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Preparation and measurement of three-qubit entanglement in a superconducting circuit

Nature volume 467, pages 574–578 (2010)Cite this article

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Abstract

Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles1. With the ample experimental2,3,4 confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation5. Although entanglement in superconducting circuits has been limited so far to two qubits6,7,8,9, the extension of entanglement to three, eight and ten qubits has been achieved among spins10, ions11 and photons12, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture13,14, we demonstrate deterministic production of three-qubit Greenberger–Horne–Zeilinger (GHZ) states15 with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830 ± 80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.

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Figure 1: Four-qubit cQED processor, and spectroscopic characterization.
Figure 2: Frequency- and time-domain characterization of two-qubit-gate primitive.
Figure 3: Building 3QE with two two-qubit gates.
Figure 4: Witnessing of 3QE using fidelity and Mermin inequalities.

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References

  1. Mermin, N. D. Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838–1840 (1990)

    CAS  Google Scholar 

  2. Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)

    Google Scholar 

  3. Pan, J.-W., Bouwmeester, D., Daniell, M., Weinfurter, H. & Zeilinger, A. Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement. Nature 403, 515–519 (2000)

    CAS  Google Scholar 

  4. Zhao, Z. et al. Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement. Phys. Rev. Lett. 91, 180401 (2003)

    Google Scholar 

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

    Google Scholar 

  6. Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006)

    CAS  Google Scholar 

  7. DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

    CAS  Google Scholar 

  8. Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009)

    CAS  Google Scholar 

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

    Google Scholar 

  10. Neumann, P. et al. Multipartite entanglement among single spins in diamond. Science 320, 1326–1329 (2008)

    CAS  Google Scholar 

  11. Häffner, H. et al. Scalable multiparticle entanglement of trapped ions. Nature 438, 643–646 (2005)

    Google Scholar 

  12. Gao, W.-B. et al. Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state. Nature Phys. 6, 331–335 (2010)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  14. 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)

    Google Scholar 

  15. Greenberger, D. M., Horne, M. A. & Zeilinger, A. in Bell’s Theorem, Quantum Theory and Conceptions of the Universe (ed. Kafatos, M.) 69–72 (Kluwer Academic, 1989)

    Google Scholar 

  16. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008)

    CAS  Google Scholar 

  17. Neeley, M. et al. Generation of three-qubit entangled states using superconducting phase qubits. Nature doi:10.1038/nature09418 (this issue).

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

    Google Scholar 

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

    Google Scholar 

  20. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  23. Reed, M. D. et al. High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity. Phys. Rev. Lett. (in the press); preprint at 〈http://arxiv.org/abs/1004.4323〉 (2010)

  24. Strauch, F. W. et al. Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003)

    Google Scholar 

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

    CAS  Google Scholar 

  26. Bishop, L. S., Ginossar, E. & Girvin, S. M. Response of the strongly-driven Jaynes-Cummings oscillator. Phys. Rev. Lett. 105, 100505 (2010)

    Google Scholar 

  27. Acín, A., Bruß, D., Lewenstein, M. & Sanpera, A. Classification of mixed three-qubit states. Phys. Rev. Lett. 87, 040401 (2001)

    Google Scholar 

  28. Altomare, F. et al. Tripartite interactions between two phase qubits and a resonant cavity. Preprint at 〈http://arxiv.org/abs/1004.0026〉 (2010)

  29. Tóth, G. & Gühne, O. Entanglement detection in the stabilizer formalism. Phys. Rev. A 72, 022340 (2005)

    Google Scholar 

  30. Kwiat, P. G., Eberhard, P. H., Steinberg, A. M. & Chiao, R. Y. Proposal for a loophole-free Bell inequality experiment. Phys. Rev. A 49, 3209–3220 (1994)

    CAS  Google Scholar 

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Acknowledgements

We thank M. Brink for experimental contributions, and L. S. Bishop, E. Ginossar, O. Gühne, C. Rigetti, D. I. Schuster and J. Siewert for discussions. We acknowledge support from LPS/NSA under ARO contract W911NF-05-1-0365, from IARPA under ARO contract W911NF-09-1-0369 and from the NSF under grants DMR-0653377 and DMR-0603369. Additional support was provided by CNR-Istituto di Cibernetica, Pozzuoli, Italy (L.F.), and by CIFAR, MITACS, MRI and NSERC (J.M.G.). 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 the US Government.

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Authors and Affiliations

  1. Departments of Physics and Applied Physics, Yale University, New Haven, 06511, Connecticut, USA

    L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, L. Frunzio, S. M. Girvin, M. H. Devoret & R. J. Schoelkopf

  2. Department of Physics and Astronomy and Institute for Quantum Computing, University of Waterloo, Waterloo, N2L 3G1, Ontario, Canada

    J. M. Gambetta

Authors
  1. L. DiCarlo
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  2. M. D. Reed
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  3. L. Sun
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  6. J. M. Gambetta
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  7. L. Frunzio
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  8. S. M. Girvin
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  10. R. J. Schoelkopf
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Contributions

L.D.C., M.D.R. and L.S. carried out measurements and data analysis. B.R.J. and J.M.C. provided further experimental contributions. J.M.G. provided theory support. L.F., L.D.C. and L.S. fabricated devices. L.D.C. and M.H.D. wrote the manuscript, with feedback from all authors. S.M.G., M.H.D. and R.J.S. designed and supervised the project.

Corresponding authors

Correspondence to L. DiCarlo or R. J. Schoelkopf.

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The authors declare no competing financial interests.

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DiCarlo, L., Reed, M., Sun, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010). https://doi.org/10.1038/nature09416

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