  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.
