Since its inception in the early 1920s, the theory of quantum mechanics has provided a framework to describe the physics of nature; or at least our interpretations about systems in nature. However, even though quantum theory works, the unsettling question of “why?’ still remains. The field of quantum information science and technology (QIST) has brought together a collection of disciplines forming a united multidisciplinary collaborative effort towards realizing a large-scale quantum processor as an attempt to understand quantum mechanics better. It has been established in the field that the most efficient architectural design of this quantum processor would be composed of numerous individual quantum computers, quantum simulators, quantum networks, quantum memories, and quantum sensors that are “wired” together creating just the hardware layer in the full stack of the machine. Realizing a module-based quantum processor on such a macroscopic scale is an ongoing and challenging endeavor in itself.

However, existing noisy intermediate-scale quantum (NISQ) devices across all the quantum applications above are still worth building, running, and studying. NISQ quantum computers can still provide quantum advantages over classical computation for given algorithms, and quantum simulators can still probe complex many-body dynamics that remain improbable to consider even on the best supercomputer. One such system is the trapped-ion quantum simulator at the center of this dissertation. Using 171Yb+ ions, we expand our “analog” quantum simulation toolbox by incorporating “digital” quantum computing techniques in each of the three experiments presented in this work.

In the first experiment, we perform a quantum approximate optimization algorithm (QAOA) to estimate the ground-state energy of a transverse-field antiferromagnetic Ising Hamiltonian with long-range interactions. For the second project, we develop and demonstrate dynamically decoupled (DD) quantum simulation sequences in which the coherence in observed dynamics evolving under the unitary operator of the target Hamiltonian is extended while the known noise is suppressed. Finally, in the third project, we implement an experimental protocol to measure the spectral form factor (SFF) and its generalization, the partial spectral form factor (PSFF), in both an ergodic many-body quantum system and in a many-body localized (MBL) model. As a result, a quantum simulator can be utilized to test universal random matrix theory (RMT) predictions, and simultaneously, probe subsystem eigenstate thermalization hypothesis (ETH) predictions of a quantum many-body system of interest.