A possible hypercomputational quantum algorithm

Andres Sicard; Mario Velez; Juan Ospina

doi:10.1117/12.602254

25 May 2005 A possible hypercomputational quantum algorithm

Andres Sicard, Mario Velez, Juan Ospina

Proceedings Volume 5815, Quantum Information and Computation III; (2005) https://doi.org/10.1117/12.602254
Event: Defense and Security, 2005, Orlando, Florida, United States

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.

Citation Download Citation

Andres Sicard, Mario Velez, and Juan Ospina "A possible hypercomputational quantum algorithm", Proc. SPIE 5815, Quantum Information and Computation III, (25 May 2005); https://doi.org/10.1117/12.602254

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