Hipercomputación desde la Computación Cuántica

The hypercomputers compute functions that cannot be computed by a Turing machine. Recently, Tien D. Kieu has proposed a hypercomputational quantum algorithm, which uses as physical referent the quantum harmonic oscillator and in principle solves Hilbert’s tenth problem. An analysis of the Kieu’s algorithm is made and it is deduced that the algorithm is based in the dynamical algebra associated with the quantum harmonic oscillator, the Weyl-Heisenberg algebra; and in a certain application of the adiabatic theorem of the quantum mechanics. With base in this analysis, an algebraic adaptation of Kieu’s algorithm is constructed, that is to say, it is constructed an algorithm à la Kieu on the Lie algebra su(1, 1). Because the algebra su(1, 1) admits realizations within the fields of quantum optics, condensed matter, and mathematical physics, among others; the adaptation constructed ample the possibilities of implementation of the algorithm on one of these systems.