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.

  • Article
  • Published:

Single electrons on solid neon as a solid-state qubit platform

Nature volume 605, pages 46–50 (2022)Cite this article

Subjects

Abstract

Progress towards the realization of quantum computers requires persistent advances in their constituent building blocks—qubits. Novel qubit platforms that simultaneously embody long coherence, fast operation and large scalability offer compelling advantages in the construction of quantum computers and many other quantum information systems1,2,3. Electrons, ubiquitous elementary particles of non-zero charge, spin and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits through either motional or spin states depends critically on their material environment3,4,5. Here we report our experimental realization of a qubit platform based on isolated single electrons trapped on an ultraclean solid neon surface in vacuum6,7,8,9,10,11,12,13. By integrating an electron trap in a circuit quantum electrodynamics architecture14,15,16,17,18,19,20, we achieve strong coupling between the motional states of a single electron and a single microwave photon in an on-chip superconducting resonator. Qubit gate operations and dispersive readout are implemented to measure the energy relaxation time T1 of 15 μs and phase coherence time T2 over 200 ns. These results indicate that the electron-on-solid-neon qubit already performs near the state of the art for a charge qubit21.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Electronic structure and device design of the single-electron circuit QED architecture on solid neon.
Fig. 2: Strong coupling and vacuum Rabi splitting between a single electron on solid neon and a single microwave photon in a superconducting resonator.
Fig. 3: Spectroscopy and time-domain characterization of a single-electron qubit on solid neon.

Similar content being viewed by others

Data availability

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

Code availability

The computer codes that are used in this study are available from the corresponding authors on request.

References

  1. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Popkin, G. Quest for qubits. Science 354, 1090–1093 (2016).

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  3. de Leon, N. P. et al. Materials challenges and opportunities for quantum computing hardware. Science 372, 253 (2021).

    Google Scholar 

  4. Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).

    Article  ADS  CAS  Google Scholar 

  5. Zwanenburg, F. A. et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961–1019 (2013).

    Article  ADS  CAS  Google Scholar 

  6. Cole, M. W. & Cohen, M. H. Image-potential-induced surface bands in insulators. Phys. Rev. Lett. 23, 1238 (1969).

    Article  ADS  CAS  Google Scholar 

  7. Cole, M. W. Electronic surface states of a dielectric film on a metal substrate. Phys. Rev. B 3, 4418 (1971).

    Article  ADS  Google Scholar 

  8. Leiderer, P. Electrons at the surface of quantum systems. J. Low Temp. Phys. 87, 247–278 (1992).

    Article  ADS  CAS  Google Scholar 

  9. Platzman, P. & Dykman, M. I. Quantum computing with electrons on liquid helium. Science 284, 1967–1969 (1999).

    Article  CAS  PubMed  Google Scholar 

  10. Smolyaninov, I. I. Electrons on solid hydrogen and solid neon surfaces. Int. J. Mod. Phys. B 15, 2075–2106 (2001).

    Article  ADS  CAS  Google Scholar 

  11. Dykman, M. I., Platzman, P. M. & Seddighrad, P. Qubits with electrons on liquid helium. Phys. Rev. B 67, 155402 (2003).

    Article  ADS  Google Scholar 

  12. Lyon, S. A. Spin-based quantum computing using electrons on liquid helium. Phys. Rev. A 74, 052338 (2006).

    Article  ADS  Google Scholar 

  13. Bradbury, F. R. et al. Efficient clocked electron transfer on superuid helium. Phys. Rev. Lett. 107, 266803 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  14. 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  PubMed  Google Scholar 

  15. Blais, A., Grimsmo, A. L. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  16. Schuster, D. I., Fragner, A., Dykman, M. I., Lyon, S. A. & Schoelkopf, R. J. Proposal for manipulating and detecting spin and orbital states of trapped electrons on helium using cavity quantum electrodynamics. Phys. Rev. Lett. 105, 040503 (2010).

    Article  ADS  CAS  PubMed  Google Scholar 

  17. Yang, G. et al. Coupling an ensemble of electrons on superfluid helium to a superconducting circuit. Phys. Rev. X 6, 011031 (2016).

    Google Scholar 

  18. Koolstra, G., Yang, G. & Schuster, D. I. Coupling a single electron on superfluid helium to a superconducting resonator. Nat. Commun. 10, 5323 (2019).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  19. Jin, D. Quantum electronics and optics at the interface of solid neon and superfluid helium. Quantum Sci. Technol. 5, 035003 (2020).

    Article  ADS  Google Scholar 

  20. Clerk, A. A., Lehnert, K. W., Bertet, P., Petta, J. R. & Nakamura, Y. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys. 16, 257–267 (2020).

    Article  CAS  Google Scholar 

  21. Chatterjee, A. et al. Semiconductor qubits in practice. Nat. Rev. Phys. 3, 157–177 (2021).

    Article  Google Scholar 

  22. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-cooper-pair box. Nature 398, 786–788 (1999).

    Article  ADS  CAS  Google Scholar 

  23. Schoelkopf, R. J. & Girvin, S. M. Wiring up quantum systems. Nature 451, 664–669 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nanotechnol. 9, 666–670 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  30. Petit, L. et al. Universal quantum logic in hot silicon qubits. Nature 580, 355–359 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Burkard, G., Gullans, M. J., Mi, X. & Petta, J. R. Superconductor-semiconductor hybrid-circuit quantum electrodynamics. Nat. Rev. Phys. 2, 129–140 (2020).

    Article  Google Scholar 

  32. Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714 (1995).

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  33. Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281 (2003).

    Article  ADS  CAS  Google Scholar 

  35. Bruzewicz, C. D., Chiaverini, J., McConnell, R. & Sage, J. M. Trapped-ion quantum computing: Progress and challenges. Appl. Phys. Rev. 6, 021314 (2019).

    Article  ADS  Google Scholar 

  36. Pino, J. M. et al. Demonstration of the trapped-ion quantum CCD computer architecture. Nature 592, 209–213 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  37. Brennen, G. K., Caves, C. M., Jessen, P. S. & Deutsch, I. H. Quantum logic gates in optical lattices. Phys. Rev. Lett. 82, 1060 (1999).

    Article  ADS  CAS  Google Scholar 

  38. Jaksch, D. et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208 (2000).

    Article  ADS  CAS  PubMed  Google Scholar 

  39. Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).

    Article  ADS  CAS  Google Scholar 

  40. Wang, Y., Kumar, A., Wu, T.-Y. & Weiss, D. S. Single-qubit gates based on targeted phase shifts in a 3D neutral atom array. Science 352, 1562–1565 (2016).

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  41. Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  42. Pla, J. J. et al. High-fidelity readout and control of a nuclear spin qubit in silicon. Nature 496, 334–338 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Chen, S., Raha, M., Phenicie, C. M., Ourari, S. & Thompson, J. D. Parallel single-shot measurement and coherent control of solid-state spins below the diffraction limit. Science 370, 592–595 (2020).

    Article  CAS  PubMed  Google Scholar 

  44. Wolfowicz, G. et al. Quantum guidelines for solid-state spin defects. Nat. Rev. Mater. 6, 906–925 (2021).

    Article  ADS  CAS  Google Scholar 

  45. Vincent, R., Klyatskaya, S., Ruben, M., Wernsdorfer, W. & Balestro, F. Electronic read-out of a single nuclear spin using a molecular spin transistor. Nature 488, 357–360 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  46. Thiele, S. et al. Electrically driven nuclear spin resonance in single-molecule magnets. Science 344, 1135–1138 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  47. Atzori, M. & Sessoli, R. The Second Quantum Revolution: Role and Challenges of Molecular Chemistry. J. Am. Chem. Soc. 141, 11339–11352 (2019).

    Article  CAS  PubMed  Google Scholar 

  48. Coronado, E. Molecular magnetism: from chemical design to spin control in molecules, materials and devices. Nat. Rev. Mater. 5, 87–104 (2020).

    Article  ADS  Google Scholar 

  49. Schuster, D. I. et al. ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys. Rev. Lett. 94, 123602 (2005).

    Article  ADS  CAS  PubMed  Google Scholar 

  50. Wallraff, A. et al. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005).

    Article  ADS  CAS  PubMed  Google Scholar 

  51. Sheludiakov, S. et al. Electrons trapped in solid neon–hydrogen mixtures below 1 K. J. Low Temp. Phys. 195, 365–377 (2019).

    Article  ADS  CAS  Google Scholar 

  52. Jacobsen, R. T., Penoncello, S. G. & Lemmon, E. W. In Thermodynamic Properties of Cryogenic Fluids (eds Weisend II, J. G. & Jeong S.) 31–287 (Springer, 1997).

  53. Pollack, G. L. The solid state of rare gases. Rev. Mod. Phys. 36, 748 (1964).

    Article  ADS  CAS  Google Scholar 

  54. Batchelder, D. N., Losee, D. L. & Simmons, R. O. Measurements of lattice constant, thermal expansion, and isothermal compressibility of neon single crystals. Phys. Rev. 162, 767 (1967).

    Article  ADS  CAS  Google Scholar 

  55. Zavyalov, V., Smolyaninov, I., Zotova, E., Borodin, A. & Bogomolov, S. Electron states above the surfaces of solid cryodielectrics for quantum-computing.’. J. Low Temp. Phys. 138, 415–420 (2005).

    Article  ADS  CAS  Google Scholar 

  56. Leiderer, P., Kono, K. & Rees, D. In Proc. 11th International Conference on Cryocrystals and Quantum Crystals (ed. Vasiliev, S.) 67–67 (University of Turku, 2016).

  57. Kajita, K. A new two-dimensional electron system on the surface of solid neon. Surf. Sci. 142, 86–95 (1984).

    Article  ADS  CAS  Google Scholar 

  58. Nilsson, A., Pettersson, L. G. & Norskov, J. Chemical Bonding at Surfaces and Interfaces (Elsevier, 2011).

  59. Ibach, H. Physics of Surfaces and Interfaces Vol. 2006 (Springer, 2006).

  60. Pozar, D. M. Microwave Engineering (Wiley, 2011).

  61. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer Science & Business Media, 2007).

  62. Schuster, D. I. Circuit Quantum Electrodynamics PhD thesis, Yale Univ. (2007).

  63. Krantz, P. et al. A quantum engineer’s guide to superconducting qubits. Appl. Phys. Rev. 6, 021318 (2019).

    Article  ADS  Google Scholar 

  64. Ithier, G. et al. Decoherence in a superconducting quantum bit circuit. Phys. Rev. B 72, 134519 (2005).

    Article  ADS  Google Scholar 

  65. Chen, Z. Metrology of Quantum Control and Measurement in Superconducting Qubits PhD thesis, Univ. of California Santa Barbara (2018).

Download references

Acknowledgements

This work was performed at the Center for Nanoscale Materials (CNM), a US Department of Energy Office of Science User Facility, and supported by the US Department of Energy, Office of Science, under Contract no. DE-AC02-06CH11357. D.J. and X.L. acknowledge addtional support from Argonne National Laboratory Directed Research and Development (LDRD) Program for device characterization effort. D.J. acknowledges additional support from the Julian Schwinger Foundation (JSF) for Physics Research for hardware component upgrade. This work was partially supported by the University of Chicago Materials Research Science and Engineering Center, which is funded by the National Science Foundation under award no. DMR-2011854. This work made use of the Pritzker Nanofabrication Facility of the Institute for Molecular Engineering at the University of Chicago, which receives support from SHyNE, a node of the National Science Foundations National Nanotechnology Coordinated Infrastructure (NSF NNCI-1542205). D.I.S. and B.D. acknowledge support from NSF grant no. DMR-1906003. K.W.M. acknowledges support from NSF grant no. PHY-1752844 (CAREER) and use of facilities at the Institute of Materials Science and Engineering at Washington University. W.G. acknowledges support from NSF grant no. DMR-2100790 and the National High Magnetic Field Laboratory, which is funded through the NSF Cooperative Agreement no. DMR-1644779 and the State of Florida. G.Y. acknowledges support from the National Science Foundation under Cooperative Agreement no. PHY-2019786 (the NSF AI Institute for Artificial Intelligence and Fundamental Interactions, http://iaifi.org/). D.J. thanks M. W. Cole, M. I. Dykman, S. K. Gray, P. Leiderer, D. Lopez and T. Rajh for inspiring discussions. The CNM team thanks MIT Lincoln Laboratory and Intelligence Advanced Research Projects Activity (IARPA) for providing the traveling-wave parametric amplifier (TWPA) used in this project.

Author information

Authors and Affiliations

  1. Center for Nanoscale Materials, Argonne National Laboratory, Lemont, IL, USA

    Xianjing Zhou, Xufeng Zhang, Xu Han, Xinhao Li, Ralu Divan & Dafei Jin

  2. Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Gerwin Koolstra

  3. The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, USA

    Ge Yang

  4. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA

    Ge Yang

  5. James Franck Institute and Department of Physics, University of Chicago, Chicago, IL, USA

    Brennan Dizdar & David I. Schuster

  6. National High Magnetic Field Laboratory, Tallahassee, FL, USA

    Wei Guo

  7. Department of Mechanical Engineering, FAMU-FSU College of Engineering, Florida State University, Tallahassee, FL, USA

    Wei Guo

  8. Department of Physics, Washington University in St. Louis, St. Louis, MO, USA

    Kater W. Murch

  9. Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA

    David I. Schuster

Authors
  1. Xianjing Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerwin Koolstra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xufeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ge Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xu Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Brennan Dizdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xinhao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ralu Divan
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Wei Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Kater W. Murch
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. David I. Schuster
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Dafei Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X. Zhou and D.J. devised the experiment and wrote the manuscript. X. Zhou performed the experiment. G.K., G.Y. and D.I.S. designed the device. G.K. and G.Y. fabricated the device. X. Zhou, X. Zhang, X.H. and D.J. built the experimental setup. B.D. simulated the device. X.L. and R.D. characterized the device. W.G. advised the sample processing and theoretical modelling. K.W.M. and D.I.S. advised the measurement and revised the manuscript. D.J. conceived the idea and led the project. All authors contributed to the manuscript.

Corresponding authors

Correspondence to Kater W. Murch or Dafei Jin.

Ethics declarations

Competing interests

Authors declare no competing interests.

Peer review

Peer review information

Nature thanks Mark Dykman, Erika Kawakami and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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 Cryostat and measurement setup for single-electron qubits on solid neon in a circuit quantum electrodynamics architecture.

Details are explained in the text where they are referred to.

Extended Data Fig. 2 Photographs of sample cell and electron source.

a, Lid part of the cell with all the coax connection. It contains 14 hermetic SMP feedthroughs for d.c. and RF signals, 2 SMP feedthroughs for electron source, and a stainless steel tube for neon filling. b, Pedestal part of the cell with a printed circuit board (PCB) mounted underneath a stack of copper sheets that suppress unwanted microwave modes. c, Two tungsten filaments, mounted in parallel on the back side of the lid in (a), as the electron source by thermionic emission. The inset shows a scanning electron microscopy (SEM) image of one tungsten filament.

Extended Data Fig. 3 Phase diagram of neon.

The solid-liquid-gas triple point is at (24.56 K, 0.43 bar) and the liquid-gas critical point is at (44.49 K, 27.69 bar).

Extended Data Fig. 4 Observed time evolution of transmission amplitude (A/A0)2 during the electron generation and deposition processes.

a, In the case of neon fully filling the channel. b, In the case of 5–10 nm neon coating the device. At t = 0, pulse train is sent to the tungsten filaments and electrons are generated and deposited onto the resonator. A sudden change in the spectrum can be seen. After about 3 s, the spectrum stabilizes and shows a frequency shift about 10 MHz for (a) and almost no shift for (b).

Extended Data Fig. 5 Coupling of a single electron and microwave photons.

a, Normalized transmission amplitude (A/A0)2 probed at the bare resonator frequency fr as a function of the resonator-guard voltage Vrg and the trap voltage Vt. b, Transmission phase ϕ, corresponding to the amplitude in (a), as a function of Vrg and Vt. c, Line scanned normalized amplitude (A/A0)2 and phase ϕ as a function of Vrg at Vt = 175 mV. A dip in amplitude and 2π phase jump occur when the qubit frequency matches the resonator frequency.

Extended Data Fig. 6 Vacuum Rabi splitting between a single electron and microwave photons.

a, Normalized transmission amplitude (A/A0)2 as a function of probe frequency Δfp = fp − fr and resonator-guard voltage ΔVrg (detuning from the resonance condition). b, Transmission amplitude (A/A0)2 versus a probe frequency when qubit and resonator is on resonance. The fitting curve with input-output theory gives a coupling strength g/2π about 4.5 MHz and qubit decay rate γ/2π about 3.4 MHz.

Extended Data Fig. 7 Two-tone qubit spectroscopy measurement with high pump power and pump frequency around the bare resonator frequency.

Besides the |0⟩ → |1⟩ transition line, which is marked with black dashed line, there are other transition lines visible. The line immediately next to the main transition line is the |1⟩ → |2⟩ transition. At Δ/2π = fq − fr = −100 MHz detuning, the anharmonicity α/2π ≡ f|1⟩→|2⟩ − f|0⟩→|1⟩ ≈ 40 MHz.

Extended Data Fig. 8 Calculated electron qubit properties based on a minimal model that encloses linear asymmetry and quartic anharmonicity.

a, Trapping potential V versus position y. The shape symmetrically leans to the left and right by tuning the resonator-guard voltage Vrg with respect to the ‘sweet spot’ voltage Vss = 339 mV. For Vrg > Vss, we take Vrg = 516 mV and for Vrg > Vss, we take Vrg = 162 mV, both of which are on-resonance conditions in experiment when the qubit frequency fq matches the resonator frequency fr. b–d, Electron wavefunctions on the ground state |0⟩, first excited state |1⟩, and second excited state |2⟩, respectively, for the three different Vrg’s. They extend about 500 nm in space and are left and right shifted with the potential changes. e, Qubit spectrum under frequency scanning Δfs = fs − fr and voltage Vrg detuning, for |0⟩ → |1⟩ and |1⟩ → |2⟩ transitions. The first transition (in red) matches well with the experimental observation shown in Fig. 3a. f, Magnified qubit spectrum of (e) in the ±100 MHz detuning range. The second transition has a positive anharmonicity α = 40 MHz above the first transition at −100 MHz detuning. The overall spectral profile also matches the experiment observation shown in Extended Data Fig. 7, taking account of the practical spectrum deformation due to the overly strong pumping near resonance.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, X., Koolstra, G., Zhang, X. et al. Single electrons on solid neon as a solid-state qubit platform. Nature 605, 46–50 (2022). https://doi.org/10.1038/s41586-022-04539-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-022-04539-x

This article is cited by

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

Advanced 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