Quantum oscillations in two coupled charge qubits


A practical quantum computer1, if built, would consist of a set of coupled two-level quantum systems (qubits). Among the variety of qubits implemented2, solid-state qubits are of particular interest because of their potential suitability for integrated devices. A variety of qubits based on Josephson junctions3,4 have been implemented5,6,7,8; these exploit the coherence of Cooper-pair tunnelling in the superconducting state5,6,7,8,9,10. Despite apparent progress in the implementation of individual solid-state qubits, there have been no experimental reports of multiple qubit gates—a basic requirement for building a real quantum computer. Here we demonstrate a Josephson circuit consisting of two coupled charge qubits. Using a pulse technique, we coherently mix quantum states and observe quantum oscillations, the spectrum of which reflects interaction between the qubits. Our results demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Two capacitively coupled charge qubits.
Figure 2: Pulse operation of device.
Figure 3: Quantum oscillations in qubits.
Figure 4: EJ1 dependence of the spectrum components obtained by Fourier transform of the oscillations at the co-resonance.


  1. 1

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000)

    Google Scholar 

  2. 2

    Clark, R. G. (ed.) Experimental Implementation of Quantum Computation (Rinton, Princeton, 2001)

  3. 3

    Averin, D. V. Quantum computing and quantum measurement with mesoscopic Josephson junctions. Fortschr. Phys. 48, 1055–1074 (2000)

    Article  Google Scholar 

  4. 4

    Makhlin, Y., Schön, G. & Shnirman, A. Quantum state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001)

    ADS  Article  Google Scholar 

  5. 5

    Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Yu, Y., Han, S., Chu, X., Chu, S.-I. & Wang, Z. Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science 296, 889–892 (2002)

    ADS  CAS  Article  Google Scholar 

  8. 8

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

    ADS  Article  Google Scholar 

  9. 9

    Friedman, J. R., Patel, V., Chen, W., Toltygo, S. K. & Lukens, J. E. Quantum superposition of distinct macroscopic states. Nature 406, 43–46 (2000)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Van der Wal, C. H. et al. Quantum superposition of macroscopic persistent-current states. Science 290, 773–777 (2000)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Bouchiat, V., Vion, D., Joyez, P., Esteve, D. & Devoret, M. H. Quantum coherence with a single Cooper pair. Phys. Scripta T 76, 165–170 (1998)

    ADS  Article  Google Scholar 

  12. 12

    Flees, D. J., Han, S. & Lukens, J. E. Interband transitions and band gap measurements in Bloch transistors. Phys. Rev. Lett. 78, 4817–4820 (1997)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Nakamura, Y., Chen, C. D. & Tsai, J. S. Spectroscopy of energy-level splitting between two macroscopic quantum states of charge coherently superposed by Josephson coupling. Phys. Rev. Lett. 79, 2328–2331 (1997)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Esteve, D. in Single Charge Tunneling (eds Grabert, H. & Devoret, M. H.) 109–137 (Plenum, New York, 1992)

    Google Scholar 

  15. 15

    Fulton, T. A., Gammel, P. L., Bishop, D. J., Dunkleberger, L. N. & Dolan, G. J. Observation of combined Josephson and charging effects in small tunnel junction circuits. Phys. Rev. Lett. 63, 1307–1310 (1989)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Bennett, C. H., Bernstein, H. J., Popescu, S. & Schumacher, B. Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    ADS  CAS  Article  Google Scholar 

Download references


We thank B. L. Altshuler, X. D. Hu, H. Im, S. Ishizaka, F. Nori, T. Sakamoto and J. Q. You for discussions. D.V.A. was supported by AFORS, and by NSA and ARDA under an ARO contract.

Author information



Corresponding author

Correspondence to J. S. Tsai.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pashkin, Y., Yamamoto, T., Astafiev, O. et al. Quantum oscillations in two coupled charge qubits. Nature 421, 823–826 (2003). https://doi.org/10.1038/nature01365

Download citation

Further reading


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.