Trapped ions have been gaining traction as a platform for quantum information processing (QIP) in both academia and industry over the last decade. Their long coherence time, high fidelity gate operations, and built-in all-to-all connectivity are some of the key features that make trapped ions promising. However, to unlock the full potential of the trapped ion platform, sophisticated quantum controls are required. In this thesis, we present our efforts in individual optical addressing to control an ion’s quantum state at an individual level, as well as efforts in generating complex and time-dependent Hamiltonians through arbitrary radio frequency (RF) waveform generation.

We present two types of individual addressing systems. One is based on a holographic beam shaping technique. We experimentally show that an intensity crosstalk level of $10^{-4}$ can be achieved, translating to a greater than 99.9% fidelity in individual quantum state control and 99.6% fidelity in individual spin readout without corrupting the adjacent ion’s quantum state.

The other addressing system is specifically optimized for coherent manipulation of qubits with Raman beams in contrast to the addressing system described in the previous paragraph. This system is based on acousto-optic deflectors (AOD). We have designed a mirrored setup to compensate for site-dependent frequency shifts that result from the intrinsic properties of the AOD. The Raman transition is a two-photon process where only the frequency difference between the two beams matters. The two AODs produce the same amount of site-dependent frequency shift, which cancels out in the frequency difference. Simulations show that the system is capable of addressing 30-50 ions with crosstalk at a sub-$10^{-4}$ level.

The presented individual addressing systems can be applied to different species operated with different wavelengths. The holographic beam shaping system has even greater flexibility in that it can be applied to various quantum systems, such as neutral atom arrays or nitrogen vacancy centers in diamonds.

In addition to the individual addressing system, we also present our efforts in constructing complex and time-dependent Hamiltonians utilizing an arbitrary waveform generator. We use it to engineer and study the Floquet Hamiltonian. This type of system is intriguing because spatiotemporal orders can emerge from a quantum chaotic system. In this thesis, we use it to generate a transverse field Ising model with an additional time-dependent Floquet drive. Under specific conditions, the Floquet drive exhibits emerging conservation in total magnetization. We experimentally demonstrate dynamic freezing behavior for the total magnetization in a four-ion system and show that the Hilbert space is fragmented into multiple sectors with different total magnetizations.

Lastly, we also present our approach in various aspects of efforts in scaling up a trapped ion quantum processor. This includes building high-stability optics boards, analysis on scalable detection with qualitative CMOS (qCMOS) technology, and the in-house design of a microscope objective tailored for experimental requirements.