Exactly-solved model of light-scattering errors in quantum simulations with metastable trapped-ion qubits

TL;DR

This paper provides an exact analytical model for light scattering errors in quantum simulations using metastable trapped-ion qubits, highlighting how leakage affects different quantum states and the robustness of spin squeezing.

Contribution

It generalizes previous models to include leakage outside the qubit manifold, offering a detailed analysis of error impacts in metastable ion-based quantum simulations.

Findings

Leakage induces significant effective magnetic fields affecting GHZ state correlations.

Spin squeezing remains largely unaffected by leakage even with hundreds of ions.

The model aids in understanding and mitigating errors in future metastable qubit experiments.

Abstract

We analytically solve a model for light scattering in Ising dynamics of metastable atomic qubits, generalizing the approach of Foss-Feig {\it et al.}~[Phys.~Rev.~A {\bf 87}, 042101 (2013)] to include leakage outside the qubit manifold. We analyze the influence of these fundamental errors in simulations of proposed experiments with metastable levels of $^{40}$Ca$^+$ ions. We find that ``effective magnetic fields" generated by leaked qubits have significant impacts on spin-spin correlation functions for Greenberger-Horne-Zeilinger state preparation or for quantum simulations with strong coupling, while spin squeezing uses a much weaker coupling and is largely insensitive to the simulated leakage errors, even with a few hundred ions. Our theory and results are expected to be useful in modeling a variety of metastable qubit experiments in the future.