Numerical simulations of a quantum algorithm for Hilbert's tenth problem

Details Numerical simulations of a quantum algorithm for Hilbert's tenth problem Numerical simulations of a quantum algorithm for Hilbert's tenth problem

2003-04-16

arxiv.org/abs/quant-ph/0304114v1

in Proceedings of SPIE Vol. 5105 Quantum Information and Computation, edited by Eric Donkor, Andrew R. Pirich, Howard E. Brand

Physics

Quantum Physics

Oral contribution to SPIE, Orlando, 2003. 7 pages, 6 colour figures

Scientific paper

10.1117/12.486889

We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem enables us to establish a connection between the solution for this class of problems and the asymptotic behaviour of solutions of a particular type of time-dependent Schr\"odinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.

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