An algorithm to factorize quantum walks into shift and coin operations

TL;DR

This paper presents an algorithm that decomposes one-dimensional quantum walks into shift and coin operations, enabling customization to various experimental setups by rephrasing the walk on different cell structures.

Contribution

The paper introduces a novel algorithm to factorize quantum walks into basic operations, facilitating their implementation across diverse experimental platforms.

Findings

Algorithm successfully decomposes quantum walks into shift and coin operations.

Enables tailoring quantum walk protocols to specific experimental constraints.

Demonstrates application by compiling a qutrit chain walk to a qubit chain.

Abstract

We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This allows to tailor quantum walk protocols to any experimental setup by rephrasing it on the cell structure determined by the experimental limitations. We give the example of a walk defined on a qutrit chain compiled to run an a qubit chain.