Explore quantum computing with trapped ions in this 43-minute conference talk by Crystal Noel from Duke University. Recorded at the Noisy Intermediate-Scale Quantum Systems: Advances and Applications conference, delve into the latest advancements in integrable models across mathematical physics, condensed-matter physics, and string theory. Discover topics such as integrable deformations of CFTs and IQFTs, integrable spin-chains and their non-equilibrium dynamics, and integrable structures on string worldsheets. Gain insights into the relationship between AdS(d+1)/CFT(d) and CFT(2) structures. Benefit from a comprehensive overview of the field, suitable for integrability practitioners from various backgrounds. Part of the KITP conference series, this talk aims to bridge gaps between different research areas and provide a pedagogical perspective on recent developments in quantum computing and related fields.