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Proceedings Paper

A possible hypercomputational quantum algorithm
Author(s): Andres Sicard; Mario Velez; Juan Ospina
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Paper Abstract

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.

Paper Details

Date Published: 25 May 2005
PDF: 8 pages
Proc. SPIE 5815, Quantum Information and Computation III, (25 May 2005); doi: 10.1117/12.602254
Show Author Affiliations
Andres Sicard, EAFIT Univ. (Colombia)
Mario Velez, EAFIT Univ. (Colombia)
Juan Ospina, EAFIT Univ. (Colombia)

Published in SPIE Proceedings Vol. 5815:
Quantum Information and Computation III
Eric J. Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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