Quantum Computation via Paraconsistent Computation

Abstract

We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum computation: quantum Turing machines and quantum circuits, and revise quantum algorithms to solve the so-called Deutsch's problem and Deutsch-Jozsa problem. Then, we show the potentialities of the PTMs model of computation simulating the presented quantum algorithms via paraconsistent algorithms. This way, we show that PTMs can resolve some problems in exponentially less time than any classical deterministic Turing machine. Finally, We show that it is not possible to simulate all characteristics (in particular entangled states) of quantum computation by the particular model of PTMs here presented, therefore we open the possibility of constructing a new model of PTMs by which it is feasible to simulate such states.