Abstract

We show how an entangled cluster state encoded in the polarization of single photons can be straightforwardly expanded by deterministically entangling additional qubits encoded in the path degree of freedom of the constituent photons. This can be achieved using a polarization–path controlled-phase gate. We experimentally demonstrate a practical and stable realization of this approach by using a Sagnac interferometer to entangle a path qubit and polarization qubit on a single photon. We demonstrate precise control over phase of the path qubit to change the measurement basis and experimentally demonstrate properties of measurement-based quantum computing using a two-photon, three-qubit cluster state.

© 2010 Optical Society of America

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
  2. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
    [CrossRef] [PubMed]
  3. J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
    [CrossRef] [PubMed]
  4. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [CrossRef] [PubMed]
  5. M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
    [CrossRef] [PubMed]
  6. N. Yoran and B. Reznik, “Deterministic linear optics quantum computation with single photon qubits,” Phys. Rev. Lett. 91, 037903 (2003).
    [CrossRef] [PubMed]
  7. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
    [CrossRef] [PubMed]
  8. R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
    [CrossRef] [PubMed]
  9. N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
    [CrossRef] [PubMed]
  10. C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
    [CrossRef]
  11. Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
    [CrossRef] [PubMed]
  12. J. Joo, P. L. Knight, J. L. O’Brien, and T. Rudolph, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326 (2007).
    [CrossRef]
  13. K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
    [CrossRef] [PubMed]
  14. G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
    [CrossRef] [PubMed]
  15. H. S. Park, J. Cho, J. Y. Lee, D.-H. Lee, and S.-K. Choi, “Two-photon four-qubit cluster state generation based on a polarization-entangled photon pair,” Opt. Express 15, 17960–17966 (2007).
    [CrossRef] [PubMed]
  16. W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
    [CrossRef]
  17. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
    [CrossRef] [PubMed]
  18. G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).
    [CrossRef] [PubMed]
  19. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
    [CrossRef]
  20. T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2001).
    [CrossRef]

2009 (2)

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).
[CrossRef] [PubMed]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

2008 (3)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef] [PubMed]

Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
[CrossRef] [PubMed]

G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
[CrossRef] [PubMed]

2007 (6)

H. S. Park, J. Cho, J. Y. Lee, D.-H. Lee, and S.-K. Choi, “Two-photon four-qubit cluster state generation based on a polarization-entangled photon pair,” Opt. Express 15, 17960–17966 (2007).
[CrossRef] [PubMed]

J. Joo, P. L. Knight, J. L. O’Brien, and T. Rudolph, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326 (2007).
[CrossRef]

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
[CrossRef] [PubMed]

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

2005 (2)

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

2004 (1)

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[CrossRef] [PubMed]

2003 (1)

N. Yoran and B. Reznik, “Deterministic linear optics quantum computation with single photon qubits,” Phys. Rev. Lett. 91, 037903 (2003).
[CrossRef] [PubMed]

2001 (3)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef] [PubMed]

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2001).
[CrossRef]

Ams, M.

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

Bell, T. B.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2001).
[CrossRef]

Bohi, P.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

Briegel, H. J.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef] [PubMed]

Chen, K.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Chen, S.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Chen, Y.-A.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Chen, Z.-B.

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Cho, J.

Choi, S.-K.

Chuang, I. L.

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

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef] [PubMed]

Dekker, P.

Gao, W.-B.

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Goebel, A.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Guhne, O.

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Imoto, N.

Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
[CrossRef] [PubMed]

Jennewein, T.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

Joo, J.

J. Joo, P. L. Knight, J. L. O’Brien, and T. Rudolph, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326 (2007).
[CrossRef]

Kaltenbaek, R.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

Kiesel, N.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Knight, P. L.

J. Joo, P. L. Knight, J. L. O’Brien, and T. Rudolph, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326 (2007).
[CrossRef]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Koashi, M.

Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
[CrossRef] [PubMed]

Kuwashiro, S.

Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
[CrossRef] [PubMed]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Langford, N. K.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2001).
[CrossRef]

Lee, D.-H.

Lee, J. Y.

Li, C.-M.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Lu, C.-Y.

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Mair, A.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Marshall, G. D.

Martini, F. D.

G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
[CrossRef] [PubMed]

Mataloni, P.

G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
[CrossRef] [PubMed]

Matthews, J. C. F.

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).
[CrossRef] [PubMed]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Nielsen, M. A.

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[CrossRef] [PubMed]

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

O’Brien, J. L.

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef] [PubMed]

J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
[CrossRef] [PubMed]

J. Joo, P. L. Knight, J. L. O’Brien, and T. Rudolph, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326 (2007).
[CrossRef]

Pan, J.-W.

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Park, H. S.

Peng, C.-Z.

W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

Politi, A.

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef] [PubMed]

Pomarico, E.

G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
[CrossRef] [PubMed]

Prevedel, R.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

Ralph, T. C.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2001).
[CrossRef]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef] [PubMed]

Raussendorf, R.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef] [PubMed]

Resch, K. J.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

Reznik, B.

N. Yoran and B. Reznik, “Deterministic linear optics quantum computation with single photon qubits,” Phys. Rev. Lett. 91, 037903 (2003).
[CrossRef] [PubMed]

Rudolph, T.

J. Joo, P. L. Knight, J. L. O’Brien, and T. Rudolph, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326 (2007).
[CrossRef]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

Schenck, E.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

Schmid, C.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Stefanov, A.

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Tiefenbacher, F.

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

Tokunaga, Y.

Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
[CrossRef] [PubMed]

Toth, G.

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N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
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G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
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P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
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R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
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P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
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N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
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N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

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T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2001).
[CrossRef]

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W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
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Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
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C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
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N. Yoran and B. Reznik, “Deterministic linear optics quantum computation with single photon qubits,” Phys. Rev. Lett. 91, 037903 (2003).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
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C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[CrossRef] [PubMed]

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C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
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C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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Nat. Photonics (1)

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Nat. Phys. (1)

C.-Y. Lu, X.-Q. Zhou, O. Guhne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Nature (3)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
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R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, “High-speed linear optics quantum computing using active feed-forward,” Nature 445, 65–69 (2007).
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Phys. Rev. A (2)

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[CrossRef]

Phys. Rev. Lett. (7)

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100, 160502 (2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, “Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing,” Phys. Rev. Lett. 100, 210501 (2008).
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Science (2)

J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
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W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Guhne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. advance online publication: 14 March 2010, .
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

A simple scheme for adding photon path qubits to a polarization cluster state. (a) The linear three-qubit cluster state can be created by preparing three qubits in the | + | 0 + | 1 state and implementing a two-qubit CZ gate between each. (b) The same cluster state can be realized if we start with the state | ϕ + 1 , 2 | 0 3 ( | 00 + | 11 ) 1 , 2 | 0 3 , implement H ̂ 2 H ̂ 3 , followed by CZ 2 , 3 . (c) A CNOT between the path and polarization of a single photon is straightforwardly implemented with a polarizing beam splitter (PBS); a CZ is realized by performing a H ̂ on the target before and after the CNOT, which for a path qubit is a 1 2 beamsplitter (BS). (d) A pair of photons were produced via Type-I spontaneous parametric downconversion in a nonlinear BiBO crystal: a 60 mW 402 nm pump laser is shone into the BiBO; a single pump photon can spontaneously split into two daughter photons, conserving momentum and energy; degenerate pairs of photons are collected into polarization maintaining fibers (PMFs). (e) Implementation of the circuit shown in (c): the polarization entangled state | ϕ + 1 , 2 is realized in post-selection by inputting a horizontal ( | H ) and vertical ( | V ) photon into a 1 2 BS; an H ̂ on qubit 2, realized with a half-wave plate (HWP), converts | ψ 1 , 2 to the two-qubit cluster state, ( | 0 + + | 1 ) 1 , 2 ; the PBS Sagnac interferometer implements a CZ between the path and polarization of photon 2 (up to a local rotation of the path qubit).

Fig. 2
Fig. 2

Real (left) and imaginary (right) parts of the experimentally measured density matrix ρ exp (bottom), which has a fidelity of F = 0.929 with expected state | ψ (top).

Fig. 3
Fig. 3

Path qubit rotation via polarization qubit measurement superimposed on the theoretical curves. The fringes of coincidence counts are pronounced as a function of α as described in the text. The solid curves represent the theoretical prediction given the reflectivity of our BS. The experimental points (open circles) with errors are fitted by the dashed curves.

Equations (2)

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| Φ 3 lin = 1 2 ( | + 1 | 0 2 | 0 3 | 1 | 1 2 | 1 3 ) ,
| ψ = ( | 1 H 1 | 1 H C | 1 H 1 | 1 V D | 1 V 1 | 1 H C | 1 V 1 | 1 V D ) 2 .

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