Numerical Simulations of a Possible Hypercomputational Quantum Algorithm
<|reference_start|>Numerical Simulations of a Possible Hypercomputational Quantum Algorithm: 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, 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.<|reference_end|>
@article{sicard2005numerical,
    title={Numerical Simulations of a Possible Hypercomputational Quantum Algorithm},
    author={Andr'es Sicard, Juan Ospina, Mario V'elez},
    journal={In "Adaptive and Natural Computing Algorithms. Proc. of the
  International Conference in Coimbra, Portugal". Bernardete Ribeiro et al.
  (eds.). SpringerWienNewYork, 2005. p. 272--275},
    year={2005},
    archivePrefix={arXiv},
    eprint={quant-ph/0504021},
    primaryClass={quant-ph cs.LO}
}