Increasing the dimensionality of quantum walks using multiple walkers

TL;DR

This paper demonstrates that adding multiple walkers to quantum walks on a line can create higher-dimensional lattice graphs, enabling complex simulations and applications in quantum computing, including BosonSampling and universal quantum computation.

Contribution

It introduces a method to transform multi-walker quantum walks into higher-dimensional structures, expanding the potential for quantum simulation and computation.

Findings

Multi-walker quantum walks can simulate higher-dimensional graphs.

Multi-walker walks are equivalent to BosonSampling models.

Higher-dimensional structures enable universal quantum computation.

Abstract

We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa. This exponential complexity opens up new applications for present-day quantum walk experiments. We discuss the applications of such higher-dimensional structures and how they relate to linear optics quantum computing. In particular we show that multi-walker quantum walks are equivalent to the BosonSampling model for linear optics quantum computation proposed by Aaronson & Arkhipov. With the addition of control over phase-defects in the lattice, which can be simulated with entangling gates, asymmetric lattice structures can be constructed which are universal for quantum computation.