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:

Multi-element logic gates for trapped-ion qubits


Precision control over hybrid physical systems at the quantum level is important for the realization of many quantum-based technologies. In the field of quantum information processing (QIP) and quantum networking, various proposals discuss the possibility of hybrid architectures1 where specific tasks are delegated to the most suitable subsystem. For example, in quantum networks, it may be advantageous to transfer information from a subsystem that has good memory properties to another subsystem that is more efficient at transporting information between nodes in the network. For trapped ions, a hybrid system formed of different species introduces extra degrees of freedom that can be exploited to expand and refine the control of the system. Ions of different elements have previously been used in QIP experiments for sympathetic cooling2, creation of entanglement through dissipation3, and quantum non-demolition measurement of one species with another4. Here we demonstrate an entangling quantum gate between ions of different elements which can serve as an important building block of QIP, quantum networking, precision spectroscopy, metrology, and quantum simulation. A geometric phase gate between a 9Be+ ion and a 25Mg+ ion is realized through an effective spin–spin interaction generated by state-dependent forces induced with laser beams5,6,7,8,9. Combined with single-qubit gates and same-species entangling gates, this mixed-element entangling gate provides a complete set of gates over such a hybrid system for universal QIP10,11,12. Using a sequence of such gates, we demonstrate a CNOT (controlled-NOT) gate and a SWAP gate13. We further demonstrate the robustness of these gates against thermal excitation and show improved detection in quantum logic spectroscopy14. We also observe a strong violation of a CHSH (Clauser–Horne–Shimony–Holt)-type Bell inequality15 on entangled states composed of different ion species.

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: Configuration of laser beams for the mixed-element entangling gate.
Figure 2: Pulse sequences for logic gates.
Figure 3: Robustness of quantum logic readout against thermal excitation.
Figure 4: Ramsey experiments with SWAP gate.

Similar content being viewed by others


  1. Wallquist, M., Hammerer, K., Rabl, P., Lukin, M. & Zoller, P. Hybrid quantum devices and quantum engineering. Phys. Scr. T137, 014001 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Lin, Y. et al. Dissipative production of a maximally entangled steady state of two quantum bits. Nature 504, 415–418 (2013)

    Article  CAS  ADS  Google Scholar 

  4. Hume, D. B. et al. High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements. Phys. Rev. Lett. 99, 120502 (2007)

    Article  CAS  ADS  Google Scholar 

  5. Sørensen, A. & Mølmer, K. Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82, 1971–1974 (1999)

    Article  ADS  Google Scholar 

  6. Sørensen, A. & Mølmer, K. Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62, 022311 (2000)

    Article  ADS  Google Scholar 

  7. Milburn, G. J., Schneider, S. & James, D. F. V. Ion trap quantum computing with warm ions. Fortschr. Phys. 48, 801–810 (2000)

    Article  CAS  Google Scholar 

  8. Solano, E., de Matos Filho, R. L. & Zagury, N. Deterministic Bell states and measurement of the motional state of two trapped ions. Phys. Rev. A 59, R2539–R2543 (1999)

    Article  CAS  ADS  Google Scholar 

  9. 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 

  10. Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)

    Article  CAS  ADS  Google Scholar 

  11. Bremner, M. J. et al. Practical scheme for quantum computation with any two-qubit entangling gate. Phys. Rev. Lett. 89, 247902 (2002)

    Article  ADS  Google Scholar 

  12. Zhang, J., Vala, J., Sastry, S. & Whaley, K. B. Exact two-qubit universal quantum circuit. Phys. Rev. Lett. 91, 027903 (2003)

    Article  ADS  Google Scholar 

  13. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 23 (Cambridge Univ. Press, 2000)

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

    Article  CAS  ADS  Google Scholar 

  15. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  16. Monroe, C. et al. Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014)

    Article  ADS  Google Scholar 

  17. Moehring, D. L. et al. Quantum networking with photons and trapped atoms. J. Opt. Soc. Am. B 24, 300–315 (2007)

    Article  CAS  ADS  Google Scholar 

  18. 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 

  19. Schulte, M., Lörch, N., Leroux, I. D., Schmidt, P. O. & Hammerer, K. Quantum algorithmic readout in multi-ion clocks. Preprint at (2015)

  20. Blakestad, R. B. et al. Near-ground-state transport of trapped-ion qubits through a multidimensional array. Phys. Rev. A 84, 033314 (2011)

    Article  Google Scholar 

  21. Langer, C. et al. Long-lived qubit memory using atomic ions. Phys. Rev. Lett. 95, 060502 (2005)

    Article  CAS  ADS  Google Scholar 

  22. Lee, P. J. et al. Phase control of trapped ion quantum gates. J. Opt. B 7, S371–S383 (2005)

    Article  CAS  Google Scholar 

  23. Monroe, C. et al. Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy. Phys. Rev. Lett. 75, 4011–4014 (1995)

    Article  CAS  ADS  MathSciNet  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  25. Rowe, M. A. et al. Experimental violation of a Bell’s inequality with efficient detection. Nature 409, 791–794 (2001)

    Article  CAS  ADS  Google Scholar 

  26. 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 

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

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  29. Chou, C. W., Hume, D. B., Koelemeij, J. C. J., Wineland, D. J. & Rosenband, T. Frequency comparison of two high-accuracy Al+ optical clocks. Phys. Rev. Lett. 104, 070802 (2010)

    Article  CAS  ADS  Google Scholar 

  30. Ballance, C. J. et al. Hybrid quantum logic and a test of Bell’s inequality using two different atomic isotopes. Nature (this issue)

  31. Levitt, M. H. Composite pulses. Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986)

    Article  CAS  ADS  Google Scholar 

  32. Huang, P. & Leibfried, D. Achromatic catadioptric microscope objective in deep ultraviolet with long working distance. Proc. SPIE 5524, 125–133 (2004)

    Article  ADS  Google Scholar 

Download references


We thank J. Bollinger and D. Hume for comments on the manuscript. This work was supported by the Office of the Director of National Intelligence (ODNI) Intelligence Advanced Research Projects Activity (IARPA), ONR, and the NIST Quantum Information Program. Y.W. was supported by the US Army Research Office through MURI grant W911NF-11-1-0400. This paper is a contribution by NIST and not subject to US copyright.

Author information

Authors and Affiliations



T.R.T. and J.P.G. conceived and designed the experiments, developed components of the experimental apparatus, and collected and analysed data. T.R.T. wrote the manuscript. Y.L., Y.W., and R.B. contributed to the development of experimental apparatus. D.L. and D.J.W. directed the experiment. All authors provided important suggestions for the experiments, discussed the results, and contributed to the editing of the manuscript.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides

Source data

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

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