This article aims to provide an introductory survey on quantum random walks. Starting from a
physical effect to illustrate the main ideas we will introduce quantum random walks, review …

Quantum random walk is the quantum counterpart of a classical random walk. The classical
random walk concept has long been used as a computational framework for designing …

Energy transfer within photosynthetic systems can display quantum effects such as
delocalized excitonic transport. Recently, direct evidence of long-lived coherence has been …

The quantum walk is the quantum analog of the well-known random walk, which forms the
basis for models and applications in many realms of science. Its properties are markedly …

We experimentally demonstrate a quantum walk on a line in phase space using one and two
trapped ions. A walk with up to 23 steps is realized by subjecting an ion to state-dependent …

We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With
a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the …

Random walks have been employed in virtually every science related discipline to model
everyday phenomena such as biochemical reaction pathways and DNA synapsis …

We demonstrate the controlled coherent transport and splitting of atomic wave packets in
spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for …

This paper reviews recent advances in continuous-time quantum walks (CTQW) and their
application to transport in various systems. The introduction gives a brief survey of the …

The development of quantum walks in the context of quantum computation, as
generalisations of random walk techniques, has led rapidly to several new quantum …