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Proceedings Article

Numerical simulations of a quantum algorithm for Hilbert's tenth problem

[+] Author Affiliations
Tien D. Kieu

Swinburne Univ. of Technology (Australia)

Proc. SPIE 5105, Quantum Information and Computation, 89 (August 5, 2003); doi:10.1117/12.486889
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From Conference Volume 5105

  • Quantum Information and Computation
  • Eric Donkor; Andrew R. Pirich; Howard E. Brandt
  • Orlando, FL | April 21, 2003

abstract

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.

© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Citation

Tien D. Kieu
"Numerical simulations of a quantum algorithm for Hilbert's tenth problem", Proc. SPIE 5105, Quantum Information and Computation, 89 (August 5, 2003); doi:10.1117/12.486889; http://dx.doi.org/10.1117/12.486889


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