Abstract:
We apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré structure. © 2006 Springer Science+Business Media, Inc.
Registro:
Documento: |
Artículo
|
Título: | Fuzzy propositional logic associated with quantum computational gates |
Autor: | Domenech, G.; Freytes, H. |
Filiación: | Instituto de Astronomía y Física del Espacio (IAFE), Ciudad Universitaria, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina Escuela de Filosofía, Universidad Nacional de Rosario, Entre Ríos 758, 2000 Rosario, Argentina Consejo Nacional de Innestigaciones Científices y Tícnices (CONICET), Argentina
|
Palabras clave: | Fuzzy logic; MV-algebras; PMV-algebras; Quantum gates |
Año: | 2006
|
Volumen: | 45
|
Número: | 1
|
Página de inicio: | 237
|
Página de fin: | 270
|
DOI: |
http://dx.doi.org/10.1007/s10773-005-9019-6 |
Título revista: | International Journal of Theoretical Physics
|
Título revista abreviado: | Int. J. Theor. Phys.
|
ISSN: | 00207748
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207748_v45_n1_p237_Domenech |
Referencias:
- Aharonov, D., Quantum computation (1998) Annual Reviews of Computational Physics VI, , D. Stauffer (Ed.), World Scientific, Singapore
- Balbes, R., Dwinger, P., (1974) Distribuive Lattices, , University of Missouri Press, Columbia, MO
- Bennett, C.H., Logical reversibility of computation (1973) IBM Journal of Research and Development, 17, pp. 525-532
- Birkhoff, G., Von Neumann, J., The logic of quantum mechanics (1936) Annals of Mathematics, 37, pp. 823-843
- Burris, S., Sankappanavar, H.P., (1981) A Course in Universal Algebra, Graduate Text in Mathematics, 78. , Springer-Verlag, Berlin
- Cattaneo, G., Dalla Chiara, M.L., Giuntini, R., Leporini, R., An unsharp logic from quantum computation (2004) International Journal of Theoretical Physics, 43, pp. 1803-1817
- Cignoli, R., D'Ottaviano, M.I., Mundici, D., (2000) Algebraic Foundations of Many-valued Reasoning, , Kluwer, Dordrecht, The Netherlands
- Dalla Chiara, M.L., Giuntini, R., Leporini, R., (2003) Quantum Computational Logic. A Survey, , arXiv:quant-ph/030529
- Deutsch, D., Ekert, A., Lupacchini, R., (2000) Machines, Logic and Quantum Physics, , arXiv:math.HO/9911150
- Domenech, G., Freytes, H., Contextual logic for quantum systems (2005) Journal of Mathematical Physics, 46, p. 012102
- Freytes, H., Injectives in residuated algebras (2004) Algebra Univers., 51, pp. 373-393
- Gudder, S., Quantum computational logic (2002) International Journal of Theoretical Physics, 42, pp. 39-47
- Hájek, P., (1998) Metamathematics of Fuzzy Logic, , Kluwer, Dordrecht, The Netherlands
- Kowalski, T., Ono, H., Residuated lattices: An algebraic glimpse at logics without contraction (2000) Preliminary Report, , Edited by the Japan Advanced Institute of Science and Technology (JAIST)
- Quantum computation: A grand mathematical challenge for the twenty-first century and the millennium (2002) Proceedings of the Symposia in Applied Mathematics, 58. , Lomonaco, S. J., Jr. (Ed.) American Mathematical Society, Washington, DC
- Montagna, F., An algebraic approach to prepositional fuzzy logic (2000) Journal of Logic, Language and Information, 9, pp. 91-124
- Mundici, D., Riecǎn, B., Probability on MV-algebras (2002) The Handbook of Measure Theory, , Pap, E. (Ed.), North Holland, Amsterdam
- Nielsen, M.A., Chuang, I.L., (2000) Quantum Computation and Quantum Information, , Cambridge University Press, Cambridge, UK
- Pavelka, J., On fuzzy logic I, II, III (1979) Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 25, pp. 45-52
Citas:
---------- APA ----------
Domenech, G. & Freytes, H.
(2006)
. Fuzzy propositional logic associated with quantum computational gates. International Journal of Theoretical Physics, 45(1), 237-270.
http://dx.doi.org/10.1007/s10773-005-9019-6---------- CHICAGO ----------
Domenech, G., Freytes, H.
"Fuzzy propositional logic associated with quantum computational gates"
. International Journal of Theoretical Physics 45, no. 1
(2006) : 237-270.
http://dx.doi.org/10.1007/s10773-005-9019-6---------- MLA ----------
Domenech, G., Freytes, H.
"Fuzzy propositional logic associated with quantum computational gates"
. International Journal of Theoretical Physics, vol. 45, no. 1, 2006, pp. 237-270.
http://dx.doi.org/10.1007/s10773-005-9019-6---------- VANCOUVER ----------
Domenech, G., Freytes, H. Fuzzy propositional logic associated with quantum computational gates. Int. J. Theor. Phys. 2006;45(1):237-270.
http://dx.doi.org/10.1007/s10773-005-9019-6