2011/12/08 by Takuya Kitagawa, Kitagawa, Takuya · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.48550/arxiv.1112.1882
Review article commissioned for Quantum Information Processing, special issue on quantum walk
arxiv created 2011/12/08 · openalex publication_date 2011/12/08 · arxiv updated 2011/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand topological phases. In this article, we review the physics of discrete quantum walks in one and two dimensions in light of topological phenomena and provide elementary explanations of topological phases and their physical consequence, namely the existence of boundary states. We demonstrate that quantum walks are versatile systems that simulate many topological phases whose classifications are known for static Hamiltonians. Furthermore, topological phenomena appearing in quantum walks go beyond what has been known in static systems; there are phenomena unique to quantum walks, being an example of periodically driven systems, that do not exist in static systems. Thus the quantum walks not only provide a powerful tool as a quantum simulator for static topological phases but also give unique opportunity to study topological phenomena in driven systems.