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Abstract:

In this paper we solve the problem how to axiomatize a system of quantum computational gates known as the Poincaré irreversible quantum computational system. A Hilbert-style calculus is introduced obtaining a strong completeness theorem. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Registro:

Documento: Artículo
Título:Quantum computational logic with mixed states
Autor:Freytes, H.; Domenech, G.
Filiación:Universidad Nacional de Rosario, Departamento de Matemática, Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Pellegrini 250, CP. 2000, Rosario, Argentina
Universidad de Buenos Aires, Instituto de Astronomía y Física del Espacio, Consejo Nacional de Investigaciones Científicas y Técnicas, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina
Palabras clave:MV-algebras; PMV-algebras; Quantum computational logic
Año:2013
Volumen:59
Número:1-2
Página de inicio:27
Página de fin:50
DOI: http://dx.doi.org/10.1002/malq.201110030
Título revista:Mathematical Logic Quarterly
Título revista abreviado:Math. Logic Q.
ISSN:09425616
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09425616_v59_n1-2_p27_Freytes

Referencias:

  • Aharanov, D., Kitaev, A., Nisan, N., Leighton, F.T., Shor, P.W., (1997) Quantum circuits with mixed states, in: Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4-6, pp. 20-30. , edited by, ACM, New York
  • Burris, S., Sankappanavar, H.P., (1981) A course in universal algebra, Graduate Text in Mathematics Vol. 78, , Springer-Verlag, New York
  • Cattaneo, G., Dalla Chiara, M., Giuntini, R., Leporini, R., An unsharp logic from quantum computation (2001) Int. J. Theor. Phys., 43, pp. 1803-1817
  • Cignoli, R., D'Ottaviano, M.I., Mundici, D., (2000) Algebraic Foundations of Many-valued Reasoning, Trends in Logic Vol. 7, , Kluwer, Dordrecht
  • Dalla Chiara, M.L., Giuntini, R., Greechie, R., (2004) Reasoning in Quantum Theory, Sharp and Unsharp Quantum Logics, Trends in Logic Vol. 22, , Kluwer, Dordrecht
  • Dalla Chiara, M.L., Giuntini, R., Leporini, R., Hendricks, V.F., Malinowski, J., Quantum Computational Logics, A Survey, in: Trends in Logic: 50 Years of Studia Logica (2003) Trends in Logic Vol. 21, pp. 213-255. , edited by and, Kluwer, Dordrecht
  • Domenech, G., Freytes, H., Fuzzy propositional logic associated with quantum computational gates (2006) Int. J. Theor. Phys., 34, pp. 228-261
  • Freytes, H., Sergioli, G., Aricó, A., Representing continuous t-norms in quantum computation with mixed states (2010) J. Phys. A: Math. Theor., 43, p. 465306
  • Giuntini, R., Ledda, A., Paoli, F., Expanding Quasi-MV Algebras by a Quantum Operator (2007) Stud. Log., 87, pp. 99-128
  • Gudder, S., Quantum Computational Logic (2003) Int. J. Theor. Phys., 42, pp. 39-47
  • Gudder, S., Greechie, R., Sequential products on effect algebras (2002) Rep. Math. Phys., 49, pp. 87-111
  • Gudder, S., Greechie, R., Uniqueness and Order in Sequential Effect Algebras (2005) Int. J. Theor. Phys., 44, pp. 755-770
  • Hájek, P., (1998) Metamathematics of Fuzzy Logic, Trends in Logic Vol. 4, , Kluwer, Dordrecht
  • Horčík, R., Cintula, P., Product Lukasiewicz Logic (2004) Arch. Math. Log., 43, pp. 477-503
  • Höhle, U., Höhle, U., Klement, E.P., Commutative, Residuated l-monoids, in: Non-classical logics and their applications to fuzzy subsets, A handbook of the mathematical foundations of fuzzy set theory, Proceedings of the Fourteenth Linz Seminar on Fuzzy Set Theory held in Linz, September 1992 (1995) Theory and Decision Library, Series B Vol. 32, pp. 53-106. , edited by and, Kluwer, Dordrecht
  • Isbell, J.R., Notes on ordered rings (1971) Algebra Univers., 1, pp. 393-399
  • Klement, E.P., Mesiar, R., Pap, E., (2000) Triangular norms, Trends in Logic Vol. 8, , Kluwer, Dordrecht
  • Kraus, K., Böhm, A., Dollard, J.D., Wootters, W.H., (1993) States, effects and operations, Fundamental notions of quantum theory, Lecture notes, 190. , edited by, and, Lecture Notes in Physics (Springer-Verlag, Berlin
  • Kreinovich, V., Longpré, L., Fast quantum computation algorithms for handling probabilistic and interval uncertainty (2004) Math. Log. Q., 50, pp. 507-518
  • Lawler, E.L., Sarkissian, I.S., An algorithm for Ulam's game and its application to error correcting codes (1995) Inf. Process. Lett., 56, pp. 89-93
  • Ledda, A., Konig, M., Paoli, F., Giuntini, R., MV-algebras and quantum computation (2006) Stud. Log., 82, pp. 245-270
  • Montagna, F., An algebraic approach to propositional fuzzy logic (2000) J. Log. Lang. Inf., 9, pp. 91-124
  • Montagna, F., Functorial representation theorems for MVδ algebras with additional operators (2001) J. Algebra, 238, pp. 99-125
  • Mundici, D., Riecǎn, B., Pap, E., (2002) Probability on MV-algebras, in: Handbook of Measure Theory, pp. 869-909. , edited by (North Holland, Amsterdam
  • Nielsen, M.A., Chuang, I.L., (2000) Quantum Computation and Quantum Information, , Cambridge University Press, Cambridge
  • Paoli, F., Ledda, A., Giuntini, R., Freytes, H., On some properties of qMV-algebras and qMV-algebras (2009) Rep. Math. Log., 44, pp. 44-85
  • Tarasov, V., Quantum computer with mixed states and four-valued logic (2002) J. Phys. A: Math. Theor, 35, pp. 5207-5235

Citas:

---------- APA ----------
Freytes, H. & Domenech, G. (2013) . Quantum computational logic with mixed states. Mathematical Logic Quarterly, 59(1-2), 27-50.
http://dx.doi.org/10.1002/malq.201110030
---------- CHICAGO ----------
Freytes, H., Domenech, G. "Quantum computational logic with mixed states" . Mathematical Logic Quarterly 59, no. 1-2 (2013) : 27-50.
http://dx.doi.org/10.1002/malq.201110030
---------- MLA ----------
Freytes, H., Domenech, G. "Quantum computational logic with mixed states" . Mathematical Logic Quarterly, vol. 59, no. 1-2, 2013, pp. 27-50.
http://dx.doi.org/10.1002/malq.201110030
---------- VANCOUVER ----------
Freytes, H., Domenech, G. Quantum computational logic with mixed states. Math. Logic Q. 2013;59(1-2):27-50.
http://dx.doi.org/10.1002/malq.201110030