Ultrastrong coupling in a scalable design for circuit QED with superconducting flux qubits


We theoretically study a circuit quantum electrodynamics architecture with superconducting flux qubits. The qubit is coupled to the transmission line resonator by an ac current originating from the current mode of the resonator. Ultrastrong coupling can be obtained by varying the capacitance between the qubit and the resonator. We propose a scalable design where the two-qubit coupling can be achieved.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5


  1. 1.

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

    Article  ADS  Google Scholar 

  2. 2.

    Blais, A., Gambetta, J., Wallraff, A., Schuster, D.I., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Quantum-information processing with circuit quantum electrodynamics. Phys. Rev. A 75, 032329 (2007)

    Article  ADS  Google Scholar 

  3. 3.

    Mooij, J.E., Orlando, T.P., Levitov, L., Tian, L., van der Wal, C.H., Lloyd, S.: Josephson persistent-current qubit. Science 285, 1036 (1999)

    Article  Google Scholar 

  4. 4.

    Chiorescu, I., Nakamura, Y., Harmans, C.J.P.M., Mooij, J.E.: Coherent quantum dynamics of a superconducting flux qubit. Science 299, 1869 (2003)

    Article  ADS  Google Scholar 

  5. 5.

    Orlando, T.P., Mooij, J.E., Tian, L., van der Wal, C.H., Levitov, L.S., Lloyd, S., Mazo, J.J.: Superconducting persistent-current qubit. Phys. Rev. B 60, 15398 (1999)

    Article  ADS  Google Scholar 

  6. 6.

    Kim, M.D., Shin, D., Hong, J.: Double-well potentials in current qubits. Phys. Rev. B 68, 134513 (2003)

    Article  ADS  Google Scholar 

  7. 7.

    Lindstrom, T., Webster, C.H., Healey, J.E., Colclough, M.S., Muirhead, C.M., Tzalenchuk, A.Y.: Circuit QED with a flux qubit strongly coupled to a coplanar transmission line resonator. Supercond. Sci. Technol. 20, 814 (2007)

    Article  ADS  Google Scholar 

  8. 8.

    Oelsner, G., van der Ploeg, S.H.W., Macha, P., Hubner, U., Born, D., Anders, S., Il’ichev, E., Meyer, H.-G., Grajcar, M., Wünsch, S., Siegel, M., Omelyanchouk, A.N., Astafiev, O.: Weak continuous monitoring of a flux qubit using coplanar waveguide resonator. Phys. Rev. B 81, 172505 (2010)

    Article  ADS  Google Scholar 

  9. 9.

    Abdumalikov Jr, A.A., Astafiev, O., Nakamura, Y., Pashkin, Y.A., Tsai, J.S.: Vacuum Rabi splitting due to strong coupling of a flux qubit and a coplanar-waveguide resonator. Phys. Rev. B 78, 180502(R) (2008)

    Article  ADS  Google Scholar 

  10. 10.

    Bourassa, J., Gambetta, J.M., Abdumalikov Jr, A.A., Astafiev, O., Nakamura, Y., Blais, A.: Ultrastrong coupling regime of cavity QED with phase-biased flux qubits. Phys. Rev. A 80, 032109 (2009)

    Article  ADS  Google Scholar 

  11. 11.

    Niemczyk, T., Deppe, F., Huebl, H., Menzel, E.P., Hocke, F., Schwarz, M.J., Garcia-Ripoll, J.J., Zueco, D., Hummer, T., Solano, E., Marx, A., Gross, R.: Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nat. Phys. 6, 772 (2010)

    Article  Google Scholar 

  12. 12.

    Forn-Diaz, P., Lisenfeld, J., Marcos, D., Garcia-Ripoll, J.J., Solano, E., Harmans, C.J.P.M., Mooij, J.E.: Observation of the Bloch-Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime. Phys. Rev. Lett. 105, 237001 (2010)

    Article  ADS  Google Scholar 

  13. 13.

    Kim, M.D., Moon, K.: Strong coupling of a cavity QED architecture for a current-biased flux qubit. J. Korean Phys. Soc. 58, 1599 (2011). arXiv:1005.1703

    Article  Google Scholar 

  14. 14.

    Steffen, M., Kumar, S., DiVincenzo, D.P., Rozen, J.R., Keefe, G.A., Rothwell, M.B., Ketchen, M.B.: High-coherence hybrid superconducting qubit. Phys. Rev. Lett. 105, 100502 (2010)

    Article  ADS  Google Scholar 

  15. 15.

    Chow, J.M., Corcoles, A.D., Gambetta, J.M., Rigetti, C., Johnson, B.R., Smolin, J.A., Rozen, J.R., Keefe, G.A., Rothwell, M.B., Ketchen, M.B., Steffen, M.: Simple all-microwave entangling gate for fixed-frequency superconducting qubits. Phys. Rev. Lett. 107, 080502 (2011)

    Article  ADS  Google Scholar 

  16. 16.

    Inomata, K., Yamamoto, T., Billangeon, P.-M., Nakamura, Y., Tsai, J.S.: Large dispersive shift of cavity resonance induced by a superconducting flux qubit in the straddling regime. Phys. Rev. B 86, 140508(R) (2012)

    Article  ADS  Google Scholar 

  17. 17.

    Martinis, J.M., Nam, S., Aumentado, J., Urbina, C.: Rabi oscillations in a large Josephson-junction qubit. Phys. Rev. Lett. 89, 117901 (2002)

    Article  ADS  Google Scholar 

  18. 18.

    Martinis, J.M.: Superconducting phase qubits. Quantum Inf. Process. 8, 81 (2009)

    Article  Google Scholar 

  19. 19.

    Berkley, A.J., Xu, H., Ramos, R.C., Gubrud, M.A., Strauch, F.W., Johnson, P.R., Anderson, J.R., Dragt, A.J., Lobb, C.J., Wellstood, F.C.: Entangled macroscopic quantum states in two superconducting qubits. Science 300, 1548 (2003)

    Article  ADS  Google Scholar 

  20. 20.

    Sillanpää, M.A., Park, J.I., Simmonds, R.W.: Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438 (2007)

    Article  ADS  Google Scholar 

  21. 21.

    Ballester, D., Romero, G., Garcia-Ripoll, J.J., Deppe, F., Solano, E.: Quantum simulation of the ultrastrong-coupling dynamics in circuit quantum electrodynamics. Phys. Rev. X 2, 021007 (2012)

    Google Scholar 

  22. 22.

    Nataf, P., Ciuti, C.: Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED. Phys. Rev. Lett. 107, 190402 (2011)

    Article  ADS  Google Scholar 

  23. 23.

    Romero, G., Ballester, D., Wang, Y.M., Scarani, V., Solano, E.: Ultrafast quantum gates in circuit QED. Phys. Rev. Lett. 108, 120501 (2012)

    Article  ADS  Google Scholar 

  24. 24.

    Majer, J., Chow, J.M., Gambetta, J.M., Koch, J., Johnson, B.R., Schreier, J.A., Frunzio, L., Schuster, D.I., Houck, A.A., Wallraff, A., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Coupling superconducting qubits via a cavity bus. Nature 449, 443 (2007)

    Article  ADS  Google Scholar 

  25. 25.

    You, J.Q., Nakamura, Y., Nori, F.: Fast two-qubit operation in inductively coupled qubits. Phys. Rev. B 71, 024532 (2005)

    Article  ADS  Google Scholar 

  26. 26.

    You, J.Q., Hu, X., Ashhab, S., Nori, F.: Low-decoherence flux qubit. Phys. Rev. B 75, 140515(R) (2007)

    Article  ADS  Google Scholar 

  27. 27.

    Tinkham, M.: Introduction to Superconductivity, vol. 2. McGraw Hill, New York (1996)

    Google Scholar 

  28. 28.

    Huang, R.-S.: Qubit-resonator system as an application to quantum computation, PhD thesis, Indiana Univ. (2004)

  29. 29.

    Casanova, J., Romero, G., Lizuain, I., García-Ripoll, J.J., Solano, E.: Deep strong coupling regime of the Jaynes–Cummings model. Phys. Rev. Lett. 105, 263603 (2010)

    Article  ADS  Google Scholar 

  30. 30.

    Göppl, M., Fragner, A., Baur, M., Bianchetti, R., Filipp, S., Fink, J.M., Leek, P.J., Puebla, G., Steffen, L., Wallraff, A.: Coplanar waveguide resonators for circuit quantum electrodynamics. J. Appl. Phys. 104, 113904 (2008)

    Article  ADS  Google Scholar 

  31. 31.

    Houck, A.A., Schreier, J.A., Johnson, B.R., Chow, J.M., Koch, J., Gambetta, J.M., Schuster, D.I., Frunzio, L., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Controlling the spontaneous emission of a superconducting transmon qubit. Phys. Rev. Lett. 101, 080502 (2008)

    Article  ADS  Google Scholar 

  32. 32.

    Filipp, S., Göppl, M., Fink, J.M., Baur, M., Bianchetti, R., Steffen, L., Wallraff, A.: Multimode mediated qubit-qubit coupling and dark-state symmetries in circuit quantum electrodynamics. Phys. Rev. A 83, 063827 (2011)

    Article  ADS  Google Scholar 

  33. 33.

    McKay, D.C., Naik, R., Reinhold, P., Bishop, L.S., Schuster, D.I.: High-contrast qubit interactions using multimode cavity QED. Phys. Rev. Lett. 114, 080501 (2015)

    Article  ADS  Google Scholar 

  34. 34.

    Simmonds, R.W., Lang, K.M., Hite, D.A., Nam, S., Pappas, D.P., Martinis, J.M.: Decoherence in Josephson phase qubits from junction resonators. Phys. Rev. Lett. 93, 077003 (2004)

    Article  ADS  Google Scholar 

  35. 35.

    Martinis, J.M., Nam, S., Aumentado, J., Lang, K.M.: Decoherence of a superconducting qubit due to bias noise. Phys. Rev. B 67, 094510 (2003)

    Article  ADS  Google Scholar 

  36. 36.

    Jaynes, E.T., Cummings, F.W.: Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89 (1963)

    Article  Google Scholar 

  37. 37.

    Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Kumar, S., Girvin, S.M., Schoelkopf, R.J.: Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162 (2004)

    Article  ADS  Google Scholar 

Download references


The author acknowledges the useful discussion with K. Moon. This work was partly supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0023467) and by the IT R&D program of MOTIE/KEIT [10043464(2012)].

Author information



Corresponding author

Correspondence to Mun Dae Kim.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kim, M.D. Ultrastrong coupling in a scalable design for circuit QED with superconducting flux qubits. Quantum Inf Process 14, 3677–3691 (2015). https://doi.org/10.1007/s11128-015-1073-2

Download citation


  • Circuit quantum electrodynamics
  • Flux qubit
  • Ultrastrong coupling
  • Scalable design