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Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback


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.

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


  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  Article  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)

    ADS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  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)

    ADS  Article  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)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  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)

    ADS  CAS  Article  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)

    ADS  MathSciNet  Article  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)

    ADS  Article  Google Scholar 

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

    ADS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  29. Slichter, D. H. et al. Measurement-induced qubit state mixing in circuit QED from upconverted dephasing noise. Preprint at (2012)

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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.

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Authors and Affiliations



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.

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Correspondence to R. Vijay or I. Siddiqi.

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The authors declare no competing financial interests.

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

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