The computing power of Turing machine based on quantum logic

11 pages•Published: 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
&#931⁰₁
&#8746&#928⁰₁&#8838
L^T_d(&#949,&#931)(L^T_w(&#949,&#931))&#8838&#928⁰₂
when the truth value lattice is locally finite and the operation &#8743
is computable, where
L^T_d(&#949,&#931)(L^T_w(&#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:	https://easychair.org/publications/paper/hsrJ
	https://doi.org/10.29007/k8cb