Quantum Fibrations: quantum computation on an arbitrary topological space

TL;DR

This paper extends quantum computation theory from graphs to arbitrary topological spaces using von Neumann algebras, broadening the scope of quantum computational models.

Contribution

It introduces a novel framework for quantum computation on topological spaces leveraging von Neumann algebras, generalizing previous graph-based models.

Findings

Develops a new mathematical framework for quantum computation on topological spaces

Demonstrates the applicability of von Neumann algebras in this context

Lays groundwork for future research in topological quantum computing

Abstract

Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.