    Article  ADS  Google Scholar 

  29. McDonnell, M. J. et al. Long-lived mesoscopic entanglement outside the Lamb-Dicke regime. Phys. Rev. Lett. 98, 063603 (2007)

    Article  CAS  ADS  Google Scholar 

  30. Schmidt, P. O. et al. Spectroscopy using quantum logic. Science 309, 749–752 (2005)

    Article  CAS  ADS  Google Scholar 

  31. Meyer, V. et al. Measurement of the 1s–2s energy interval in muonium. Phys. Rev. Lett. 84, 1136–1139 (2000)

    Article  CAS  ADS  Google Scholar 

  32. Machnes, S. et al. Superfast laser cooling. Phys. Rev. Lett. 104, 183001 (2010)

    Article  CAS  ADS  Google Scholar 

  33. Schäfer, V. M. et al. Optical injection and spectral filtering of high-power ultraviolet laser diodes. Opt. Lett. 40, 4265–4268 (2015)

    Article  ADS  Google Scholar 

  34. Degenhardt, C. et al. Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms. IEEE Trans. Instrum. Meas. 54, 771–775 (2005)

    Article  CAS  Google Scholar 

  35. Gulde, S. T. Experimental Realization of Quantum Gates and the Deutsch–Josza Algorithm with Trapped 40Ca+-Ions. PhD thesis, Univ. Innsbruck (2003)

  36. Woodrow, S. R. Linear Paul Trap Design for High-fidelity, Scalable Quantum Information Processing. MSc thesis, Univ. Oxford (2015)

  37. Allcock, D. T. C. et al. Dark-resonance Doppler cooling and high fluorescence in trapped Ca-43 ions at intermediate magnetic field. New J. Phys. 18, 023043 (2016)

    Article  ADS  Google Scholar 

  38. Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000)

    Article  CAS  ADS  Google Scholar 

Download references


This work was supported by the UK EPSRC ‘Networked Quantum Information Technologies’ Hub, and the UK Defence, Science and Technology Laboratory. V.M.S. acknowledges funding from Balliol College, Oxford. C.J.B. acknowledges funding from Magdalen College, Oxford. We thank S. R. Woodrow for work on the trap design, T. P. Harty for contributions to the apparatus and W. Zhang for the loan of the AWG. We acknowledge the use of the University of Oxford Advanced Research Computing facility ( The experiments benefitted from the use of the ARTIQ control system (

Author information

Authors and Affiliations



C.J.B. performed the numerical modelling. V.M.S. and C.J.B. designed and performed the experiments and analysed the data. K.T. built the ion trap and characterized the fast AOMs. L.J.S. and T.G.B. built optical and control systems. V.M.S., C.J.B., A.M.S. and D.M.L. wrote the manuscript, which all authors discussed.

Corresponding author

Correspondence to D. M. Lucas.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Table 1 Gate parameters used for the fastest gate (seven segments) and for the highest-fidelity gate (five segments)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing