# 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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## Data availability

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

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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.

## Author information

Authors

### Contributions

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.

### Corresponding authors

Correspondence to Chi Zhang or Markus Hennrich.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

### Supplementary Information

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

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Reprints and Permissions

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