Abstract: Quantum mechanics prescribes exponential scaling of the Hilbert space dimension in many-body systems, which presents both challenges and new opportunities for understanding strongly correlated matter, especially since novel custom-built systems are now available. I will describe such efforts on engineering quantum systems atom by atom, precisely controlling them with laser-driven interactions, and increasing the system size up to a regime where the capabilities of classical computers are challenged.
I will focus on the platform of trapped atomic ions, where a combination of excellent coherence time and high-fidelity measurements has enabled many applications, ranging from simulating condensed matter physics, to quantum computation. We represent spin qubits with electronic levels of ions in a Coulomb crystal, and entangle them through tailored laser pulses. I will present recent experiments using these systems to study dynamical phase with individual resolution for more than 50 spins, as well as non-equilibrium driven matter. I then conclude with future prospects.