A possible hypercomputational quantum algorithm

Details A possible hypercomputational quantum algorithm A possible hypercomputational quantum algorithm

2004-06-18

arxiv.org/abs/quant-ph/0406137v2

In E. J. Donkor, A. R. Pirich, and H. E. Brandt, editors, "Quantum Information and Computation III", volume 5815 of Proc. of S

Physics

Quantum Physics

Title changed. Updated to the published version. Oral contribution to Quantum Information and Computation III, part of the SPI

Scientific paper

10.1117/12.602254

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.

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