Towards an experimental realization of a quantum walk with a coin: Superconducting circuit quantum electrodynamics & trapped ion

The quantum walk is one of the most important protocols for quantum computing as well as being a beautiful quantization of the ubiquitous random walk of stochastic processes. The random walk is demonstrated by a quincunx (Galton Board), and a quantum quincunx would demonstrate quantum walks in an analogous way. However, experimentally realizing a quantum walk with one walker whose motion is governed by a single two-sided coin is elusive. The challenge arises because of the need to flip coherently the coin and then to entangle the coin and walker's motion, all in an environment with controllable decoherence to interpolate between the quantum walk and the random walk. I will discuss how a quantum walk on a circle in phase space could be realized via supeconducting circuit quantum electrodynamics, with the Cooper pair box serving as a charge qubit, and how a quantum walk on a line could be realized by a single trapped ion with a two-level electronic structure.