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Strong parametric dispersive shifts in a statically decoupled two-qubit cavity QED system

Nature Physics volume 19, pages 1445–1451 (2023)Cite this article

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Abstract

Qubits in cavity quantum electrodynamic (QED) architectures are often operated in the dispersive regime, in which the operating frequency of the cavity depends on the energy state of the qubit, and vice versa. The ability to tune these dispersive shifts provides additional options for performing either quantum measurements or logical manipulations. Here we couple two transmon qubits to a lumped-element cavity through a shared superconducting quantum interference device (SQUID). Our design balances the mutual capacitive and inductive circuit components so that both qubits are statically decoupled from the cavity with low flux sensitivity, offering protection from decoherence processes. Parametric driving of the SQUID flux enables independent, dynamical tuning of each qubit’s interaction with the cavity. As a practical demonstration, we perform pulsed parametric dispersive readout of both qubits. The dispersive frequency shifts of the cavity mode follow the theoretically expected magnitude and sign. This parametric approach creates an extensible, tunable cavity QED framework with various future applications, such as entanglement and error correction via multi-qubit parity readout, state and entanglement stabilization, and parametric logical gates.

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Fig. 1: A flux- and parametrically tunable two-qubit cavity QED system.
Fig. 2: Cavity spectrum and parametric dispersive shifts of the R transmon.
Fig. 3: Static dispersive shifts of the R transmon.
Fig. 4: Cavity photon-induced dephasing.
Fig. 5: Demonstration of joint state readout of both L and R transmons.

Data availability

The data that support the findings of this study are available from the NIST Public Data Repository at https://doi.org/10.18434/mds2-3027. Source data are provided with this paper.

References

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

    ADS  Google Scholar 

  2. 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  Google Scholar 

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

  4. Chow, J. M. et al. Implementing a strand of a scalable fault-tolerant quantum computing fabric. Nat. Commun. 5, 4015 (2014).

    ADS  Google Scholar 

  5. Pechal, M. et al. Microwave-controlled generation of shaped single photons in circuit quantum electrodynamics. Phys. Rev. X 4, 041010 (2014).

    Google Scholar 

  6. Campagne-Ibarcq, P. et al. Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions. Phys. Rev. Lett. 120, 200501 (2018).

    ADS  Google Scholar 

  7. Frattini, N. E. et al. 3-wave mixing Josephson dipole element. Appl. Phys. Lett. 110, 222603 (2017).

    ADS  Google Scholar 

  8. Pfaff, W. et al. Controlled release of multiphoton quantum states from a microwave cavity memory. Nat. Phys. 13, 882–887 (2017).

    Google Scholar 

  9. Allman, M. S. et al. rf-SQUID-mediated coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. Phys. Rev. Lett. 104, 177004 (2010).

    ADS  Google Scholar 

  10. Srinivasan, S. J., Hoffman, A. J., Gambetta, J. M. & Houck, A. A. Tunable coupling in circuit quantum electrodynamics using a superconducting charge qubit with a V-shaped energy level diagram. Phys. Rev. Lett. 106, 083601 (2011).

    ADS  Google Scholar 

  11. Allman, M. S. et al. Tunable resonant and nonresonant interactions between a phase qubit and LC resonator. Phys. Rev. Lett. 112, 123601 (2014).

    ADS  Google Scholar 

  12. Whittaker, J. D. et al. Tunable-cavity QED with phase qubits. Phys. Rev. B 90, 024513 (2014).

    ADS  Google Scholar 

  13. Zhang, G., Liu, Y., Raftery, J. J. & Houck, A. A. Suppression of photon shot noise dephasing in a tunable coupling superconducting qubit. npj Quantum Inf. 3, 1 (2017).

    ADS  Google Scholar 

  14. Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014).

    ADS  Google Scholar 

  15. Neill, C. et al. A blueprint for demonstrating quantum supremacy with superconducting qubits. Science 360, 195–198 (2018).

    ADS  MathSciNet  Google Scholar 

  16. Sung, Y. et al. Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler. Phys. Rev. X 11, 021058 (2021).

    Google Scholar 

  17. Stehlik, J. et al. Tunable coupling architecture for fixed-frequency transmon superconducting qubits. Phys. Rev. Lett. 127, 080505 (2021).

    ADS  Google Scholar 

  18. Jin, X. Y. et al. Versatile parametric coupling between two statically decoupled transmon qubits. Preprint at https://arxiv.org/abs/2305.02907 (2023).

  19. Hutchings, M. D. et al. Tunable superconducting qubits with flux-independent coherence. Phys. Rev. Appl. 8, 044003 (2017).

    ADS  Google Scholar 

  20. Chávez-Garcia, J. M. et al. Weakly flux-tunable superconducting qubit. Phys. Rev. Appl. 18, 034057 (2022).

    ADS  Google Scholar 

  21. Bertet, P., Harmans, C. J. P. M. & Mooij, J. E. Parametric coupling for superconducting qubits. Phys. Rev. B 73, 064512 (2006).

    ADS  Google Scholar 

  22. Tian, L., Allman, M. S. & Simmonds, R. W. Parametric coupling between macroscopic quantum resonators. New J. Phys. 10, 115001 (2008).

    ADS  Google Scholar 

  23. Zakka-Bajjani, E. et al. Quantum superposition of a single microwave photon in two different ‘colour’ states. Nat. Phys. 7, 599–603 (2011).

    Google Scholar 

  24. Nguyen, F., Zakka-Bajjani, E., Simmonds, R. W. & Aumentado, J. Quantum interference between two single photons of different microwave frequencies. Phys. Rev. Lett. 108, 163602 (2012).

    ADS  Google Scholar 

  25. Reagor, M. et al. Demonstration of universal parametric entangling gates on a multi-qubit lattice. Sci. Adv. 4, 2 (2018).

    Google Scholar 

  26. Noguchi, A. et al. Fast parametric two-qubit gates with suppressed residual interaction using the second-order nonlinearity of a cubic transmon. Phys. Rev. A 102, 062408 (2018).

    ADS  Google Scholar 

  27. Mundada, P., Zhang, G., Hazard, T. & Houck, A. Suppression of qubit crosstalk in a tunable coupling superconducting circuit. Phys. Rev. Appl. 12, 054023 (2019).

    ADS  Google Scholar 

  28. Ganzhorn, M. et al. Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform. Phys. Rev. Res. 2, 033447 (2020).

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

    ADS  Google Scholar 

  30. Rosenblum, S. et al. A CNOT gate between multiphoton qubits encoded in two cavities. Nat. Commun. 9, 652 (2018).

    ADS  Google Scholar 

  31. Yin, Y. et al. Catch and release of microwave photon states. Phys. Rev. Lett. 110, 107001 (2013).

    ADS  Google Scholar 

  32. Srinivasan, S. J. et al. Time-reversal symmetrization of spontaneous emission for quantum state transfer. Phys. Rev. A 89, 033857 (2014).

    ADS  Google Scholar 

  33. Rosenblum, S. et al. Fault-tolerant detection of a quantum error. Science 361, 266–270 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  34. Doucet, E., Reiter, F., Ranzani, L. & Kamal, A. High fidelity dissipation engineering using parametric interactions. Phys. Rev. Res. 2, 023370 (2020).

    Google Scholar 

  35. Brown, T. et al. Trade off-free entanglement stabilization in a superconducting qutrit–qubit system. Nat. Commun. 13, 3994 (2022).

    ADS  Google Scholar 

  36. Xiao, Z. et al. Perturbative diagonalization for time-dependent strong interactions. Phys. Rev. Appl. 18, 024009 (2022).

    ADS  Google Scholar 

  37. McClure, D. T. et al. Rapid driven reset of a qubit readout resonator. Phys. Rev. Appl. 5, 011001 (2016).

    ADS  Google Scholar 

  38. Yeh, J.-H., LeFebvre, J., Premaratne, S., Wellstood, F. C. & Palmer, B. S. Microwave attenuators for use with quantum devices below 100 mK. J. Appl. Phys. 121, 224501 (2017).

    ADS  Google Scholar 

  39. Yan, F. et al. Distinguishing coherent and thermal photon noise in a circuit quantum electrodynamical system. Phys. Rev. Lett. 120, 260504 (2018).

    ADS  Google Scholar 

  40. Wang, Z. et al. Cavity attenuators for superconducting qubits. Phys. Rev. Appl. 11, 014031 (2019).

    ADS  Google Scholar 

  41. Roch, N. et al. Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits. Phys. Rev. Lett. 112, 170501 (2014).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  43. Andersen, C. K. et al. Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits. npj Quantum Inf. 5, 69 (2019).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  45. Gambetta, J. et al. Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006).

    ADS  Google Scholar 

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

    Google Scholar 

  47. Sete, E. A., Martinis, J. M. & Korotkov, A. N. Quantum theory of a bandpass Purcell filter for qubit readout. Phys. Rev. A 92, 012325 (2015).

    ADS  Google Scholar 

  48. Eddins, A. et al. High-efficiency measurement of an artificial atom embedded in a parametric amplifier. Phys. Rev. X 9, 011004 (2019).

    Google Scholar 

  49. Royer, B., Puri, S. & Blais, A. Qubit parity measurement by parametric driving in circuit QED. Sci. Adv. 4, eaau1695 (2018).

    ADS  Google Scholar 

  50. Hertzberg, J. B. et al. Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors. npj Quantum Inf. 7, 129 (2021).

    ADS  Google Scholar 

Download references

Acknowledgements

This work was partially performed with financial assistance from award no. 70NANB18H006 from the US Department of Commerce, National Institute of Standards and Technology. T.N., Z.X., E.D., L.R., L.G. and A.K. received support from the Department of Energy under grant no. DE-SC0019461. We thank D. Slichter and A. Sirois for commenting on the paper.

Author information

Authors and Affiliations

  1. National Institute of Standards and Technology, Boulder, CO, USA

    T. Noh, X. Y. Jin, K. Cicak, J. Aumentado & R. W. Simmonds

  2. Department of Physics, University of Colorado, Boulder, CO, USA

    T. Noh & X. Y. Jin

  3. Department of Physics and Applied Physics, University of Massachusetts, Lowell, MA, USA

    T. Noh, Z. Xiao, E. Doucet & A. Kamal

  4. Quantum Engineering and Computing, Raytheon BBN Technologies, Cambridge, MA, USA

    L. C. G. Govia & L. Ranzani

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  1. T. Noh
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Contributions

T.N. conducted the experiment. T.N. and R.W.S. analysed the data. R.W.S. designed and K.C. fabricated the device. X.Y.J. and J.A. contributed to the measurement set-up and software. Z.X., E.D., L.C.G.G., L.R. and A.K. provided theoretical support and suggestions for the experiment. T.N. and R.W.S. wrote the paper and supplementary information. R.W.S. conceived the experiment and supervised the project. All authors contributed to the preparation of the paper.

Corresponding authors

Correspondence to T. Noh or R. W. Simmonds.

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Extended data

Extended Data Fig. 1 Cavity spectrum and parametric dispersive shifts of the L transmon.

As with Fig. 2 in the main text for the R transmon, we performed the same measurements with the L transmon. (a) A typical cavity spectrum while sweeping the pump frequency ωp. The upper and lower panel shows the result with the L transmon in the ground state \(\left\vert {g}_{L}\right\rangle\) and the first excited state \(\left\vert {e}_{L}\right\rangle\), respectively. (b) The dispersive shifts as a function of the pump detuning frequency, ΔpL = ωp − (ωC − ωL), at various calibrated pump amplitudes, δϕp = 0.028 (red), 0.056 (orange), 0.084 (yellow), 0.112 (green), 0.14 (blue), and 0.168 (purple). The solid lines are the fits to the data from the theory. See the main text for more details.

Source data

Extended Data Fig. 2 Static dispersive shifts of the L transmon.

As with Fig. 3 in the main text for the R transmon, we performed the same measurements with the L transmon. (a) The static dispersive shift ∣2χsL/2π∣ as a function of the L transmon frequency. For empty squares, the dispersive shift was measured by comparing the cavity response with the L transmon in either state \({\left\vert g\right\rangle }_{L}\) or \({\left\vert e\right\rangle }_{L}\). For filled circles, the dispersive shift was extracted by measuring additional dephasing ΓnL while driving the cavity with a weak coherent state. The solid line represents a fit to the data based on the circuit model. (b) Additional dephasing as a function of average photon number \(\bar{n}\) of a weak coherent drive at three different flux biases where the R tranmon frequencies are 5.784 (red square), 5.826 (yellow circle), and 5.858 GHz (green triangle), respectively. Solid lines are linear fits to the data.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–9, Discussion and Table I.

Source data

Source Data Fig. 1

Cavity, R transmon, and L transmon spectroscopy data for Fig. 1d.

Source Data Fig. 2

Cavity spectrum at various pump frequencies for top 2D color maps in Fig. 2a. Cavity spectrum at two pump frequencies for bottom plots in Fig.2a. Dispersive shift as a function of pump frequency at various pump amplitudes for Fig. 2b. Parametric coupling strength as a function of pump amplitude for Fig. 2c.

Source Data Fig. 3

Static dispersive shift as a function of R transmon frequency for Fig. 3a. Additional dephasing of R transmon as a function of the average photon number at three different flux biases for Fig. 3b.

Source Data Fig. 4

T2* as a function of R transmon frequency at various average photon numbers.

Source Data Fig. 5

Cavity spectrum with four different two-transmon states for Fig. 5a, b, and c.

Source Data Extended Data Fig. 1

Cavity spectrum at various pump frequencies for top 2D color maps in Extended Data Fig. 1a. Dispersive shift as a function of pump frequency at various pump amplitudes for Extended Data Fig. 1b.

Source Data Extended Data Fig. 2

Static dispersive shift as a function of L transmon frequency for Extended Data Fig. 2a. Additional dephasing of L transmon as a function of the average photon number at three different flux biases for Extended Data Fig. 2b.

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Noh, T., Xiao, Z., Jin, X.Y. et al. Strong parametric dispersive shifts in a statically decoupled two-qubit cavity QED system. Nat. Phys. 19, 1445–1451 (2023). https://doi.org/10.1038/s41567-023-02107-2

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