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

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.

arXiv comment6+23 pages, 4+5 figures. v2 includes minor revisions

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