Representing continuoust-norms in quantum computation with mixed states
Héctor Freytes, Giuseppe Sergioli, Antonino Salvatore Aricò · Journal of Physics A Mathematical and Theoretical · 2010
A model of quantum computation is discussed in (Aharanov et al 1997 Proc. 13th Annual ACM Symp. on Theory of Computation, STOC pp 20–30) and ( Tarasov 2002 J. Phys. A: Math. Gen. 35 5207–35 ) in which quantum gates are represented by quantum operations acting on mixed states. It allows one to use a quantum computational model in which connectives of a four-valued logic can be realized as quantum gates. In this model, we give a representation of certain functions, known as t -norms (Menger 1942 Proc. Natl Acad. Sci. USA 37 57–60), that generalize the triangle inequality for the probability distribution-valued metrics. As a consequence an interpretation of the standard operations associated with the basic fuzzy logic (Hájek 1998 Metamathematics of Fuzzy Logic ( Trends in Logic vol 4) (Dordrecht: Kluwer)) is provided in the frame of quantum computation.