  The term `hypermachine' denotes any data processing device (theoretical or
that can be implemented) capable of carrying out tasks that cannot be performed
by a Turing machine. We present a possible quantum algorithm for a classically
non-computable decision problem, Hilbert's tenth problem; more specifically, we
present a possible hypercomputation model based on quantum computation. Our
algorithm is inspired by the one proposed by Tien D. Kieu, but we have selected
the infinite square well instead of the (one-dimensional) simple harmonic
oscillator as the underlying physical system. Our model exploits the quantum
adiabatic process and the characteristics of the representation of the
dynamical Lie algebra su(1,1) associated to the infinite square well.
