# Quantum Algorithm for Hilbert's Tenth Problem

@article{Kieu2001QuantumAF, title={Quantum Algorithm for Hilbert's Tenth Problem}, author={Tien D. Kieu}, journal={International Journal of Theoretical Physics}, year={2001}, volume={42}, pages={1461-1478} }

We explore in the framework of Quantum Computation the notion of 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…

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