Numerical Simulations of a Possible Hypercomputational Quantum Algorithm

  • Andrés Sicard
  • Juan Ospina
  • Mario Vélez


The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, the Hilbert’s tenth problem. The numerical simulations were realized for three types of Diophantine equations: with and without solutions in non-negative integers, and without solutions by way of various traditional mathematical packages.


Coherent State Turing Machine Quantum Algorithm Diophantine Equation Adiabatic Theorem 


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Copyright information

© Springer-Verlag/Wien 2005

Authors and Affiliations

  • Andrés Sicard
    • 1
  • Juan Ospina
    • 1
  • Mario Vélez
    • 1
  1. 1.Logic and Computation GroupEAFIT University, A.A.MedellínColombia

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