Hypercomputation based on quantum computing
Andrés Sicard, Mario Vélez, Juan Ospina · arXiv (Cornell University) · 2004
Abstract. We present a quantum algorithm for a (classically) incomputable decision problem: the Hilbert’s tenth problem; namely, we present a hypercomputation model based on quantum computation. The model is inspired by the one proposed by Tien D. Kieu. Our model exploits the quantum adiabatic process and the characteristics of the representation of the dynamical algebra su(1, 1) associated to the infinite square well. Furthermore, it is demonstrated that the model proposed is a universal quantum computation model.