Topological Phases on Quantum Walks and an Application for Controlling of Amplitudes of Photons

Abstract

A quantum walk, that is, a synthetic quantum system whose dynamics is described by a time-evolution operator, provides potential applications for quantum computing and information as well as quantum simulators. It is further interesting that the quantum walk possesses novel topological phases akin to those of Floquet topological insulators. In this article, we present how to study topological phases on a nonunitary quantum walk with parity and time-reversal symmetry. Accordingly, we show that the quantum walk provides a potential application for controlling of probability amplitudes of photons.