Quantum computing will be one of the most incredible breakthroughs in science and technology of our generation. Although the ultimate goal of building quantum computers that hold thousands of error-corrected qubits is still beyond our reach, we have made substantial progress. Compared with the first-generation prototypes, holding a few qubits with gate errors of several percent, the latest generation systems can apply more than a hundred gates (with fidelities above $99%$) to tens of fully connected qubits. This thesis focuses on the applications of such state-of-the-art ion-trap quantum computers.

The latest generation ion-trap quantum computers have become complex enough that automation is necessary for optimal operations. We present a full-stack automation scheme implemented on a system at the University of Maryland. With the automation scheme, the system can operate without human interference for a few days.

With automation, such systems can efficiently demonstrate different categories of applications. We present the experimental study of several hybrid algorithms aiming for generation modeling and efficient quantum state preparation. We also present a gate-based digital quantum simulation with the trotterization method. Our result accurately reproduced all the features expected from running the algorithms.

Verifying quantum computations with classical simulation is getting increasingly challenging as quantum computers evolve. We present two approaches to validate quantum computations. First, we demonstrate a method based on random measurement for comparing the results from different quantum computers. Our comparison captures the similarities between quantum computers made with the same technology. We then present experimental works in verifying quantum advantage classically with interactive protocols. We show that our results, at scale with real-time interaction, can demonstrate quantum advantages.