Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Device description.
Fig. 2: Quantum state transfer between node A and node B.
Fig. 3: Deterministic transfer of a three-qubit GHZ state.
Fig. 4: Deterministic generation of multi-qubit entanglement in a quantum network.

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.

References

  1. 1.

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 2nd edn (Cambridge Univ. Press, 2010).

  2. 2.

    Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999).

    ADS  CAS  Google Scholar 

  3. 3.

    Duan, L.-M., Lukin, M. D., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).

    ADS  CAS  PubMed  Google Scholar 

  4. 4.

    Jiang, L., Taylor, J. M., Sørensen, A. S. & Lukin, M. D. Distributed quantum computation based on small quantum registers. Phys. Rev. A 76, 062323 (2007).

    ADS  Google Scholar 

  5. 5.

    Kurpiers, P. et al. Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558, 264–267 (2018).

    ADS  CAS  PubMed  Google Scholar 

  6. 6.

    Axline, C. J. et al. On-demand quantum state transfer and entanglement between remote microwave cavity memories. Nat. Phys. 14, 705–710 (2018).

    CAS  Google Scholar 

  7. 7.

    Campagne-Ibarcq, P. et al. Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions. Phys. Rev. Lett. 120, 200501 (2018).

    ADS  CAS  PubMed  Google Scholar 

  8. 8.

    Leung, N. et al. Deterministic bidirectional communication and remote entanglement generation between superconducting qubits. npj Quantum Inf. 5, 18 (2019).

    ADS  Google Scholar 

  9. 9.

    Zhong, Y. P. et al. Violating Bell’s inequality with remotely connected superconducting qubits. Nat. Phys. 15, 741–744 (2019).

    CAS  Google Scholar 

  10. 10.

    Humphreys, P. C. et al. Deterministic delivery of remote entanglement on a quantum network. Nature 558, 268–273 (2018); publisher correction 562, E2 (2018).

    ADS  CAS  PubMed  Google Scholar 

  11. 11.

    Bienfait, A. et al. Phonon-mediated quantum state transfer and remote qubit entanglement. Science 364, 368–371 (2019).

    ADS  CAS  PubMed  Google Scholar 

  12. 12.

    Greenberger, D. M., Horne, M. A., Shimony, A. & Zeilinger, A. Bell’s theorem without inequalities. Am. J. Phys. 58, 1131–1143 (1990).

    ADS  MathSciNet  MATH  Google Scholar 

  13. 13.

    Neeley, M. et al. Generation of three-qubit entangled states using superconducting phase qubits. Nature 467, 570–573 (2010).

    ADS  CAS  PubMed  Google Scholar 

  14. 14.

    DiCarlo, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010).

    ADS  CAS  PubMed  Google Scholar 

  15. 15.

    Gühne, O. & Seevinck, M. Separability criteria for genuine multiparticle entanglement. New J. Phys. 12, 053002 (2010).

    ADS  MATH  Google Scholar 

  16. 16.

    Monroe, C. et al. Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014).

    ADS  Google Scholar 

  17. 17.

    Chou, K. S. et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 368–373 (2018).

    ADS  CAS  PubMed  Google Scholar 

  18. 18.

    Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).

    ADS  CAS  PubMed  Google Scholar 

  19. 19.

    Rosenberg, D. et al. Solid-state qubits: 3D integration and packaging. IEEE Microw. Mag. 21, 72–85 (2020).

    Google Scholar 

  20. 20.

    Magnard, P. et al. Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems. Phys. Rev. Lett. 125, 260502 (2020).

    ADS  CAS  PubMed  Google Scholar 

  21. 21.

    Bochmann, J., Vainsencher, A., Awschalom, D. D. & Cleland, A. N. Nanomechanical coupling between microwave and optical photons. Nat. Phys. 9, 712–716 (2013).

    CAS  Google Scholar 

  22. 22.

    Mirhosseini, M., Sipahigil, A., Kalaee, M. & Painter, O. Superconducting qubit to optical photon transduction. Nature 588, 599–603 (2020).

    ADS  CAS  PubMed  Google Scholar 

  23. 23.

    Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

    ADS  CAS  PubMed  Google Scholar 

  24. 24.

    Liao, S.-K. et al. Satellite-to-ground quantum key distribution. Nature 549, 43–47 (2017).

    ADS  CAS  PubMed  Google Scholar 

  25. 25.

    Chang, H.-S. et al. Remote entanglement via adiabatic passage using a tunably-dissipative quantum communication system. Phys. Rev. Lett. 124, 240502 (2020).

    ADS  CAS  PubMed  Google Scholar 

  26. 26.

    Burkhart, L. D. et al. Error-detected state transfer and entanglement in a superconducting quantum network. Preprint at https://arxiv.org/abs/2004.06168 (2020).

  27. 27.

    Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014).

    ADS  PubMed  Google Scholar 

  28. 28.

    Wang, Y.-D. & Clerk, A. A. Using dark modes for high-fidelity optomechanical quantum state transfer. New J. Phys. 14, 105010 (2012).

    ADS  Google Scholar 

  29. 29.

    Strauch, F. W. et al. Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003).

    ADS  PubMed  Google Scholar 

  30. 30.

    Julsgaard, B., Kozhekin, A. & Polzik, E. S. Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400–403 (2001).

    ADS  CAS  PubMed  Google Scholar 

  31. 31.

    Chou, C.-W. et al. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature 438, 828–832 (2005).

    ADS  CAS  PubMed  Google Scholar 

  32. 32.

    Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007).

    ADS  CAS  PubMed  Google Scholar 

  33. 33.

    Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012).

    ADS  CAS  PubMed  Google Scholar 

  34. 34.

    Lee, K. C. et al. Entangling macroscopic diamonds at room temperature. Science 334, 1253–1256 (2011).

    ADS  CAS  PubMed  Google Scholar 

  35. 35.

    Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).

    ADS  CAS  PubMed  Google Scholar 

  36. 36.

    Roch, N. et al. Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits. Phys. Rev. Lett. 112, 170501 (2014).

    ADS  CAS  PubMed  Google Scholar 

  37. 37.

    Narla, A. et al. Robust concurrent remote entanglement between two superconducting qubits. Phys. Rev. X 6, 031036 (2016).

    Google Scholar 

  38. 38.

    Dickel, C. et al. Chip-to-chip entanglement of transmon qubits using engineered measurement fields. Phys. Rev. B 97, 064508 (2018).

    ADS  CAS  Google Scholar 

  39. 39.

    Kurpiers, P. et al. Quantum communication with time-bin encoded microwave photons. Phys. Rev. Appl. 12, 044067 (2019).

    ADS  CAS  Google Scholar 

  40. 40.

    Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007).

    ADS  PubMed  Google Scholar 

  41. 41.

    Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).

    ADS  CAS  PubMed  Google Scholar 

  42. 42.

    Baksic, A., Ribeiro, H. & Clerk, A. A. Speeding up adiabatic quantum state transfer by using dressed states. Phys. Rev. Lett. 116, 230503 (2016).

    ADS  PubMed  Google Scholar 

  43. 43.

    Zhou, B. B. et al. Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system. Nat. Phys. 13, 330–334 (2017).

    CAS  Google Scholar 

  44. 44.

    Cirac, J. I., Zoller, P., Kimble, H. J. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).

    ADS  CAS  Google Scholar 

  45. 45.

    Korotkov, A. N. Flying microwave qubits with nearly perfect transfer efficiency. Phys. Rev. B 84, 014510 (2011).

    ADS  Google Scholar 

  46. 46.

    Sete, E. A., Mlinar, E. & Korotkov, A. N. Robust quantum state transfer using tunable couplers. Phys. Rev. B 91, 144509 (2015).

    ADS  Google Scholar 

  47. 47.

    Yin, Y. et al. Catch and release of microwave photon states. Phys. Rev. Lett. 110, 107001 (2013).

    ADS  PubMed  Google Scholar 

  48. 48.

    Wenner, J. et al. Catching time-reversed microwave coherent state photons with 99.4% absorption efficiency. Phys. Rev. Lett. 112, 210501 (2014).

    ADS  Google Scholar 

  49. 49.

    Srinivasan, S. J. et al. Time-reversal symmetrization of spontaneous emission for quantum state transfer. Phys. Rev. A 89, 033857 (2014).

    ADS  Google Scholar 

  50. 50.

    Pechal, M. et al. Microwave-controlled generation of shaped single photons in circuit quantum electrodynamics. Phys. Rev. X 4, 041010 (2014).

    Google Scholar 

  51. 51.

    Zeytinoğlu, S. et al. Microwave-induced amplitude-and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics. Phys. Rev. A 91, 043846 (2015).

    ADS  Google Scholar 

  52. 52.

    Xiang, Z. L., Zhang, M., Jiang, L. & Rabl, P. Intracity quantum communication via thermal microwave networks. Phys. Rev. X 7, 011035 (2017).

    Google Scholar 

  53. 53.

    Vermersch, B., Guimond, P.-O., Pichler, H. & Zoller, P. Quantum state transfer via noisy photonic and phononic waveguides. Phys. Rev. Lett. 118, 133601 (2017).

    ADS  CAS  PubMed  Google Scholar 

  54. 54.

    Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006).

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  55. 55.

    Neeley, M. et al. Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nat. Phys. 4, 523–526 (2008).

    CAS  Google Scholar 

Download references

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

Affiliations

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.

Additional information

Peer review information Nature thanks Damian Markham and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

This file contains Supplementary Figures S1–11 and Supplementary Tables S1–3.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing