Scalable quantum computing with trapped ions and selected application examples

I will describe the challenges on the way to a scalable, eventually fault tolerant quantum computers [1]. Efforts from physics, informatics [2,3] & mathematics but also engineering [4] are concentrated in demonstrator setups. As a first glance into the power of quantum computing, I will describe a couple of usecases: the VQE-simulation of a two-flavor Schwinger quark model executed on a trapped-ion quantum processor [5], and the quantum autoencoder [6], as a simple instance of machine learning on this hardware. Using, and extending the toolset of quantum computing are investigating circuits that realize quantum thermodnamic processes [7,8,9]. **References** [1] Hilder et al., Phys. Rev. X.12.011032 (2022) [2] Kreppel et al., Quantum 7, 1176 (2023) [3] Durandeau et al., Quantum 7, 1175 (2023) [4] Kaustal et al., AVS Qu. Sci. 2, 014101 (2020) [5] Melzer et al., arXiv:2504.20824 [6] Locher et al., Quantum 7, 942 (2023) [7] Fox et al., Entropy 26(11), 952 (2024) [8] Onishchenko et al., Nat. Comm. 15, 6974 (2024) [9] Stahl et al., arXiv:2404.14838