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# High-fidelity laser-free universal control of trapped ion qubits

## Abstract

Universal control of multiple qubits—the ability to entangle qubits and to perform arbitrary individual qubit operations1—is a fundamental resource for quantum computing2, simulation3 and networking4. Qubits realized in trapped atomic ions have shown the highest-fidelity two-qubit entangling operations5,6,7 and single-qubit rotations8 so far. Universal control of trapped ion qubits has been separately demonstrated using tightly focused laser beams9,10,11,12 or by moving ions with respect to laser beams13,14,15, but at lower fidelities. Laser-free entangling methods16,17,18,19,20 may offer improved scalability by harnessing microwave technology developed for wireless communications, but so far their performance has lagged the best reported laser-based approaches. Here we demonstrate high-fidelity laser-free universal control of two trapped-ion qubits by creating both symmetric and antisymmetric maximally entangled states with fidelities of $${1}_{-0.0017}^{+0}$$ and $${0.9977}_{-0.0013}^{+0.0010}$$, respectively (68 per cent confidence level), corrected for initialization error. We use a scheme based on radiofrequency magnetic field gradients combined with microwave magnetic fields that is robust against multiple sources of decoherence and usable with essentially any trapped ion species. The scheme has the potential to perform simultaneous entangling operations on multiple pairs of ions in a large-scale trapped-ion quantum processor without increasing control signal power or complexity. Combining this technology with low-power laser light delivered via trap-integrated photonics21,22 and trap-integrated photon detectors for qubit readout23,24 provides an opportunity for scalable, high-fidelity, fully chip-integrated trapped-ion quantum computing.

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## Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

## Code availability

All simulation code or analysis code that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank C. J. Ballance, T. P. Harty, J. P. Gaebler, S. B. Libby, D. M. Lucas, V. M. Schäfer and T. R. Tan for helpful discussions. We thank M. Affolter and A. L. Collopy for insightful comments on the manuscript. At the time the work was performed, R.S., S.C.B., H.M.K., A.K., and D.T.C.A. were supported as associates in the Professional Research Experience Program (PREP) operated jointly by the National Institute of Standards and Technology (NIST) and the University of Colorado Boulder under award number 70NANB18H006 from the US Department of Commerce, NIST. This work was supported by the NIST Quantum Information Program and ONR.

## Author information

Authors

### Contributions

R.S. and H.M.K. carried out the experiments, assisted by S.C.B., D.T.C.A and D.H.S.; D.H.S., R.S., H.M.K., A.K. and R.T.S. analysed the data and performed numerical simulations, with support from E.K. and S.G.; D.T.C.A., D.H.S., R.S., S.C.B. and H.M.K. built and maintained the experimental apparatus; R.S. wrote the manuscript with input from all authors; A.C.W., D.L., D.H.S. and D.J.W. secured funding for the work; and D.H.S. and D.T.C.A. supervised the work with support from A.C.W., D.L., S.G., E.K. and D.J.W.

### Corresponding authors

Correspondence to R. Srinivas or D. H. Slichter.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Tracy Northup, Christian Roos and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Supplementary information

### Supplementary Information

This file contains Supplementary Sections 1–4, including Supplementary Figs. 1–5, Table 1 and References.

### Source Data

This file contains source data for Supplementary Fig. 3.

### Source Data

This file contains source data for Supplementary Fig. 4.

### Source Data

This file contains source data for Supplementary Fig. 5.

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Srinivas, R., Burd, S.C., Knaack, H.M. et al. High-fidelity laser-free universal control of trapped ion qubits. Nature 597, 209–213 (2021). https://doi.org/10.1038/s41586-021-03809-4

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• DOI: https://doi.org/10.1038/s41586-021-03809-4

• ### QDataSet, quantum datasets for machine learning

• Elija Perrier
• Akram Youssry
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Scientific Data (2022)

• ### Laser-free qubit control

• Giulia Pacchioni

Nature Reviews Materials (2021)