Realization of a quantum walk with one and two trapped ions

TL;DR

This paper reports the experimental realization of a quantum walk using trapped ions, demonstrating non-classical behavior, reversibility, and an extension with two ions to include a 'stay' option, advancing quantum simulation capabilities.

Contribution

It introduces an experimental implementation of a quantum walk with trapped ions, including techniques for state analysis and an extension to two ions with additional movement options.

Findings

Successfully implemented up to 23 steps of quantum walk

Measured probability distributions show non-classical behavior

Demonstrated reversibility of the quantum walk

Abstract

We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin tossing operations. To analyze the ion's motional state after each step we apply a technique that directly maps the probability density distribution onto the ion's internal state. The measured probability distributions and the position's second moment clearly show the non-classical character of the quantum walk. To further highlight the difference between the classical (random) and the quantum walk, we demonstrate the reversibility of the latter. Finally, we extend the quantum walk by using two ions, giving the walker the additional possibility to stay instead of taking a step.