## Experimental realization of a quantum quincunx by use of linear optical elements

JOSA B, Vol. 22, Issue 2, pp. 499-504 (2005)

http://dx.doi.org/10.1364/JOSAB.22.000499

Acrobat PDF (158 KB)

### Abstract

We report the experimental realization of a quantum analog of the classical Galton quincunx and discuss its possible use as a device for quantum computation. Our quantum quincunx is implemented with linear optical elements that allow an incoming photon to interfere with itself while traversing all possible paths from the source to the detector. We show that the experimentally determined intensity distributions are in excellent agreement with theory.

© 2005 Optical Society of America

**OCIS Codes**

(200.0200) Optics in computing : Optics in computing

(230.0230) Optical devices : Optical devices

**Citation**

Binh Do, Michael L. Stohler, Sunder Balasubramanian, Daniel S. Elliott, Christopher Eash, Ephraim Fischbach, Michael A. Fischbach, Arthur Mills, and Benjamin Zwickl, "Experimental realization of a quantum quincunx by use of linear optical elements," J. Opt. Soc. Am. B **22**, 499-504 (2005)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-22-2-499

Sort: Year | Journal | Reset

### References

- Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
- T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
- B. C. Travaglione and G. J. Milburn, "Implementing the quantum random walk," Phys. Rev. A 65, 032310 (2002).
- M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
- B. C. Sanders, S. D. Bartlett, B. Tregenna, and P. L. Knight, "Quantum quincunx in cavity quantum electrodynamics," e-print quant-ph/0207028, http://www.arxiv.org/abs/quant-ph?0207028.
- A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, "Exponential algorithmic speedup by quantum walk," e-print quant-ph/0209131, http://www.arxiv.org/abs/quant-ph?0209131.
- A. M. Childs, E. Farhi, and S. Gutmann, "An example of the difference between quantum and classical random walks," e-print quant-ph/0103020, http://www.arxiv.org/abs/quant-ph?0103020.
- A. Nayak and A. Vishwanath, "Quantum walk on the line," e-print quant-ph/0010117, http://www.arxiv.org/abs/quant-ph?0010117.
- D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," e-print quant-ph/0012090, http://www.arxiv.org/abs/quant-ph?0012090.
- Z. Zhao, J. Du, H. Li, T. Yang, Z.-B. Chen, and J.-W. Pan, "Implement quantum random walks with linear optics elements," e-print quant-ph/0212149, http://www.arxiv.org/abs/quant-ph?0212149.
- W. Dur, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, "Quantum random walks in optical lattices," e-print quant-ph/0207137, http://www.arxiv.org/abs/quant-ph?0207137.
- F. Galton, "Typical laws of heredity," Nature 15, 492-495 , 512-514, 532-533 (1877).
- M. L. Stohler, "Quantum game theory," Ph.D. thesis (Purdue University, West Lafayette, Ind.), manuscript available from the author.
- D. P. Divincenzo, "Quantum computation," Science 270, 255-261 (1995).
- C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000).
- J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
- T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
- L. K. Grover, "Quantum mechanics helps in searching for a needle in a haystack," Phys. Rev. Lett. 79, 325-328 (1997).
- D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. London 439, 553-558 (1992).
- J. Preskill, "Quantum information and computation," Caltech Lecture Notes, http://www.theory.caltech.edu/people/preskill/ph229/lecture, Sec. 6.
- P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput. 26, 1484-1509 (1997).
- E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
- F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
- P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
- S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
- C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
- I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
- N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
- L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
- J. A. Jones and M. Mosca, "Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer," J. Chem. Phys. 109, 1648-1653 (1998).
- I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
- J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
- M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
- A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
- A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
- W. Dur, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, "Quantum random walks in optical lattices," e-print quant-ph/0207137, http://www.arxiv.org/abs/quant-ph?0207137.
- D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," e-print quant-ph/0012090, http://www.arxiv.org/abs/quant-ph?0012090.
- A. M. Childs, R. Cleve, E. Deotto, E. Fahri, S. Gutmann, and D. A. Spielman, "Exponential algorithmic speedup by quantum walk," e-print quant-ph/0209131, http://www.arxiv.org/abs/quant-ph?0209131.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.