Limit Theorems for Quantum Walks on the Union of Planes

TL;DR

This paper extends previous work on quantum walks from lines to planes, establishing new limit theorems for quantum walks on these more complex graph structures.

Contribution

It introduces a generalized construction of quantum walks on the union of planes and derives associated limit theorems, expanding the theoretical framework.

Findings

Derived limit theorems for quantum walks on the union of planes

Extended previous line-based quantum walk models to planar structures

Provided mathematical foundation for quantum walks on complex graphs

Abstract

We extend the construction given by [Chisaki et.al, arXiv:1009.1306v1] from lines to planes, and obtain the associated limit theorems for quantum walks on such a graph.