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Experimental one-way quantum computing

Nature volume 434, pages 169–176 (2005)Cite this article

Abstract

Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.

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Figure 1: Few-qubit cluster states and the quantum circuits they implement.
Figure 2: Density matrix of the four-qubit cluster state in the laboratory basis.
Figure 3: Output Bloch vectors from single qubit rotations using a three-qubit linear cluster |Φlin3〉.
Figure 4: The output density matrices from two different two-qubit computations.
Figure 5: Grover's algorithm in a cluster state quantum computer.
Figure 6: The experimental set-up to produce and measure cluster states.

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References

  1. Deutsch, D. & Ekert, E. Quantum computation. Phys. World 11, 47–52 (1998)

    Article  CAS  Google Scholar 

  2. Braunstein, S. L. & Lo, H.-K. (eds) Experimental proposals for quantum computation. Fortschr. Phys. 48 (special focus issue 9–11), 767–1138 (2000).

  3. Shor, P. W. in Proc. 35th Annu. Symp. Foundations of Computer Science (ed. Goldwasser, S.) 124–134 (IEEE Computer Society Press, Los Alamitos, 1994)

    Book  Google Scholar 

  4. Grover, L. K. Quantum mechanics helps in search for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)

    Article  ADS  CAS  Google Scholar 

  5. Bennett, C. & DiVicenzo, D. Quantum information and computation. Nature 404, 247–255 (2000)

    Article  ADS  CAS  Google Scholar 

  6. Ekert, A. & Josza, R. Quantum algorithms: entanglement enhanced information processing. Phil. Trans. R. Soc. Lond. A 356, 1769–1782 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  7. Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)

    Article  ADS  CAS  Google Scholar 

  8. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)

    Article  ADS  CAS  Google Scholar 

  9. Linden, N. & Popescu, S. Good dynamics versus bad kinematics: Is entanglement needed for quantum computation? Phys. Rev. Lett. 87, 047901 (2001)

    Article  ADS  CAS  Google Scholar 

  10. Josza, R. & Linden, N. On the role of the entanglement in quantum computational speed-up. Proc. R. Soc. Lond. A 459, 2011–2032 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  11. Nielsen, M. A. Quantum computation by measurement and quantum memory. Phys. Lett. A 308, 96–100 (2003)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  12. Biham, E., Brassard, G., Kenigsberg, D. & Mor, T. Quantum computing without entanglement. Theor. Comput. Sci. 320, 15–33 (2004)

    Article  MathSciNet  Google Scholar 

  13. Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001)

    Article  ADS  CAS  Google Scholar 

  14. Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)

    Article  ADS  CAS  Google Scholar 

  15. Raussendorf, R. & Briegel, H. J. Computational model underlying the one-way quantum computer. Quant. Inform. Comput. 2, 344–386 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Raussendorf, R., Brown, D. E. & Briegel, H. J. The one-way quantum computer—a non-network model of quantum computation. J. Mod. Opt. 49, 1299–1306 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  17. Raussendorf, R., Brown, D. E. & Briegel, H. J. Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312 (2003)

    Article  ADS  Google Scholar 

  18. Nielsen, M. & Dawson, C. M. Fault-tolerant quantum computation with cluster states. Preprint at http://arXiv.org/quant-ph/0405134 (2004).

  19. Mandel, O. et al. Controlled collisions for multiparticle entanglement of optically trapped ions. Nature 425, 937–940 (2003)

    Article  ADS  CAS  Google Scholar 

  20. O'Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C. & Branning, D. Demonstration of an all-optical quantum controlled-not gate. Nature 426, 264–267 (2003)

    Article  ADS  CAS  Google Scholar 

  21. Pittman, T. B., Fitch, M. J., Jacobs, B. C. & Franson, J. D. Experimental controlled-not logic gate of single photons in the coincidence basis. Phys. Rev. A. 68, 032316 (2003)

    Article  ADS  Google Scholar 

  22. Gasparoni, S., Pan, J.-W., Walther, P., Rudolph, T. & Zeilinger, A. Realization of a photonic controlled-NOT gate sufficient for quantum computation. Phys. Rev. Lett. 92, 020504 (2004)

    Article  Google Scholar 

  23. Sanaka, K., Jennewein, T., Pan, J.-W., Resch, K. & Zeilinger, A. Experimental nonlinear sign-shift for linear optics quantum computation. Phys. Rev. Lett. 92, 017902 (2004)

    Article  ADS  Google Scholar 

  24. Nielsen, M. A. Optical quantum computation using cluster states. Phys. Rev. Lett. 93, 040503 (2004)

    Article  ADS  Google Scholar 

  25. Brown, D. E. & Rudolph, T. Efficient linear optical quantum computation. Preprint at http://arXiv.org/quant-ph/0405157 (2004).

  26. Walther, P. et al. De Broglie wavelength of a non-local four-photon state. Nature 429, 158–161 (2004)

    Article  ADS  CAS  Google Scholar 

  27. Hein, M., Eisert, J. & Briegel, H.-J. Multi-party entanglement in graph states. Phys. Rev. A 69, 062311 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  28. Roos, C. F. et al. Control and measurement of three-qubit entangled states. Science 304, 1478–1480 (2004)

    Article  ADS  CAS  Google Scholar 

  29. Weinstein, Y. et al. Quantum process tomography of the quantum Fourier transform. J. Chem. Phys. 121, 6117–6133 (2004)

    Article  ADS  CAS  Google Scholar 

  30. Hradil, Z. Quantum-state estimation. Phys. Rev. A 55, R1561–R1564 (1997)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  31. Banaszek, K., Ariano, A., Paris, M. & Sacchi, M. Maximum-likelihood estimation of the density matrix. Phys. Rev. A 61, 010304 (1999)

    Article  Google Scholar 

  32. James, D., Kwiat, P., Munro, W. & White, A. Measurement of qubits. Phys. Rev. A 64, 052312 (2001)

    Article  ADS  Google Scholar 

  33. Toth, G. & Guehne, O. Detecting genuine multipartite entanglement with two local measurements. Preprint at http://arXiv.org/quant-ph/0405165 (2004).

  34. Dür, W. & Briegel, H.-J. Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92, 180403 (2004)

    Article  ADS  Google Scholar 

  35. Greenberger, D. M., Horne, M. A. & Zeilinger, A. in Bell's Theorem, Quantum Theory and Concepts of the Universe (ed. Kafatos, M.) (Kluwer, Dordrecht, 1989)

    Google Scholar 

  36. Zeilinger, A., Horne, M. & Greenberger, D. in Squeezed States and Quantum Uncertainty (eds Han, D., Kim, Y. S. & Zachary, W. W.) (NASA Conference Publication 3135, NASA, College Park, 1992)

    MATH  Google Scholar 

  37. Dür, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 62314–62325 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  38. SenDe, A., Sen, U., Wiesniak, M., Kaszlikowski, D. & Zukowski, M. Multi-qubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states. Phys. Rev. A 68, 623306 (2003)

    Google Scholar 

  39. Horodecki, M., Horodecki, P. & Horodecki, R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  40. Peres, A. Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1415 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  41. Chuang, I. L. & Nielsen, M. A. Prescription for experimental determination of the dynamics of a quantum black box. J. Mod. Opt. 44, 2455–2467 (1997)

    Article  ADS  Google Scholar 

  42. Poyatos, J. F., Cirac, J. I. & Zoller, P. Complete characterization of a quantum process: the two-bit quantum gate. Phys. Rev. Lett. 78, 390–393 (1997)

    Article  ADS  CAS  Google Scholar 

  43. Schumacher, B. Quantum coding. Phys. Rev. A 51, 2738–2747 (1995)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  44. Coffman, V., Kundu, J. & Wootters, W. K. Distributed entanglement. Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

  45. Horodecki, R., Horodecki, P. & Horodecki, M. Violating Bell inequality by mixed spin-1/2 states: necessary and sufficient condition. Phys. Lett. A 200, 340–344 (1995)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  46. Ahn, J., Weinacht, T. C. & Bucksbaum, P. H. Information storage and retrieval through quantum phase. Science 287, 463–465 (2000)

    Article  ADS  CAS  Google Scholar 

  47. Bhattacharya, N., van Linden van den Heuvell, H. B. & Spreeuw, R. J. C. Implementation of quantum search algorithm using classical Fourier optics. Phys. Rev. Lett. 88, 137901 (2002)

    Article  ADS  CAS  Google Scholar 

  48. Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of a fast quantum searching. Phys. Rev. Lett. 80, 3408–3411 (1997)

    Article  ADS  Google Scholar 

  49. Jones, J. A., Mosca, M. & Hansen, R. H. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344–346 (1998)

    Article  ADS  Google Scholar 

  50. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4342 (1995)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank H. J. Briegel, D. Browne and M. Zukowski for theoretical discussions, and C. Först for assistance with graphics. This work was supported by the Austrian Science Foundation (FWF), NSERC, the European Commission under project RAMBOQ, and by the Alexander von Humboldt Foundation.

Author information

Authors and Affiliations

  1. Institute of Experimental Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    P. Walther, K. J. Resch, E. Schenck, V. Vedral, M. Aspelmeyer & A. Zeilinger

  2. QOLS, Blackett Laboratory, Imperial College London, SW7 2BW, London, UK

    T. Rudolph

  3. Department of Physics, Ludwig Maximilians University, D-80799, Munich, Germany

    H. Weinfurter

  4. Max Planck Institute for Quantum Optics, D-85741, Garching, Germany

    H. Weinfurter

  5. The Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090, Vienna, Austria

    V. Vedral

  6. The School of Physics and Astronomy, University of Leeds, LS2 9JT, Leeds, UK

    V. Vedral

  7. IQOQI, Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria

    A. Zeilinger

  8. Ecole normale supérieure, 45, rue d'Ulm, 75005, Paris, France

    E. Schenck

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Supplementary information

Supplementary Tables 1-2

The state fidelities of the output qubits from one-qubit and two-qubit quantum computations. (DOC 189 kb)

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Walther, P., Resch, K., Rudolph, T. et al. Experimental one-way quantum computing. Nature 434, 169–176 (2005). https://doi.org/10.1038/nature03347

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