We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem enables us to establish a connection between the solution for this class of problems and the asymptotic behavior of solutions of a particular type of time-dependent Schrodinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.
Tien D Kieu, Tien D Kieu,
"Numerical simulations of a quantum algorithm for Hilbert's tenth problem", Proc. SPIE 5105, Quantum Information and Computation, (4 August 2003); doi: 10.1117/12.486889; https://doi.org/10.1117/12.486889