Quantum walks are a fascinating concept. They reveal the counterintuitive and complex dynamics imprinted on all particles underlying the laws of quantum mechanics. Amongst other phenomena, quantum walks show that atoms, electrons and photons propagate drastically faster than any classical particle due to their wavelike nature.

In this book we give an introduction into the world of quantum walks and discuss their applications in quantum simulations and quantum computing. We present three innovative, optical experiments, which expose the astonishing properties of particles on a quantum walk. With the so-called Quantum Walks in Time-architecture we reveal the complete spectrum of single particle dynamics—rangingfrom a fast ballistic spread up to a strict localization effect—and investigate experimentally challenging two-particle effects, as the creation of bound states.