2,477 research outputs found
An anatomy of a quantum adiabatic algorithm that transcends the Turing computability
We give an update on a quantum adiabatic algorithm for the Turing
noncomputable Hilbert's tenth problem, and briefly go over some relevant issues
and misleading objections to the algorithm.Comment: 7 pages, no figure. Submitted to the Proceedings of the conference
"Foundations of Quantum Information" (April 2004, Camerino, Italy
A reformulation of Hilbert's tenth problem through Quantum Mechanics
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the
domain of integer arithmetics into either a problem involving a set of
infinitely coupled differential equations or a problem involving a Shr\"odinger
propagator with some appropriate kernel. Either way, Mathematics and Physics
could be combined for Hilbert's tenth problem and for the notion of effective
computability
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