Engineering Trapped-Ion Systems for Large Scale Quantum Simulation*

Laser cooled trapped ions offer unprecedented control over both internal and external degrees of freedom at the single-particle level. They are considered among the foremost candidates for realizing quantum simulation and computation platforms that can outperform classical computers at specific tasks. In this talk I will show how linear arrays of trapped ¹⁷¹Yb⁺ ions can be used as a versatile platform for studying quantum dynamics of strongly correlated many-body quantum systems.
In particular I will describe how to realize time-crystalline phases in a Floquet setting, where the spin system exhibits persistent time-correlations under many-body-localized dynamics. I will also present our observation of a new type of out-of-equilibrium dynamical phase transition in a spin system with over 50 spins. Moreover I will show our latest efforts towards scaling up the trapped-ion quantum simulator using a cryo-pumped vacuum chamber where we can trap more than 100 ions indefinitely. The reliable production and lifetime of large linear ion chains enabled us to investigate quasi-particle excitations showing confinement in the quench dynamics and the implementation of Quantum Approximate Optimization Algorithms (QAOA) with up to 40 spins.