Abstract

The quantum walk is the quantum-mechanical analogue of the classical random walk.

The main difference between the two lies in the role of the coin: whereas in the classical

random walk the coin is a classical object with two possible measurement outcomes

("heads" or "tails", see picture), in the quantum walk the coin is a quantum-mechanical

object – for example, a two-level system such as aspin-1/2 particle - which can be

measured along different bases and hence has a multi-sided character. In recent years,

the first implementations of quantum walks have been demonstrated in various

areas of physics, ranging from quantum optics to atomic physics.

 

In this colloquium I will tell about the strikingly different dynamic behavior between classical and

quantum random walks, discuss the use of quantum walks to speed-up quantum dynamics,

and comment on how their implementation in actual physics systems, with particular focus

on solid-state nanostructures.