A fuzzy approach to quantum logical computation

The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a formula is identified with a quantum information quantity, represented by a density operator, whose dimension depends on the logical complexity of the formula. At the same time, the logical connectives are interpreted as operations defined in terms of quantum gates. In this framework, some possible relations between fuzzy representations based on continuous t-norms for quantum gates and the probabilistic behavior of quantum computational finite-valued connectives are investigated.