Time and spatial parity operations with trapped ions

TL;DR

This paper presents a method to implement and measure fundamental symmetry operations like time and spatial parity, as well as Galilean boosts, in trapped-ion quantum simulators, enabling advanced quantum symmetry studies.

Contribution

It introduces a novel approach to realize and measure parity and boost operations in trapped-ion systems by embedding models into an enlarged Hilbert space.

Findings

Analytical and numerical validation with prototypical examples

Feasibility demonstrated with current trapped-ion technology

Framework applicable to other quantum platforms

Abstract

We propose a physical implementation of time and spatial parity transformations, as well as Galilean boosts, in a trapped-ion quantum simulator. By embedding the simulated model into an enlarged simulating Hilbert space, these fundamental symmetry operations can be fully realized and measured with ion traps. We illustrate our proposal with analytical and numerical techniques of prototypical examples with state-of-the-art trapped-ion platforms. These results pave the way for the realization of time and spatial parity transformations in other models and quantum platforms.