Quantum random walks without walking

TL;DR

This paper proposes a novel quantum walk scheme on complex graphs that eliminates the need for physical movement, using coin flips instead, which could simplify experimental implementations in quantum systems.

Contribution

It introduces a new quantum walk method that operates without physical traversal, broadening the scope of feasible quantum walk experiments on complex networks.

Findings

Allows quantum walks on arbitrary graphs without physical movement

Suitable for implementation in systems like BECs in optical lattices

Simplifies experimental realization of quantum walks

Abstract

Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a BEC trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.