Hypercomputability of quantum adiabatic processes: Fact versus Prejudices

Abstract

We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by the algorithm in its physical implementation.

25 pages, 4 figures. Invited paper for a special issue of the Journal of Applied Mathematics and Computation

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Cited by in corpus (4)

• Reply to Andrew Hodges
• On the identification of the ground state based on occupation probabilities: An investigation of Smith's apparent counterexamples
• Mathematical computability questions for some classes of linear and non-linear differential equations originated from Hilbert's tenth problem
• Hypercomputation: Towards an extension of the classical notion of Computability?