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# Deterministic multi-qubit entanglement in a quantum network

## Abstract

The generation of high-fidelity distributed multi-qubit entanglement is a challenging task for large-scale quantum communication and computational networks1,2,3,4. The deterministic entanglement of two remote qubits has recently been demonstrated with both photons5,6,7,8,9,10 and phonons11. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily owing to limited state-transfer fidelities. Here we report a quantum network comprising two superconducting quantum nodes connected by a one-metre-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the cable to one qubit in each node, we transfer quantum states between the nodes with a process fidelity of 0.911 ± 0.008. We also prepare a three-qubit Greenberger–Horne–Zeilinger (GHZ) state12,13,14 in one node and deterministically transfer this state to the other node, with a transferred-state fidelity of 0.656 ± 0.014. We further use this system to deterministically generate a globally distributed two-node, six-qubit GHZ state with a state fidelity of 0.722 ± 0.021. The GHZ state fidelities are clearly above the threshold of 1/2 for genuine multipartite entanglement15, showing that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers16,17.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank P. J. Duda, A. Clerk and K. J. Satzinger for discussions. We thank W. D. Oliver and G. Calusine at MIT Lincoln Lab for providing the travelling-wave parametric amplifier (TWPA) used in this work. Devices and experiments were supported by the Air Force Office of Scientific Research and the Army Research Laboratory. É.D. was supported by LDRD funds from Argonne National Laboratory; A.N.C. was supported in part by the DOE, Office of Basic Energy Sciences, and D.I.S. acknowledges support from the David and Lucile Packard Foundation. This work was partially supported by the University of Chicago’s MRSEC (NSF award DMR-2011854) and made use of the Pritzker Nanofabrication Facility, which receives support from SHyNE, a node of the National Science Foundation’s National Nanotechnology Coordinated Infrastructure (NSF grant number NNCI1542205), with additional support from NSF QLCI for HQAN (NSF award 2016136).

## Author information

Authors

### Contributions

Y.Z. designed and fabricated the devices, performed the measurement and analysed the data. H.-S.C. provided help with the measurement. A.B. and É.D. provided help with the infrastructure setup. A.N.C. and D.I.S. advised on all efforts. All authors contributed to discussions and production of the manuscript.

### Corresponding author

Correspondence to Andrew N. Cleland.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Damian Markham 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 Figures S1–11 and Supplementary Tables S1–3.

## Rights and permissions

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Zhong, Y., Chang, HS., Bienfait, A. et al. Deterministic multi-qubit entanglement in a quantum network. Nature 590, 571–575 (2021). https://doi.org/10.1038/s41586-021-03288-7

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• DOI: https://doi.org/10.1038/s41586-021-03288-7

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