Autonomously stabilized entanglement between two superconducting quantum bits

Abstract

Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors1, but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes2,3,4,5. The next step is to prepare and stabilize a state of a composite system6,7,8. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset9, single-qubit state stabilization10, and the creation11 and stabilization6 of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence12,13,14,15, obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits16, will be an essential tool for the implementation of quantum error correction.

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Figure 1: Bell state stabilization set-up schematic and frequency landscape of autonomous feedback loop.
Figure 2: Convergence of two qubit-state to the target Bell state.
Figure 3: Fidelity improved by monitoring the feedback loop.

References

  1. 1

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2004)

    Google Scholar 

  2. 2

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

    CAS  Article  ADS  Google Scholar 

  3. 3

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

    CAS  Article  ADS  Google Scholar 

  4. 4

    Ristè, D., Bultink, C. C., Lehnert, K. W. & DiCarlo, L. Feedback control of a solid-state qubit using high-fidelity projective measurement. Phys. Rev. Lett. 109, 240502 (2012)

    Article  ADS  Google Scholar 

  5. 5

    Campagne-Ibarcq, P. et al. Persistent control of a superconducting qubit by stroboscopic measurement feedback. Phys. Rev. X 3, 021008 (2013)

    Google Scholar 

  6. 6

    Krauter, H. et al. Entanglement generated by dissipation and steady state entanglement of two macroscopic objects. Phys. Rev. Lett. 107, 080503 (2011)

    Article  ADS  Google Scholar 

  7. 7

    Brakhane, S. et al. Bayesian feedback control of a two-atom spin-state in an atom-cavity system. Phys. Rev. Lett. 109, 173601 (2012)

    Article  ADS  Google Scholar 

  8. 8

    Ristè, D. et al. Deterministic entanglement of superconducting qubits by parity measurement and feedback. Nature 502, 350–354 (2013)

    Article  ADS  Google Scholar 

  9. 9

    Geerlings, K. et al. Demonstrating a driven reset protocol for a superconducting qubit. Phys. Rev. Lett. 110, 120501 (2013)

    CAS  Article  ADS  Google Scholar 

  10. 10

    Murch, K. W. et al. Cavity-assisted quantum bath engineering. Phys. Rev. Lett. 109, 183602 (2012)

    CAS  Article  ADS  Google Scholar 

  11. 11

    Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011)

    CAS  Article  ADS  Google Scholar 

  12. 12

    Poyatos, J. F., Cirac, J. I. & Zoller, P. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996)

    CAS  Article  ADS  Google Scholar 

  13. 13

    Kerckhoff, J., Nurdin, H. I., Pavlichin, D. S. & Mabuchi, H. Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. Phys. Rev. Lett. 105, 040502 (2010)

    Article  ADS  Google Scholar 

  14. 14

    Kastoryano, M. J., Reiter, F. & Sørensen, A. S. Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)

    CAS  Article  ADS  Google Scholar 

  15. 15

    Sarlette, A., Raimond, J. M., Brune, M. & Rouchon, P. Stabilization of nonclassical states of the radiation field in a cavity by reservoir engineering. Phys. Rev. Lett. 107, 010402 (2011)

    CAS  Article  ADS  Google Scholar 

  16. 16

    Lin, Y. et al. Dissipative production of a maximally entangled steady state of two quantum bits. Nature http://dx.doi.org/10.1038/nature12801 (this issue)

  17. 17

    Leghtas, Z. et al. Stabilizing a bell state of two superconducting qubits by dissipation engineering. Phys. Rev. A 88, 023849 (2013)

    Article  ADS  Google Scholar 

  18. 18

    Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    CAS  Article  ADS  Google Scholar 

  19. 19

    Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502 (2008)

    Article  ADS  Google Scholar 

  20. 20

    Nigg, S. E. et al. Black-box superconducting circuit quantization. Phys. Rev. Lett. 108, 240502 (2012)

    Article  ADS  Google Scholar 

  21. 21

    Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007)

    CAS  Article  ADS  Google Scholar 

  22. 22

    Lalumière, K., Gambetta, J. M. & Blais, A. Tunable joint measurements in the dispersive regime of cavity QED. Phys. Rev. A 81, 040301 (2010)

    Article  ADS  Google Scholar 

  23. 23

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

    Article  ADS  Google Scholar 

  24. 24

    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 

  25. 25

    Filipp, S. et al. Two-qubit state tomography using a joint dispersive readout. Phys. Rev. Lett. 102, 200402 (2009)

    CAS  Article  ADS  Google Scholar 

  26. 26

    Bergeal, N. et al. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature 465, 64–68 (2010)

    CAS  Article  ADS  Google Scholar 

  27. 27

    Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)

    CAS  Article  ADS  Google Scholar 

  28. 28

    Slichter, D. H. et al. Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise. Phys. Rev. Lett. 109, 153601 (2012)

    CAS  Article  ADS  Google Scholar 

  29. 29

    Reichle, R. et al. Experimental purification of two-atom entanglement. Nature 443, 838–841 (2006)

    CAS  Article  ADS  Google Scholar 

  30. 30

    Leghtas, Z. et al. Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett. 111, 120501 (2013)

    Article  ADS  Google Scholar 

  31. 31

    Lecocq, F. et al. Junction fabrication by shadow evaporation without a suspended bridge. Nanotechnology 22, 315302 (2011)

    Article  Google Scholar 

  32. 32

    Rigetti, C. Quantum Gates for Superconducting Qubits 174–176. PhD thesis, Yale Univ. (2009)

  33. 33

    Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Phys. Rev. Lett. 101, 080502 (2008)

    CAS  Article  ADS  Google Scholar 

  34. 34

    Sears, A. P. et al. Photon shot noise dephasing in the strong-dispersive limit of circuit QED. Phys. Rev. B 86, 180504 (2012)

    Article  ADS  Google Scholar 

  35. 35

    Hatridge, M. et al. Quantum back-action of an individual variable-strength measurement. Science 339, 178–181 (2013)

    MathSciNet  CAS  Article  ADS  Google Scholar 

  36. 36

    Johnson, J. E. et al. Heralded state preparation in a superconducting qubit. Phys. Rev. Lett. 109, 050506 (2012)

    CAS  Article  ADS  Google Scholar 

  37. 37

    Chow, J. M. et al. Detecting highly entangled states with a joint qubit readout. Phys. Rev. A 81, 062325 (2010)

    Article  ADS  Google Scholar 

  38. 38

    Motzoi, F., Gambetta, J. M., Rebentrost, P. & Wilhelm, F. K. Simple pulses for elimination of leakage in weakly nonlinear qubits. Phys. Rev. Lett. 103, 110501 (2009)

    CAS  Article  ADS  Google Scholar 

  39. 39

    Reed, M. D. Entanglement and Quantum Error Correction with Superconducting Qubits Ch. 5. PhD thesis, Yale Univ. (2013)

  40. 40

    Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013)

    CAS  Article  ADS  Google Scholar 

  41. 41

    Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990)

    CAS  Article  ADS  Google Scholar 

  42. 42

    Reed, M. D. et al. Fast reset and suppressing spontaneous emission of a superconducting qubit. Appl. Phys. Lett. 96, 203110 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Facility use was supported by the Yale Institute for Nanoscience and Quantum Engineering and the National Science Foundation (NSF) MRSEC DMR 1119826. This research was supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) W911NF-09-1-0369, by the US Army Research Office W911NF-09-1-0514, and by the NSF DMR 1006060 and DMR 0653377. M.M. acknowledges partial support from the Agence National de la Recherche under the project EPOQ2 ANR-09-JCJC-0070. S.M.G. and Z.L. acknowledge support from the NSF DMR 1004406. 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.

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Authors

Contributions

S.S. performed the experiment and analysed the data with assistance from M.H. and Z.L. Z.L. proposed the autonomous feedback protocol and performed numerical simulations under the guidance of M.M. K.M.S., A.N. and L.F. contributed to the experimental apparatus, and U.V. contributed to the theoretical modelling under the guidance of S.M.G. M.H.D. supervised the project. S.S., M.H. and M.H.D. wrote the manuscript. All authors provided suggestions for the experiment, discussed the results and contributed to the manuscript.

Corresponding authors

Correspondence to S. Shankar or M. H. Devoret.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Experiment schematic.

The qubit–cavity set-up as well as the JPC amplifier is mounted on the base stage of a dilution refrigerator (bottom of diagram) which is operated at less than 20 mK. The room-temperature set-up consists of electronics used for qubit control (top left) and for qubit measurement (top right). The experiment is controlled by an arbitrary waveform generator (AWG), which produces analogue waveforms and also supplies digital markers (not shown) to the pulsed microwave sources. The drives for stabilization and qubit control are generated from four microwave sources in the present experiment, although the two cavity drives, and , could be produced in principle from the same source. These drives were combined with a measurement drive and sent through filtered and attenuated lines to the cavity input at the base of the fridge. The cavity output is directed to the signal port of a JPC, whose idler is terminated in a 50-Ω load. The JPC is powered by a drive applied to its pump port. The fridge input for JPC tuning is used solely for initial tune up and is terminated during the stabilization experiment. The cavity output signal is amplified in reflection by the JPC and then output from the fridge after further amplification. The output signal is demodulated at room temperature and then digitized by an analogue-to-digital converter along with a reference copy of the measurement drive.

Extended Data Figure 2 Single-shot readout of the observable |gg〉〈gg|.

a, Histogram of measurement outcomes recorded by the projective readout used for tomography. Outcome Im = 0 implies that no microwave field was received in the I quadrature for that measurement. The GG histogram (blue dots) was recorded with the qubits initially prepared in |gg〉 with a fidelity of 99.5%. The histogram (red dots) was recorded after identical preparation followed by a π-pulse on Alice. Solid lines are Gaussian fits. The horizontal axis of measurement outcomes Im is scaled by the average of the standard deviations of the two Gaussians, showing 5.5 standard deviations between the centres of the two distributions. Dashed line indicates the threshold that distinguishes GG from : an outcome of is associated with GG, whereas is associated with . b. Summary of the fidelity of a single projective readout of the state of the two qubits assuming the separatrix .

Extended Data Figure 3 Calibration of systematic errors in tomography.

Fidelity of two-qubit Clifford states measured by tomography identical to that used in the Bell state stabilization protocol. Clifford states are prepared by starting in |gg〉 with a fidelity of 99.5% and then performing individual single-qubit rotations. The fidelity varies from a maximum of 94% for the state |−Z, −Z〉, to a minimum of 87% for the state |+Y, +Z〉, averaging 90% over the 36 states (dashed line).

Extended Data Figure 4 Predicted fidelity to |ϕ〉 as a function of drive parameters and Ωn under the conditions of the present experiment.

Ω0 is taken to be κ/2 in this simulation. A broad distribution of parameter values resulting in a fidelity of about 70% indicates the robustness of the autonomous feedback protocol to variations in the drives.

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Shankar, S., Hatridge, M., Leghtas, Z. et al. Autonomously stabilized entanglement between two superconducting quantum bits. Nature 504, 419–422 (2013). https://doi.org/10.1038/nature12802

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