Quantum walk of a trapped ion in phase space

TL;DR

This paper demonstrates a high-fidelity quantum walk of a single trapped ion, revealing quantum interference effects and proposing methods to scale the process to hundreds of steps.

Contribution

It presents the first implementation of a quantum walk with a single ion in phase space, achieving high fidelity and proposing a scalable protocol.

Findings

Achieved over 99% fidelity in three quantum walk steps

Observed non-classical, asymmetric probability distributions due to quantum interference

Identified motional squeezing as a limitation and proposed a method to overcome it

Abstract

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 line. We clearly reveal the differences to its classical counterpart if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.