Hypercomputability of quantum adiabatic processes: Fact versus Prejudices
arXiv:quant-ph/0504101
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