Implementing quantum walks

The random walk (RW), which is ubiquitous in physics, chemistry, mathematics, and computer science, underpins Brownian motion and diffusion processes, is used in satisfiability proofs, and is intimately connected with the Wiener measure. Quantization of the RW has led to new quantum algorithms and fascinating physics such as decoherence-induced diffusion reduction. Our goal is to see the quantum walk (QW) realized in the laboratory. However, compromises have to be made to the ideal QW in order to realize the QW experimentally, such as side-stepping the requirement of direct coin flipping in cavity quantum electrodynamics (QED) and finding an alternative to measuring the position distribution for a quantum walk in an ion trap. Here we discuss how QW can be implemented by making compromises to the ideal QW but nonetheless demonstrating a true QW in the laboratory.