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Resonant microwave-mediated interactions between distant electron spins


Nonlocal qubit interactions are a hallmark of advanced quantum information technologies1,2,3,4,5. The ability to transfer quantum states and generate entanglement over distances much larger than qubit length scales greatly increases connectivity and is an important step towards maximal parallelism and the implementation of two-qubit gates on arbitrary pairs of qubits6. Qubit-coupling schemes based on cavity quantum electrodynamics2,7,8 also offer the possibility of using high-quality-factor resonators as quantum memories3,9. Extending qubit interactions beyond the nearest neighbour is particularly beneficial for spin-based quantum computing architectures, which are limited by short-range exchange interactions10. Despite the rapidly maturing device technology for silicon spin qubits11,12,13,14,15,16, experimental progress towards achieving long-range spin–spin coupling has so far been restricted to interactions between individual spins and microwave photons17,18,19,20. Here we demonstrate resonant microwave-mediated coupling between two electron spins that are physically separated by more than four millimetres. An enhanced vacuum Rabi splitting is observed when both spins are tuned into resonance with the cavity, indicating a coherent interaction between the two spins and a cavity photon. Our results imply that microwave-frequency photons may be used to generate long-range two-qubit gates between spatially separated spins.

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Fig. 1: Cavity coupler for spins.
Fig. 2: Tuning two spatially separated spins into resonance.
Fig. 3: Resonant coupling of the two spins via a cavity photon.

Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.


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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  3. 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).

    Article  ADS  CAS  Google Scholar 

  4. Monroe, C. & Kim, J. Scaling the ion trap quantum processor. Science 339, 1164–1169 (2013).

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  6. Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454, 385–410 (1998).

    Article  ADS  Google Scholar 

  7. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    Article  ADS  CAS  Google Scholar 

  8. Trif, M., Golovach, V. N. & Loss, D. Spin dynamics in InAs nanowire quantum dots coupled to a transmission line. Phys. Rev. B 77, 045434 (2008).

    Article  ADS  CAS  Google Scholar 

  9. Pfaff, W. et al. Controlled release of multiphoton quantum states from a microwave cavity memory. Nat. Phys. 13, 882–887 (2017).

    Article  CAS  Google Scholar 

  10. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).

    Article  ADS  CAS  Google Scholar 

  11. Yoneda, J. et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102–106 (2018).

    Article  ADS  CAS  Google Scholar 

  12. Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).

    Article  ADS  CAS  Google Scholar 

  13. Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633–637 (2018).

    Article  ADS  CAS  Google Scholar 

  15. Fujita, T., Baart, T. A., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent shuttle of electron-spin states. npj Quant. Inf. 3, 22 (2017).

    Article  ADS  Google Scholar 

  16. Mills, A. R. et al. Shuttling a single charge across a one-dimensional array of silicon quantum dots. Nat. Commun. 10, 1063 (2019).

    Article  ADS  CAS  Google Scholar 

  17. Viennot, J. J., Dartiailh, M. C., Cottet, A. & Kontos, T. Coherent coupling of a single spin to microwave cavity photons. Science 349, 408–411 (2015).

    Article  ADS  CAS  Google Scholar 

  18. Mi, X. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018).

    Article  ADS  CAS  Google Scholar 

  19. Samkharadze, N. et al. Strong spin-photon coupling in silicon. Science 359, 1123–1127 (2018).

    Article  ADS  CAS  Google Scholar 

  20. Landig, A. J. et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018).

    Article  ADS  CAS  Google Scholar 

  21. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    Article  ADS  CAS  Google Scholar 

  22. Zajac, D. M., Hazard, T. M., Mi, X., Nielsen, E. & Petta, J. R. Scalable gate architecture for a one-dimensional array of semiconductor spin qubits. Phys. Rev. Appl. 6, 054013 (2016).

    Article  ADS  CAS  Google Scholar 

  23. Cottet, A. & Kontos, T. Spin quantum bit with ferromagnetic contacts for circuit QED. Phys. Rev. Lett. 105, 160502 (2010).

    Article  ADS  CAS  Google Scholar 

  24. Benito, M., Mi, X., Taylor, J. M., Petta, J. R. & Burkard, G. Input-output theory for spin-photon coupling in Si double quantum dots. Phys. Rev. B 96, 235434 (2017).

    Article  ADS  Google Scholar 

  25. Astner, T. et al. Coherent coupling of remote spin ensembles via a cavity bus. Phys. Rev. Lett. 118, 140502 (2017).

    Article  ADS  CAS  Google Scholar 

  26. Vandersypen, L. M. K. et al. Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent. npj Quant. Inf. 3, 34 (2017).

    Article  ADS  Google Scholar 

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This work was funded by Army Research Office grant W911NF-15-1-0149 and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4535. The devices were fabricated in the Princeton University Quantum Device Nanofabrication Laboratory. We thank L. Edge, J. Kerckhoff, T. Ladd and E. Pritchett of HRL Laboratories, LLC for providing the 28Si heterostructure used in these experiments, for device simulation support and for technical comments on the manuscript. We acknowledge discussions with M. Benito and G. Burkard.

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Authors and Affiliations



F.B. and X.G.C. carried out the measurements with input from X.M. and J.R.P.; F.B. and X.M. fabricated the device. M.J.G. provided theory support. F.B., X.G.C., M.J.G. and J.R.P. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to J. R. Petta.

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Competing interests

X.M., J.R.P. and Princeton University have filed a non-provisional patent application related to spin–photon transduction (US patent application number 16534431).

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Peer review information Nature thanks Hendrik Bluhm 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.

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Supplementary Information

This file contains master equation theory, fits of data to the theory, and measurements of the angular dependence of the spin-photon coupling rates.

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Borjans, F., Croot, X.G., Mi, X. et al. Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195–198 (2020).

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