Robust Quantum Control & Verification & Quantum Simulation with Trapped Ions

This PhD thesis reports on the development of a wide variety of theoretical and experimental capabilities in the field of quantum information processing using trapped ions. The presentation is organized in two distinct parts. The first part presents a series of published articles containing theoretical results, and their experimental validation, advancing a range of tools and techniques in error-resilient quantum control and robust verification procedures. One of the fundamental challenges in realizing a general purpose quantum computer is the management of error in fragile quantum systems. A familiar aspect of this challenge is decoherence, a process by which the system looses its stored quantum information, rendering it useless for subsequent computation. This collection of works focuses on reducing sources of quantum decoherence and precisely quantifying residual errors in real quantum systems dominated by realistic temporally-correlated noise processes, of central importance in any future architecture for quantum computing. The second part focuses on the design, construction and characterization of a complex experimental system capable of supporting a broad calls of quantum simulation experiments with hundreds of spin qubits using 9Be+ ions in a Penning trap. The trap design is optimized to suppress non-harmonic trapping potentials while providing wide optical access for engineering enhanced spin-motion coupling across large ion crystals. A superconducting magnet, equipped with a fully closed-cycle dual LN2/LHe recondensor, provides the magnetic field for trapping and produces the 55-GHz Zeeman-split qubit states suitable for microwave control. A custom UV laser system for driving the relevant transitions in neutral and ionized beryllium, as well as UV-compatible fibers and in-bore optomechanics for delivering microwave and laser beams to the trap, is presented. The thesis concludes with a brief outlook towards future theoretical and experimental studies, and extensions of the experimental setu