Abstract:
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier transform and Grover’s search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to measure directly the Wigner function in a given phase-space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm. © 2002 The American Physical Society.
Registro:
Documento: |
Artículo
|
Título: | Quantum computers in phase space |
Autor: | Miquel, C.; Paz, J.P.; Saraceno, M. |
Filiación: | Departamento de Física, “Juan José Giambiagi", Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina Institute for Theoretical Physics, Santa Barbara, CA, 93106-4030, United States Unidad de Actividad Física, Buenos Aires, Argentina
|
Año: | 2002
|
Volumen: | 65
|
Número: | 6
|
Página de inicio: | 14
|
DOI: |
http://dx.doi.org/10.1103/PhysRevA.65.062309 |
Título revista: | Physical Review A - Atomic, Molecular, and Optical Physics
|
Título revista abreviado: | Phys Rev A
|
ISSN: | 10502947
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v65_n6_p14_Miquel |
Referencias:
- Hillery, M., O’Connell, R.F., Scully, M.O., Wigner, E.P., (1984) Phys. Rep., 106, p. 121
- Bianucci, P., Miquel, C., Paz, J.P., Saraceno, M., (2002) Phys. Rev. E, 65, p. 46226
- Davidovich, L., Latin-American School of Physics XXXI ELAF AIP Conf. Proc., 464. , Proceedings of the First PASI Conference on Chaos, Decoherence and Entanglement 2000, available at http://kaiken.df.uba.ar
- Zurek, W.H., (1991) Phys. Today, 44, p. 36
- Paz, J.P., Habib, S., Zurek, W.H., (1992) Phys. Rev. D, 47, p. 488
- See J. P. Paz and W. H. Zurek, in Coherent Matter Waves Proceedings of the Les Houches Session LXXII, edited by R. Kaiser, C. Westbrook, and F. David (Springer Verlag, Berlin, 2001), pp. 533–614, and references therein; I. Chuang and M. Nielsen, Quantum Information and Computation (Cambridge University Press, Cambridge, 2000); Wooters, W.K., (1987) Ann. Phys. (N.Y.), 176, p. 1
- Leonhardt, U., (1995) Phys. Rev. Lett., 74, p. 4101
- Leonhardt, U., (1996) Phys. Rev. A, 53, p. 2998
- Hannay, J.H., Berry, M.V., (1980) Physica D, 1, p. 267
- Rivas, A., Ozorio de Almeida, A.M., (1999) Ann. Phys. (San Diego), 276, p. 223
- Bouzouina, A., De Bievre, S., (1996) Commun. Math. Phys., 178, p. 83
- Bertrand, J., Bertrand, P., (1987) Found. Phys., 17, p. 397
- Fano, U., (1957) Rev. Mod. Phys., 29, p. 75
- Schwinger, J., (1960) Proc. Natl. Acad. Sci. U.S.A., 46, p. 570
- Schwinger, J., (1960) Proc. Natl. Acad. Sci. U.S.A., 46, p. 893
- J. P. Paz and M. Saraceno (unpublished); V. I. Arnold and A. Avez, Ergodic Problems in Classical Mechanics (Benjamin, New York, 1968); Georgeot, B., Shepelyansky, D.L., (2001) Phys. Rev. Lett., 86, p. 2890
- Georgeot, B., Shepelyansky, D.L., (2001) Phys. Rev. Lett., 86, p. 5393
- Balasz, N.L., Voros, A., (1990) Ann. Phys. (N.Y.), 190, p. 1
- Voros, A., Saraceno, M., (1994) Physica D, 79, p. 206
- Saraceno, M., (1990) Ann. Phys. (N.Y.), 199, p. 37
- Schack, R., (1998) Phys. Rev. A, 57, p. 1634
- Schack, R., Brun, T., (1999) Phys. Rev. A, 59, p. 2649
- Schack, R., Caves, C.M., (2000) Appl. Algebr. Eng. Commun., 10, p. 305
- Soklakov, A.N., Schack, R., (2000) Phys. Rev. E, 61, p. 5108
- Miquel, C., Paz, J.P., Saraceno, M., Knill, E., Laflamme, R., Negrevergne, C., ; Dunn, T.J., (1994) Phys. Rev. Lett., 74, p. 884
- Leibfried, D., (1996) Phys. Rev. Lett., 77, p. 4281
- Leibfried, D., (1998) Phys. Today, 51, p. 22
- Lutterbach, L.G., Davidovich, L., (1997) Phys. Rev. Lett., 78, p. 2547
- Lutterbach, L.G., Davidovich, L., (1998) Opt. Express, 3, p. 147
- Nogues, G., (2000) Phys. Rev. A, 62, p. 54101
- Maitre, X., (1997) Phys. Rev. Lett., 79, p. 769
- Miquel, C., Paz, J.P., Perazzo, R., (1996) Phys. Rev. A, 54, p. 2605
- Nielsen, M.A., Knill, E., Laflamme, R., (1998) Nature (London), 396, p. 52
- Cory, D.G., (1998) Phys. Rev. Lett., 81, p. 2152
- Knill, E., Chuang, I., Laflamme, R., (1998) Phys. Rev. A, 57, p. 3348
Citas:
---------- APA ----------
Miquel, C., Paz, J.P. & Saraceno, M.
(2002)
. Quantum computers in phase space. Physical Review A - Atomic, Molecular, and Optical Physics, 65(6), 14.
http://dx.doi.org/10.1103/PhysRevA.65.062309---------- CHICAGO ----------
Miquel, C., Paz, J.P., Saraceno, M.
"Quantum computers in phase space"
. Physical Review A - Atomic, Molecular, and Optical Physics 65, no. 6
(2002) : 14.
http://dx.doi.org/10.1103/PhysRevA.65.062309---------- MLA ----------
Miquel, C., Paz, J.P., Saraceno, M.
"Quantum computers in phase space"
. Physical Review A - Atomic, Molecular, and Optical Physics, vol. 65, no. 6, 2002, pp. 14.
http://dx.doi.org/10.1103/PhysRevA.65.062309---------- VANCOUVER ----------
Miquel, C., Paz, J.P., Saraceno, M. Quantum computers in phase space. Phys Rev A. 2002;65(6):14.
http://dx.doi.org/10.1103/PhysRevA.65.062309