Quantum random walk on the integer lattice: examples and phenomena

TL;DR

This paper analyzes quantum random walks on integer lattices, revealing new features of their limiting distributions through analytical methods, and discusses computational techniques and conjectures.

Contribution

It applies advanced analytical methods to quantum random walks, uncovering features of their limit distributions not visible in empirical data.

Findings

Identification of novel features in limit distributions

Analytical techniques for quantum walk analysis

Discussion of computational methods and conjectures

Abstract

We apply results from Baryshnikov, Brady, Bressler and Pemantle (2008) to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using analytic machinery we show some features of the limit distribution that are not evident in an empirical intensity plot of the time 10,000 distribution. Some conjectures are stated and computational techniques are discussed as well.