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# Implementation of XY entangling gates with a single calibrated pulse

## Abstract

Near-term applications of quantum information processors will rely on optimized circuit implementations to minimize the circuit depth, reducing the negative impact of gate errors in noisy intermediate-scale quantum (NISQ) computers. One approach to minimize the circuit depth is the use of a more expressive gate set. The XY two-qubit gate set can offer reductions in circuit depth for generic circuits, as well as improved performance for problems with symmetries that match the gate set. Here we report an implementation of the family of XY entangling gates in a transmon-based superconducting qubit architecture using a gate decomposition strategy that requires only a single calibrated pulse. The approach allows us to implement XY gates with a median fidelity of 97.35 ± 0.17%, approaching the coherence-limited gate fidelity of the two-qubit pair. We also show that the XY gate can be used to implement instances of the quantum approximate optimization algorithm, achieving a reduction in circuit depth of ~30% compared with the use of CZ gates only. Finally, we extend our decomposition scheme to other gate families, which can allow for further reductions in circuit depth.

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## Data availability

The experimental data and circuits used for the QAOA experiment are provided in ref. 54.

## Code availability

The code used for data analysis is provided in ref. 54.

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## Acknowledgements

Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. We thank the Rigetti quantum software team for providing tooling support, the Rigetti fabrication team for manufacturing the device, the Rigetti technical operations team for fridge build out and maintenance, the Rigetti cryogenic hardware team for providing the chip packaging, and the Rigetti control systems and embedded software teams for creating the Rigetti AWG control system. We additionally thank M. Scheer and E. Peterson for convincing us that the composite pulse decomposition would be a valid implementation of the XY gates. We thank P. Karalekas for his help in setting up the QAOA demo. Finally, we thank Z. Wang, N.C. Rubin, E.G. Rieffel and D. Venturelli for valuable conversations.

## Author information

Authors

### Contributions

D.M.A., C.A.R. and M.P.d.S. drafted the manuscript, puzzled out the implementation of frame phases and brainstormed effective ways to benchmark the gate. D.M.A. performed the experiments. N.D. provided theory to describe the turn-on phase of shaped flux pulses and the formula for the coherence-limited gate fidelity. B.R.J., C.A.R. and M.P.d.S. organized the effort.

### Corresponding author

Correspondence to Nicolas Didier.

## Ethics declarations

### Competing interests

N.D. is an employee of Rigetti Computing. All other authors declare no competing interests.

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

## Extended data

### Extended Data Fig. 1 Circuit identities.

Circuit diagrams visually representing equations (3)–(9) in the main text. The diagrams are numbered according to the corresponding equation. Time flows from left to right in these diagrams—that is, the leftmost operations are applied first.

## Rights and permissions

Reprints and Permissions

Abrams, D.M., Didier, N., Johnson, B.R. et al. Implementation of XY entangling gates with a single calibrated pulse. Nat Electron 3, 744–750 (2020). https://doi.org/10.1038/s41928-020-00498-1

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• DOI: https://doi.org/10.1038/s41928-020-00498-1

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