# A two-qubit gate between phosphorus donor electrons in silicon

## Abstract

Electron spin qubits formed by atoms in silicon have large (tens of millielectronvolts) orbital energies and weak spin–orbit coupling, giving rise to isolated electron spin ground states with coherence times of seconds1,2. High-fidelity (more than 99.9 per cent) coherent control of such qubits has been demonstrated3, promising an attractive platform for quantum computing. However, inter-qubit coupling—which is essential for realizing large-scale circuits in atom-based qubits—has not yet been achieved. Exchange interactions between electron spins4,5 promise fast (gigahertz) gate operations with two-qubit gates, as recently demonstrated in gate-defined silicon quantum dots6,7,8,9,10. However, creating a tunable exchange interaction between two electrons bound to phosphorus atom qubits has not been possible until now. This is because it is difficult to determine the atomic distance required to turn the exchange interaction on and off while aligning the atomic circuitry for high-fidelity, independent spin readout. Here we report a fast (about 800 picoseconds) $$\sqrt{{\bf{SWAP}}}$$ two-qubit exchange gate between phosphorus donor electron spin qubits in silicon using independent single-shot spin readout with a readout fidelity of about 94 per cent on a complete set of basis states. By engineering qubit placement on the atomic scale, we provide a route to the realization and efficient characterization of multi-qubit quantum circuits based on donor qubits in silicon.

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## Data availability

The data pertaining to this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

The research was supported by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project number CE170100012), the US Army Research Office under contract number W911NF-17-1-0202 and Silicon Quantum Computing Pty Ltd. M.Y.S. acknowledges an Australian Research Council Laureate Fellowship. This work was performed in part at the NSW node of the Australian National Fabrication Facility.

### Reviewer information

Nature thanks Benjamin D’Anjou and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

Y.H., S.K.G. and L.K. fabricated the device. Y.H., S.K.G. and D.K. performed the measurements. Y.H., S.K.G., D.K, L.K. and J.G.K. analysed the data. The manuscript was written by Y.H., S.K.G. and M.Y.S. with input from all other authors. M.Y.S. conceived and supervised the project.

### Corresponding author

Correspondence to M. Y. Simmons.

## Ethics declarations

### Competing interests

M.Y.S. is a director of the company Silicon Quantum Computing Pty Ltd.

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 Fig. 1 Determination of the number of donors in a qubit from the quantum dot charging energies.

a, RF-SET Coulomb diamonds. b, Gate–gate map around the (1, 3) ↔ (2, 2) charge transition and definitions of $${\rm{\delta }}{V}_{{\rm{g}}}^{{\rm{D}}{\rm{D}}}$$, $${\rm{\Delta }}{V}_{{\rm{g}}}^{{\rm{S}}}$$, $${\rm{\delta }}{V}_{{\rm{g}}}^{{\rm{S}}}$$ and $${\rm{\delta }}{V}_{{\rm{g}}}^{{\rm{D}}}$$. c, Gate–gate map for the regime with two electrons on donor qubits and definition of $${\rm{\Delta }}{V}_{{\rm{g}}}^{{\rm{D}}}$$.

### Extended Data Fig. 2 Experimental set-up for the two-qubit gate in a millikelvin dilution refrigerator.

The schematic shows the electrical connections from the device to the control computer at the different temperature stages of the dilution refrigerator from the top to bottom. An STM image of the device attached to the cold finger of the refrigerator at 50 mK is shown in the lower orange pane. The RF-reflectormetry circuit attached to the device employs a variable attenuator (‘Var. Atten.’) to control the power coupled through a directional coupler (‘Dir. Cplr.’) and sent to the source contact of the SET (red lines). The blue line is for d.c. current/voltage measurements of the SET. The slow signals (black components) and fast signals (green components) are combined using bias tees at 50 mK before being sent to the left and right gate electrodes.

## Supplementary information

### Supplementary Information

This file contains Supplementary Information Sections 1–5, Supplementary Tables 1–3, Supplementary References and Supplementary Figures 1–4.

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He, Y., Gorman, S.K., Keith, D. et al. A two-qubit gate between phosphorus donor electrons in silicon. Nature 571, 371–375 (2019). https://doi.org/10.1038/s41586-019-1381-2

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