Logics from quantum computation

International Journal of Quantum Information

Volumn 3, Issue 2, 2005, Pages 293-337

  Dalla Chiara, Maria Luisa ^a   Giuntini, Roberto ^b   Leporini, Roberto ^c  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF CAGLIARI   (Italy)

^c UNIVERSITY OF BERGAMO   (Italy)

Author keywords

Quantum computation; Quantum logic

Indexed keywords

COMPUTER CIRCUITS; LOGIC PROGRAMMING; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; SEMANTICS;

COMPUTATIONAL LOGIC; COMPUTATIONAL SEMANTICS; HOLISTIC SEMANTICS; LOGICAL GATES; PHYSICAL MODEL; QUANTUM CIRCUIT; QUANTUM LOGIC; SUBFORMULAS;

COMPUTATION THEORY;

EID: 33746286034     PISSN: 02197499     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219749905000943     Document Type: Article

References (17)

1. G. Cattaneo, M. L. Dalla Chiara, R. Giuntini and R. Leporini, An unsharp logic from quantum computation, to appear in Int. J. Theor. Phys. 43 (2004).
2. G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Ann. Math. 37, 823-843 (1936).
3. M. L. Dalla Chiara and R. Giuntini, Quantum logics, in Handbook of Philosophical Logic, eds. G. Gabbay and F. Guenthner, Vol. VI (Kluwer, Dordrecht, 2002), pp. 129-228.
4. J. P. Rawling and S. A. Selesnick, Orthologic and quantum logic: Models and computational elements, J. ACM 47, 721-751 (2000).
5. S. A. Selesnick, Foundation for quantum computing, Int. J. Theor. Phys. 42, 383-426 (2003).
6. M. S. Ying, Automata theory based on quantum logic I, Int. J. Theor. Phys. 39, 985-995 (2000).
7. M. S. Ying, Automata theory based on quantum logic II, Int. J. Theor. Phys. 39, 2545-2557 (2000).
8. D. W. Qiu, Automata theory based on quantum logic: Some characterizations, Inf. Comput. 190, 179-195 (2004).
9. S. Gudder, Quantum computational logic, Int. J. Theor. Phys. 42, 39-47 (2003).
10. C. A. Petri, Grundsätzliches zur Beschreibung diskreter Prozesse, in Proc. 3rd Colloquium über Automatentheorie, Hannover, 1965 (Birkhäuser Verlag, Basel, 1967), pp. 121-140. English version: Fundamentals of the Representation of Discrete Processes, ISF Report 82.04 (1982), translated by H. J. Genrich and P. S. Thiagarajan.
11. T. Toffoli, Reversible computing, in Automata, Languages and Programming, eds. J. W. de Bakker, J. van Leeuwen (Springer, 1980), pp. 632-644. Also available as TechnicalMemo MIT/LCS/TM-151, MIT Laboratory for Computer Science, February 1980.
12. D. Deutsch, A. Ekert and R. Lupacchini, Machines, logic and quantum physics, Bull. Symb. Logic 3, 265-283 (2000).
13. G. Cattaneo, M. L. Dalla Chiara, R. Giuntini and R. Leporini, Quantum computational structures, Mathematica Slovaca 54, 87-108 (2004).
14. Z. Zawirski, Relation of many-valued logic to probability calculus (in Polish, original title: "Stosunek logiki wielowartościowej do rachunku prawdopodobienstwa") (Poznańskie Towarzystwo Przyjaciół Nauk, 1934).
15. D. Bouwmeester, A. Ekert and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, Berlin, 2000).
16. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
17. G. J. Milburn, Quantum optical Fredkin gate, Phys. Rev. Lett. 62, 2124-2127 (1989).