Numerical Simulations of a Possible Hypercomputational Quantum Algorithm

Abstract

The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, Hilbert's tenth problem. The numerical simulations were realized for three types of Diophantine equations: with and without solutions in non-negative integers, and without solutions by way of various traditional mathematical packages.