Scaling roadmap for modular trapped-ion QEC and lattice-surgery teleportation

We present a footprint study for the scaling of modular quantum error correction (QEC) protocols designed for triangular color codes, including a lattice-surgery-based logical teleportation gadget, and compare the performance of various possible architectures based on trapped ions. The differences in these architectures arise from the technology that enables the connectivity between physical qubits and the modularity required for the QEC gadgets, which is either based on laser-beam deflectors focused to independent modules hosting mid-size ion crystals, or integrated photonics guided to segmented modules of the trap and allowing for the manipulation of smaller ion crystals. Our approach integrates the transpilation of the QEC gadgets into native trapped-ion primitives and a detailed account of the specific laser addressing and ion transport leading to different amounts of crosstalk errors, motional excitation and idle qubit errors. Combining a microscopically-informed noise model with an efficient Pauli-frame simulator and different scalable decoders, we assess the near-term performance of the color-code memory and teleportation protocols on these architectures. Our analysis demonstrates that modular color-code teleportation is achievable in these near-term trapped-ion architectures, and identifies the integrated-photonics connectivity as the most promising route for longer-term scaling.