Multi-walker discrete time quantum walks on arbitrary graphs, their properties, and their photonic implementation

TL;DR

This paper generalizes discrete time quantum walks to multiple walkers on arbitrary graphs, providing a formalism for analysis and exploring potential linear optics implementations for quantum computing.

Contribution

It introduces a formalism for multi-walker quantum walks on arbitrary graphs, expanding the theoretical framework and discussing experimental implementation prospects.

Findings

Formalism for analyzing multi-walker quantum walks

Application examples demonstrating the formalism

Discussion on physical implementation in linear optics

Abstract

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one dimensional graphs, and several experimental demonstrations have been performed. In this paper we discuss generalizing the model of discrete time quantum walks to the case of an arbitrary number of walkers acting on arbitrary graph structures. We present a formalism which allows for analysis of such situations, and several example scenarios for how our techniques can be applied. We consider the most important features of quantum walks -- measurement, distinguishability, characterization, and the distinction between classical and quantum interference. We also discuss the potential for physical implementation in the context of linear optics, which is of relevance to present day experiments.