Experimental one-way quantum computing


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.


  1. 1

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

  2. 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. 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)

  4. 4

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

  5. 5

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

  6. 6

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

  7. 7

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

  8. 8

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

  9. 9

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

  10. 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)

  11. 11

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

  12. 12

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

  13. 13

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

  14. 14

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

  15. 15

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

  16. 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)

  17. 17

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

  18. 18

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

  19. 19

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

  20. 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)

  21. 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)

  22. 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)

  23. 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)

  24. 24

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

  25. 25

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

  26. 26

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

  27. 27

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

  28. 28

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

  29. 29

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

  30. 30

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

  31. 31

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

  32. 32

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

  33. 33

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

  34. 34

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

  35. 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)

  36. 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)

  37. 37

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

  38. 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)

  39. 39

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

  40. 40

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

  41. 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)

  42. 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)

  43. 43

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

  44. 44

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

  45. 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)

  46. 46

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

  47. 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)

  48. 48

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

  49. 49

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

  50. 50

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

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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.

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Correspondence to P. Walther or A. Zeilinger.

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The authors declare that they have no competing financial interests.

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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