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:

Electron charge qubit with 0.1 millisecond coherence time

Nature Physics volume 20, pages 116–122 (2024)Cite this article

Subjects

Abstract

Electron charge qubits are compelling candidates for solid-state quantum computing because of their inherent simplicity in qubit design, fabrication, control and readout. However, electron charge qubits built on conventional semiconductors and superconductors suffer from severe charge noise that limits their coherence time to the order of one microsecond. Here we report electron charge qubits that exceed this limit, based on isolated single electrons trapped on an ultraclean solid neon surface in a vacuum. Quantum information is encoded in the motional states of an electron that is strongly coupled with microwave photons in an on-chip superconducting resonator. The measured relaxation and coherence times are both on the order of 0.1 ms, surpassing all existing charge qubits and rivalling state-of-the-art superconducting transmon qubits. The simultaneous strong coupling of two qubits with a common resonator is also demonstrated, as the first step towards two-qubit entangling gates for universal quantum computing.

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: Design and properties of an eNe charge qubit.
Fig. 2: Time-domain characterization of an eNe charge qubit.
Fig. 3: DD, single-shot readout fidelity and single-qubit gate fidelity of an eNe charge qubit.
Fig. 4: Spectroscopic characterization of two eNe charge qubits coupled to a resonator.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding authors upon request. Source data are provided with this paper.

Code availability

The codes used to perform the experiments and to analyse the data in this work are available from the corresponding authors upon request.

References

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  3. Siddiqi, I. Engineering high-coherence superconducting qubits. Nat. Rev. Mater. 6, 875–891 (2021).

    Article  ADS  Google Scholar 

  4. Stano, P. & Loss, D. Review of performance metrics of spin qubits in gated semiconducting nanostructures. Nat. Rev. Phys. 4, 672–688 (2022).

    Article  Google Scholar 

  5. Muhonen, J. T. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nat. Nanotechnol. 9, 986–991 (2014).

    Article  ADS  Google Scholar 

  6. Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014).

    Article  ADS  Google Scholar 

  7. 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  Google Scholar 

  8. Nguyen, L. B. et al. High-coherence fluxonium qubit. Phys. Rev. X 9, 041041 (2019).

    Google Scholar 

  9. Somoroff, A. et al. Millisecond coherence in a superconducting qubit. Phys. Rev. Lett. 130, 267001 (2023).

    Article  ADS  Google Scholar 

  10. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2021).

    Article  ADS  Google Scholar 

  11. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Inf. 8, 3 (2022).

    Article  ADS  Google Scholar 

  12. Heinrich, A. J. et al. Quantum-coherent nanoscience. Nat. Nanotechnol. 16, 1318–1329 (2021).

    Article  ADS  Google Scholar 

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

  14. Kim, D. et al. Microwave-driven coherent operation of a semiconductor quantum dot charge qubit. Nat. Nanotechnol. 10, 243–247 (2015).

    Article  ADS  Google Scholar 

  15. Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Sci. Adv. 2, e1600694 (2016).

    Article  ADS  Google Scholar 

  16. Osman, A. et al. Simplified Josephson-junction fabrication process for reproducibly high-performance superconducting qubits. Appl. Phys. Lett. 118, 064002 (2021).

    Article  ADS  Google Scholar 

  17. Pashkin, Y. A., Astafiev, O., Yamamoto, T., Nakamura, Y. & Tsai, J. S. Josephson charge qubits: a brief review. Quantum Inf. Process. 8, 55–80 (2009).

    Article  Google Scholar 

  18. Samkharadze, N. et al. High-kinetic-inductance superconducting nanowire resonators for circuit QED in a magnetic field. Phys. Rev. Applied 5, 044004 (2016).

    Article  ADS  Google Scholar 

  19. Kroll, J. et al. Magnetic-field-resilient superconducting coplanar-waveguide resonators for hybrid circuit quantum electrodynamics experiments. Phys. Rev. Applied 11, 064053 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  21. D’Anjou, B. & Burkard, G. Optimal dispersive readout of a spin qubit with a microwave resonator. Phys. Rev. B 100, 245427 (2019).

    Article  ADS  Google Scholar 

  22. Hu, X., Liu, Y. & Nori, F. Strong coupling of a spin qubit to a superconducting stripline cavity. Phys. Rev. B 86, 035314 (2012).

    Article  ADS  Google Scholar 

  23. Zhou, X. et al. Single electrons on solid neon as a solid-state qubit platform. Nature 605, 46–50 (2022).

    Article  ADS  Google Scholar 

  24. 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  Google Scholar 

  25. Wilen, C. D. et al. Correlated charge noise and relaxation errors in superconducting qubits. Nature 594, 369–373 (2021).

    Article  ADS  Google Scholar 

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

  27. Mallet, F. et al. Single-shot qubit readout in circuit quantum electrodynamics. Nat. Phys. 5, 791–795 (2009).

    Article  Google Scholar 

  28. Stefanazzi, L. et al. The QICK (Quantum Instrumentation Control Kit): readout and control for qubits and detectors. Rev. Sci. Instrum. 93, 044709 (2022).

    Article  Google Scholar 

  29. Knill, E. et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008).

    Article  ADS  Google Scholar 

  30. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

    Article  ADS  Google Scholar 

  31. Divincenzo, D. P., Bacon, D., Kempe, J., Burkard, G. & Whaley, K. B. Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000).

    Article  ADS  Google Scholar 

  32. 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  Google Scholar 

  33. Jacobsen, R. T., Penoncello, S. G. & Lemmon, E. W. Thermodynamic properties of cryogenic fluids. in Thermodynamic Properties of Cryogenic Fluids 31–287 (Springer, 1997).

  34. Sheludiakov, S. et al. Electron spin resonance study of atomic hydrogen stabilized in solid neon below 1 K. Phys. Rev. B 97, 104108 (2018).

    Article  ADS  Google Scholar 

  35. 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  Google Scholar 

  36. Kawakami, E., Elarabi, A. & Konstantinov, D. Image-charge detection of the Rydberg states of surface electrons on liquid helium. Phys. Rev. Lett. 123, 086801 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Allen, L. & Eberly, J. H. Optical Resonance and Two-Level Atoms (Dover, 1987).

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

    Article  ADS  Google Scholar 

  42. Purcell, E. M. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946).

    Google Scholar 

  43. Sete, E. A., Gambetta, J. M. & Korotkov, A. N. Purcell effect with microwave drive: suppression of qubit relaxation rate. Phys. Rev. B 89, 104516 (2014).

    Article  ADS  Google Scholar 

  44. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Inf. 8, 93 (2022).

    Article  ADS  Google Scholar 

  45. Gambetta, J., Braff, W. A., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement. Phys. Rev. A 76, 012325 (2007).

    Article  ADS  Google Scholar 

  46. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014).

    Article  ADS  Google Scholar 

  47. Tavis, M. & Cummings, F. Exact solution for an n-molecule-radiation-field Hamiltonian. Phys. Rev. 170, 379–384 (1968).

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  50. Chen, Q., Martin, I., Jiang, L. & Jin, D. Electron spin coherence on a solid neon surface. Quantum Sci. Technol. 7, 045016 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Klein, M. L. & Venables, J. A. Rare Gas Solids Vol. I (Academic, 1976).

  53. Shearrow, A. et al. Atomic layer deposition of titanium nitride for quantum circuits. Appl. Phys. Lett. 113, 212601 (2018).

    Article  ADS  Google Scholar 

  54. Xu, M., Han, X., Fu, W., Zou, C.-L. & Tang, H. X. Frequency-tunable high-Q superconducting resonators via wireless control of nonlinear kinetic inductance. Appl. Phys. Lett. 114, 192601 (2019).

    Article  ADS  Google Scholar 

  55. Han, X. et al. Superconducting cavity electromechanics: the realization of an acoustic frequency comb at microwave frequencies. Phys. Rev. Lett. 129, 107701 (2022).

    Article  ADS  Google Scholar 

  56. Lu, Y. et al. Universal stabilization of a parametrically coupled qubit. Phys. Rev. Lett. 119, 150502 (2017).

    Article  ADS  Google Scholar 

  57. McKay, D. C. et al. Universal gate for fixed-frequency qubits via a tunable bus. Phys. Rev. Applied 6, 064007 (2016).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Work performed at the Center for Nanoscale Materials, a US Department of Energy (DOE), Office of Science User Facility, was supported by the US DOE, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357. D.J., X.H., X.L. and Q.C. acknowledge support from the Argonne National Laboratory Directed Research and Development (LDRD). D.J. and X. Zhou acknowledge support from the Julian Schwinger Foundation for Physics Research. 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 Foundation National Nanotechnology Coordinated Infrastructure (NSF NNCI-1542205). D.I.S. and B.D. acknowledge support from the National Science Foundation DMR grant DMR-1906003. D.I.S. and C.S.W. acknowledge support from Q-NEXT, one of the US DOE Office of Science National Quantum Information Science Research Centers. G.Y. acknowledges support from the National Science Foundation under Cooperative Agreement PHY-2019786 (the NSF AI Institute for Artificial Intelligence and Fundamental Interactions). X. Zhang acknowledges support from ONR YIP (N00014-23-1-2144). D.J. thanks A. J. Leggett for inspiring discussions. The qubit manipulation and measurement in this work utilized the highly efficient and effective OPX+, Octave and QDAC-II made by Quantum Machines and QDevil.

Author information

Author notes

  1. These authors contributed equally: Xianjing Zhou, Xinhao Li.

Authors and Affiliations

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

    Xianjing Zhou, Xinhao Li, Qianfan Chen, Xu Han & Dafei Jin

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

    Xianjing Zhou, Yizhong Huang, Xu Han, David I. Schuster & Dafei Jin

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

    Gerwin Koolstra

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

    Ge Yang

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

    Ge Yang

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

    Brennan Dizdar, Christopher S. Wang & David I. Schuster

  7. Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA

    Xufeng Zhang

  8. Department of Applied Physics, Stanford University, Stanford, CA, USA

    David I. Schuster

  9. Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN, USA

    Dafei Jin

Authors
  1. Xianjing Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinhao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qianfan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gerwin Koolstra
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ge Yang
    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. Yizhong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Christopher S. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Xu Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Xufeng Zhang
    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, X.L. and D.J. devised the experiment and wrote the manuscript. X. Zhou and X.L. performed the experiment. Q.C. performed the calculations. G.K., G.Y. and D.I.S. designed the device. X.L., G.K., G.Y. and Y.H. fabricated the device. B.D. simulated the device. X. Zhou, X.L., X.H., X. Zhang and D.J. built the experimental setup. C.S.W. 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 David I. Schuster or Dafei Jin.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Robert Joynt 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

Extended Data Fig. 1 Qubit-resonator coupled spectrum, ac Stark shift, and dispersive shift.

a, Schematic of the qubit-resonator coupled spectrum. ωq = 2πfq is the bare qubit frequency, ωr = 2πfr is the bare resonator frequency, and g is the coupling strength. In the resonant regime, fr = fq, the qubit and resonator hybridize and a vacuum Rabi splitting 2g opens up. In the dispersive regime, the detuning ∣Δ = ωq − ωr∣ ≫ g, the actual qubit frequency exhibits the dispersive shift χ and the ac Stark shift \(2\chi \bar{n}\), in which \(\bar{n}\) is the average intra-resonator photon number, whereas the actual resonator frequency exhibits a + χ or − χ shift, when the qubit is kept in the excited or ground state, respectively. b, Observation of the ac Stark shift. The transmission phase ϕ at fp = fr is plotted versus fd and probe power Pp, when the qubit is on the sweet spot in Fig. 1d. With increasing Pp, the qubit frequency is red-shifted because of the ac Stark effect. In the inset, the frequency shift δfac shows a linear dependence on Pp (equivalent to the average intra-resonator photon number \(\bar{n}\)). c, Measurement of the state-dependent dispersive shift. Normalized transmission amplitude \({(A/{A}_{0})}^{2}\) (top) and phase ϕ (bottom) are plotted versus the probe frequency fp when the qubit is in the ground state \(\left\vert 0\right\rangle\) or excited state \(\left\vert 1\right\rangle\). The grey line corresponds to fp = fr, where fr is the bare resonator frequency. The measured dispersive shift is χ/2π = − 0.13 MHz.

Source data

Source data

Source Data Fig. 1

Numerical source data for Fig. 1.

Source Data Fig. 2

Numerical source data for Fig. 2.

Source Data Fig. 3

Numerical source data for Fig. 3.

Source Data Fig. 4

Numerical source data for Fig. 4.

Source Data Extended Data Fig. 1

Numerical source data for Extended Fig. 1.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, X., Li, X., Chen, Q. et al. Electron charge qubit with 0.1 millisecond coherence time. Nat. Phys. 20, 116–122 (2024). https://doi.org/10.1038/s41567-023-02247-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02247-5

This article is cited by

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