Quantum walk on a line for a trapped ion

TL;DR

This paper demonstrates how to implement a multi-step quantum walk using a single trapped ion, with the ability to interpolate between quantum and classical behaviors by adjusting the coin flip phase, making experimental realization feasible.

Contribution

It introduces a method to realize a quantum walk in a trapped ion system, including a way to interpolate between quantum and random walks via phase randomization.

Findings

Quantum walk signature observed in ion's position and phonon number

Feasible implementation of quantum walk in ion traps

Interpolation between quantum and classical walk achieved

Abstract

We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible.