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.

Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback

Nature volume 490, pages 77–80 (2012)Cite this article

Subjects

Abstract

The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single (probabilistic) outcome. The timescale of this ‘instantaneous’ process can be stretched using weak measurements1,2, such that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback3,4,5,6,7,8. Here we implement quantum feedback control in a solid-state system, namely a superconducting quantum bit (qubit) coupled to a microwave cavity9. A weak measurement of the qubit is implemented by probing the cavity with microwave photons, maintaining its average occupation at less than one photon. These photons are then directed to a high-bandwidth, quantum-noise-limited amplifier10,11, which allows real-time monitoring of the state of the cavity (and, hence, that of the qubit) with high fidelity. We demonstrate quantum feedback control by inhibiting the decay of Rabi oscillations, allowing them to persist indefinitely12. Such an ability permits the active suppression of decoherence and enables a method of quantum error correction based on weak continuous measurements13,14. Other applications include quantum state stabilization4,7,15, entanglement generation using measurement16, state purification17 and adaptive measurements18,19.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Figure 1: Experimental set-up.
Figure 2: Rabi oscillations and feedback.
Figure 3: Tomography and feedback efficiency.

Similar content being viewed by others

References

  1. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2009)

    Book  Google Scholar 

  2. Gardiner, C. W. & Zoller, P. Quantum Noise (Springer, 2004)

    MATH  Google Scholar 

  3. Wiseman, H. M. & Milburn, G. J. Quantum theory of optical feedback via homodyne detection. Phys. Rev. Lett. 70, 548–551 (1993)

    Article  ADS  CAS  Google Scholar 

  4. Hofmann, H. F., Mahler, G. & Hess, O. Quantum control of atomic systems by homodyne detection and feedback. Phys. Rev. A 57, 4877–4888 (1998)

    Article  ADS  CAS  Google Scholar 

  5. Korotkov, A. N. Selective quantum evolution of a qubit state due to continuous measurement. Phys. Rev. B 63, 115403 (2001)

    Article  ADS  Google Scholar 

  6. Smith, W. P., Reiner, J. E., Orozco, L. A., Kuhr, S. & Wiseman, H. M. Capture and release of a conditional state of a cavity QED system by quantum feedback. Phys. Rev. Lett. 89, 133601 (2002)

    Article  ADS  CAS  Google Scholar 

  7. Gillett, G. G. et al. Experimental feedback control of quantum systems using weak measurements. Phys. Rev. Lett. 104, 080503 (2010)

    Article  ADS  CAS  Google Scholar 

  8. Sayrin, C. et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77 (2011)

    Article  ADS  CAS  Google Scholar 

  9. Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    Article  ADS  Google Scholar 

  10. Hatridge, M., Vijay, R., Slichter, D. H., Clarke, J. & Siddiqi, I. Dispersive magnetometry with a quantum limited SQUID parametric amplifier. Phys. Rev. B 83, 134501 (2011)

    Article  ADS  Google Scholar 

  11. Vijay, R., Slichter, D. H. & Siddiqi, I. Observation of quantum jumps in a superconducting artificial atom. Phys. Rev. Lett. 106, 110502 (2011)

    Article  ADS  CAS  Google Scholar 

  12. Ruskov, R. & Korotkov, A. N. Quantum feedback control of a solid-state qubit. Phys. Rev. B 66, 041401 (2002)

    Article  ADS  Google Scholar 

  13. Ahn, C., Doherty, A. C. & Landahl, A. J. Continuous quantum error correction via quantum feedback control. Phys. Rev. A 65, 042301, 2002.

  14. Tornberg, L. & Johansson, G. High-fidelity feedback-assisted parity measurement in circuit QED. Phys. Rev. A 82, 012329 (2010)

    Article  ADS  Google Scholar 

  15. Wang, J. & Wiseman, H. M. Feedback-stabilization of an arbitrary pure state of a two-level atom. Phys. Rev. A 64, 063810 (2001)

    Article  ADS  Google Scholar 

  16. Ruskov, R. & Korotkov, A. N. Entanglement of solid-state qubits by measurement. Phys. Rev. B 67, 241305 (2003)

    Article  ADS  Google Scholar 

  17. Combes, J. & Jacobs, K. Rapid state reduction of quantum systems using feedback control. Phys. Rev. Lett. 96, 010504 (2006)

    Article  ADS  Google Scholar 

  18. Jacobs, K. Feedback control for communication with non-orthogonal states. Quantum Inf. Comput. 7, 127–138 (2007)

    MathSciNet  MATH  Google Scholar 

  19. Cook, R. L., Martin, P. J. & Geremia, J. M. Optical coherent state discrimination using a closed-loop quantum measurement. Nature 446, 774–777 (2007)

    Article  ADS  CAS  Google Scholar 

  20. Schrödinger, E. The present situation in quantum mechanics. Proc. Am. Phil. Soc. 124, 323–338 (1980)

    Google Scholar 

  21. Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  22. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011)

    Article  ADS  Google Scholar 

  23. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)

    Article  ADS  Google Scholar 

  24. 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  Google Scholar 

  25. 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  Google Scholar 

  26. Palacios-Laloy, A. et al. Experimental violation of a Bell’s inequality in time with weak measurement. Nature Phys. 6, 442–447 (2010)

    Article  ADS  CAS  Google Scholar 

  27. Korotkov, A. N. & Averin, D. V. Continuous weak measurement of quantum coherent oscillations. Phys. Rev. B 64, 165310 (2001)

    Article  ADS  Google Scholar 

  28. Steffen, M. et al. State tomography of capacitively shunted phase qubits with high fidelity. Phys. Rev. Lett. 97, 050502 (2006)

    Article  ADS  Google Scholar 

  29. Slichter, D. H. et al. Measurement-induced qubit state mixing in circuit QED from upconverted dephasing noise. Preprint at http://arxiv.org/abs/1206.6946 (2012)

Download references

Acknowledgements

We thank M. Sarovar for several discussions and Z. Minev for assistance with numerical simulations. This research was supported in part (R.V., C.M. and I.S.) by the US Army Research Office (W911NF-11-1-0029) and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the Army Research Office (K.W.M., S.J.W. and A.N.K.). All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the US government. D.H.S. acknowledges support from a Hertz Foundation Fellowship endowed by Big George Ventures. A.N.K. also acknowledges funding from an ARO MURI.

Author information

Author notes

  1. D. H. Slichter

    Present address: Present address: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.,

Authors and Affiliations

  1. Department of Physics, Quantum Nanoelectronics Laboratory, University of California, Berkeley, 94720, California, USA

    R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik & I. Siddiqi

  2. Department of Electrical Engineering, University of California, Riverside, 92521, California, USA

    A. N. Korotkov

Authors
  1. R. Vijay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Macklin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. H. Slichter
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. J. Weber
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. W. Murch
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. R. Naik
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. N. Korotkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. I. Siddiqi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

R.V., C.M. and D.H.S. performed the experiment, which is based on a proposal by A.N.K. R.V. analysed the data, performed numerical simulations and wrote the manuscript. S.J.W. and K.W.M. fabricated the qubit and cavity. R.N. helped with cavity design by performing electromagnetic simulations. A.N.K. provided theoretical support and helped with numerical simulations. All authors helped in editing the manuscript. All work was carried out under the supervision of I.S.

Corresponding authors

Correspondence to R. Vijay or I. Siddiqi.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-3 and Supplementary References. (PDF 293 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vijay, R., Macklin, C., Slichter, D. et al. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 77–80 (2012). https://doi.org/10.1038/nature11505

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature11505

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