Quantum Computing in Non Euclidean Geometry

TL;DR

This paper explores a novel view of quantum computation through non-Euclidean geometry, linking information, geometry, and quantum phenomena to suggest super-Turing capabilities rooted in the universe's global geometric structure.

Contribution

It introduces a non-Euclidean geometric framework for quantum processes, connecting Fisher information with quantum potentials and proposing a universe-wide geometric reflection of local quantum events.

Findings

Quantum phenomena influence the universe's geometry.

Fisher information relates to quantum potentials and Schrödinger equation.

Local physical changes are reflected globally in the universe's geometry.

Abstract

The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics and quantum computing. We stress the connection between metric and information as measure of change. Because computation is not restricted to calculus but is the environment changing via physical processes, super-Turing potentialities derive from an incomputable information source embedded into the geometry of the universe in accordance with Bell's constraints. In the general relativity we define the geometry of the space time. In our approach quantum phenomena define the geometry of the parameters of the probability distribution that include also the space time parameters. To study this new approach to the computation we use the new theory of Morphogenic systems.