Fuzzy propositional logic associated with quantum computational gates

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 Spri...

Descripción completa

Detalles Bibliográficos
Autor principal: Domenech, Graciela
Otros Autores: Freytes, H.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2006
Acceso en línea:Registro en Scopus
DOI
Handle
Registro en la Biblioteca Digital
Aporte de:Registro referencial: Solicitar el recurso aquí
Descripción
Sumario: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.
Bibliografía: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
ISSN:00207748
DOI:10.1007/s10773-005-9019-6