Abstract
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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
References
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).
Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).
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).
Monroe, C. & Kim, J. Scaling the ion trap quantum processor. Science 339, 1164–1169 (2013).
Axline, C. J. et al. On-demand quantum state transfer and entanglement between remote microwave cavity memories. Nat. Phys. 14, 705–710 (2018).
Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454, 385–410 (1998).
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).
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).
Pfaff, W. et al. Controlled release of multiphoton quantum states from a microwave cavity memory. Nat. Phys. 13, 882–887 (2017).
Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).
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).
Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).
Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018).
Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633–637 (2018).
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).
Mills, A. R. et al. Shuttling a single charge across a one-dimensional array of silicon quantum dots. Nat. Commun. 10, 1063 (2019).
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).
Mi, X. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018).
Samkharadze, N. et al. Strong spin-photon coupling in silicon. Science 359, 1123–1127 (2018).
Landig, A. J. et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018).
Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).
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).
Cottet, A. & Kontos, T. Spin quantum bit with ferromagnetic contacts for circuit QED. Phys. Rev. Lett. 105, 160502 (2010).
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).
Astner, T. et al. Coherent coupling of remote spin ensembles via a cavity bus. Phys. Rev. Lett. 118, 140502 (2017).
Vandersypen, L. M. K. et al. Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent. npj Quant. Inf. 3, 34 (2017).
Acknowledgements
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.
Author information
Authors and Affiliations
Contributions
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
Ethics declarations
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).
Additional information
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.
Supplementary information
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.
Rights and permissions
About this article
Cite this article
Borjans, F., Croot, X.G., Mi, X. et al. Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195–198 (2020). https://doi.org/10.1038/s41586-019-1867-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-019-1867-y
This article is cited by
-
Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe
Nature Communications (2024)
-
Strong tunable coupling between two distant superconducting spin qubits
Nature Physics (2024)
-
Strong coupling between a microwave photon and a singlet-triplet qubit
Nature Communications (2024)
-
Quantum neural networks with multi-qubit potentials
Scientific Reports (2023)
-
Reducing charge noise in quantum dots by using thin silicon quantum wells
Nature Communications (2023)
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.