In this talk, I will review the fundamental principles of quantum information processing and provide an update on the Innsbruck trapped-ion quantum computer [1]. Using strings of trapped ions, we realize a programmable quantum processor capable of performing universal operations. I will give an overview of the experimental quantum toolbox and discuss current strategies for scaling the system to larger sizes.

The versatility of this platform is illustrated through both analog and digital quantum simulations. By exploiting the trapped-ion toolbox for entanglement-enhanced Ramsey interferometry, we identify optimal parameters for quantum metrology [2]. Employing universal quantum computation, we explore the dynamics of the Lattice Schwinger model [3] - a one-dimensional gauge theory of quantum electrodynamics - and, using a hybrid quantum-classical variational approach, we determine steady-state properties of the corresponding Hamiltonian [4]. Finally, with a trapped-ion qudit quantum processor, in which quantum information is encoded in multiple internal states, we simulate a two-dimensional lattice gauge theory [5}.

[1] I. Pogorelov et al., PRX Quantum 2, 020343 (2021)
[2] C. D. Marciniak et al., Nature 603, 604 (2022)
[3] E. A. Martinez et al., Nature 534, 516 (2016)
[4] C. Kokail et al., Nature 569, 355–360 (2019)
[5] M. Meth et al., Nature Physics 21, 570 (2025)