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The computing power of Turing machine based on quantum logic

11 pagesPublished: June 22, 2012

Abstract

Turing machines based on quantum logic can solve undecidable
problems. In this paper we will give recursion-theoretical
characterization of the computational power of this kind of quantum
Turing machines. In detail, for the unsharp case, it is proved that
&#931<sup>0</sup><sub>1</sub>
&#8746&#928<sup>0</sup><sub>1</sub>&#8838
L<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))&#8838&#928<sup>0</sup><sub>2</sub>
when the truth value lattice is locally finite and the operation &#8743
is computable, where
L<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))denotes the
class of quantum language accepted by these Turing machine in
depth-first model (respectively, width-first model);
for the sharp case, we can obtain similar results for usual orthomodular lattices.

Keyphrases: quantum logic, super-Turing computational power, Turing machine

In: Andrei Voronkov (editor). Turing-100. The Alan Turing Centenary, vol 10, pages 278--288

Links:
BibTeX entry
@inproceedings{Turing-100:computing_power_of_Turing,
  author    = {Yun Shang and Xian Lu and Ruqian Lu},
  title     = {The computing power of Turing machine based on quantum logic},
  booktitle = {Turing-100. The Alan Turing Centenary},
  editor    = {Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {10},
  pages     = {278--288},
  year      = {2012},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/hsrJ},
  doi       = {10.29007/k8cb}}
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