Physics – Quantum Physics
Scientific paper
2001-10-24
Int.J.Theor.Phys. 42 (2003) 1461-1478
Physics
Quantum Physics
Scientific paper
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 algorithm for Hilbert's tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle--that is, if certain hamiltonian and its ground state can be physically constructed according to the proposal--quantum computability would surpass classical computability as delimited by the Church-Turing thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.
No associations
LandOfFree
Quantum Algorithm for Hilbert's Tenth Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Algorithm for Hilbert's Tenth Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Algorithm for Hilbert's Tenth Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-651257