We are currently witnessing a revolution in quantum technologies. Today’s controllable quantum devices have reached a complexity that makes it practically intractable to fully simulate their dynamics using current classical supercomputers. Decades of fundamental research and development have led us to this point. In the coming years, billions of dollars in investments from governments and private entities are expected worldwide. Although general-purpose fault-tolerant quantum computers are expected to impact computing profoundly, today’s quantum devices are best suited for their analog quantum operation, where a well-controlled quantum simulator mimics the dynamics of the other quantum system being studied. This affords an advantage over classical simulators at the cost of a restricted set of physical phenomena that can be studied. Today’s quantum devices are already providing insights into large-scale entanglement, the underlying physics of high-temperature superconductivity, disordered quantum systems, and much more. Enhancing the capabilities of today’s analog quantum simulators requires adding more classes of interactions, reducing errors due to calibration and noise, and increasing the system size to allow larger-scale simulations.

The work described in this thesis directly addresses these core points for a system of trapped ions, which are ideal quantum simulators of the coupled dynamics of a large number of magnetic spins. First, the theory and experiment pertaining to the simulation of the anisotropic XY model on trapped ions has been presented. The theoretical proposal does not require added technical improvements over what has existed in the field for over a decade. The experimental validation is performed on a system with two 171Yb+ ions. This directly enhances the repertoire of trapped ions simulators and opens avenues to the exploration of high-temperature superconductivity, superfluidity, and spin liquids. The second result is the demonstration of the highest resolution readout of optical intensity and polarization using a single 171Yb+ ion as the field probe. The technique utilized the intensity- and polarization-dependent optical pumping of the ions as a signature to detect light parameters. This will be useful for the characterization of the optical addressing fields in trapped ion quantum simulators and hence for the calibration of large-scale quantum devices. Finally, the design and construction of a large-scale ion trapping apparatus for quantum simulation are described. The ion trap allows for the trapping of more than 50 ions, and the vacuum chamber used to house the trap with pressure below 1.5E-12 mbar (measurement limited by pressure gauge saturation) likely sets a record for the lowest pressure achieved on a room-temperature trapped ions system. This increases the useful simulation time of large-scale trapped-ion devices and paves the way for further enhancement of the scale of the simulations performed. Together, these results are another step in advancing the capabilities of today’s quantum devices to explore physical phenomena far beyond the capability of classical supercomputers.