Gauge theories such as quantum electrodynamics, in principle, give us a precise understanding of the interactions between subatomic particles, but often the calculations involved are beyond current computational capabilities. Quantum simulators based on experimental many-body systems could be a solution to this problem. Scientists exploit the current state-of-the-art experimental technology for manipulating cold trapped ions and propose a simulator of the one-dimensional version of quantum electrodynamics.
<!--HTML--> 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)
Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus - together with rapid advances in quantum-computing hardware - has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional
q-deformed
SU(2)3 Yang-Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of
SU(2)3, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement
F-moves. In our demonstrations, the quantum circuits execute up to 47 sequential
F-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of
F-moves.