385 citations · 429 across the 11 of their papers we have counts for
4 papers · 2 filters
Hilbert's Incompleteness, Chaitin's number and Quantum Physics
Tien D Kieu
To explore the limitation of a class of quantum algorithms originally proposed for the Hilbert's tenth problem, we consider two further classes of mathematically non-decidable prob…
Reply to ``The quantum algorithm of Kieu does not solve the Hilbert's tenth problem"
Tien D Kieu
The arguments employed in quant-ph/0111009, to claim that the quantum algorithm in quant-ph/0110136 does not work, are so general that were they true then the adiabatic theorem its…
A reformulation of Hilbert's tenth problem through Quantum Mechanics
Tien D Kieu
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…
Quantum Algorithm for Hilbert's Tenth Problem
Tien D Kieu
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algo…