Disentangling phonons from spins in ion-trap-based quantum spin simulators

TL;DR

This paper rigorously analyzes how phonon creation impacts the fidelity of quantum spin dynamics in trapped ion simulators, revealing that phonons do not affect Ising model measurements but influence other models and observables.

Contribution

It provides an exact operator factorization approach to disentangle phonon effects, clarifying their role in different quantum spin models in ion-trap systems.

Findings

Phonons do not affect Ising spin state probabilities.

Phonons influence Heisenberg and XY model dynamics.

Phonons impact measurements of certain observables.

Abstract

We compute how phonon creation affects the fidelity of the quantum spin dynamics in trapped ion simulators. A rigorous treatment of the quantum dynamics is made by employing an exact operator factorization of the evolution operator. Although it is often assumed that phonon creation modifies the dynamics of the spin evolution, for an Ising spin-spin interaction in an external magnetic field, phonons have \textit{no effect} on the probabilities of spin product states measured in the direction of the Ising model axis. Phonons play a much more important role in influencing the effective spin dynamics for Heisenberg or XY model spin simulators or for other observables, like witness operators in the Ising model.