I describe the approach of trapped ion qubits for quantum computing. In Mainz we follow the seminal proposal by David Wineland for a scalable architecture [1], which requires trap technologies and fabrication methods, control electronics for quantum register reconfigurations [2], but also the improvements qubit coherence [3], and its characterization [4]. We have realized multi-qubit operations [5], eventually leading to quantum error correction algorithms [6,7]. I conclude reporting on a novel fast entanglement operation just by applying electric displacement pulses shuttling Rydberg ion crystals [8].

[1] D. Kielpinski, C. Monroe, D. J. Wineland, Nature 417, 709 (2002)

[2] H. Kaufmann, et al., Phys. Rev. A 95, 052319 (2016)

[3] T. Ruster et al., Appl. Phys. B, 122, 1 (2016)

[4] T. Ruster, et al., Phys. Rev. X 7, 031050 (2017)

[5] H. Kaufmann et al, Phys. Rev. Lett. 119, 150503 (2017)

[6] A. Bermudez et al., Phys. Rev. X 7, 041061 (2017)

[7] D. Nigg, et al, Science 345, 302 (2014)

[8] J. Vogel, W.Li, A. Mokhberi, I. Lesanowsky, F. Schmidt-Kaler, arXiv:1905.05111