Hamiltonian Simulations of QCD and Other Gauge Theories

The phase diagram of Quantum Chromodynamics has a complex array of emergent phenomena, which necessitates developing a wide range of computational tools to probe its varied properties. The same is true for many other gauge theories of phenomenological interest. One such tool, which has seen rapid development in recent years, is quantum computation. In contrast to simulations that are carried out on classical computers, which use the Lagrangian formulation and have been ongoing for many decades, simulating physical theories on quantum devices necessitates utilizing the Hamiltonian formulation. For gauge theories, much effort has focused on constructing various approaches, using myriad bases, truncation schemes and degrees of gauge fixing. Ideally, a formulation would be systematically improvable, efficient for fine lattices, and gauge invariant. No such formulation has yet been developed and so at least one of these desired properties must be sacrificed. In this talk, I review the progress of the past several years in developing a variety of formulations of gauge theories that can be implemented onto modern-day digital quantum devices. I also discuss the large array of numerical results that have been calculated using various quantum devices, formulations and computational methods. Lastly, I conclude with an eye to the future, of what we might expect to see in the next five to ten years in this field.