Green function approach for scattering quantum walks

TL;DR

This paper develops a Green function method for analyzing scattering quantum walks, providing a closed-form, path-sum expression applicable to complex topologies and enabling detailed system insights.

Contribution

The paper introduces a novel Green function approach with step and path operators for scattering quantum walks, allowing exact analysis on arbitrary graphs.

Findings

Closed-form Green function expression for quantum walks

Application to a diamond-shaped graph example

Method enables detailed system analysis

Abstract

In this work a Green function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position dependent quantum amplitudes. By introducing the step and path operators, it is shown how to extract any information about the system from the Green function. The method relevant features are demonstrated by discussing in details an example, a general diamond-shaped graph.