A beautiful description of nature’s fundamental forces has
been devised through gauge fields introducing local symmetries or
conserved charges.  Though classical techniques continue to provide
invaluable information on the emergent properties of gauge field
theories relevant to experimental programs throughout the scientific
domains, some experimentally relevant parameter regimes e.g., where
coherent dynamics demand exponentially large Hilbert spaces, remain
beyond current or foreseeable computational capabilities.  While
leveraging quantum architectures directly within a computational
framework is expected to explore such parameter regimes more
naturally, the inefficient utilization of Hilbert space in the
presence of local symmetries demands careful considerations in the
presence of quantum noise. During this talk, we will discuss current
strategies and perspectives for representing quantum fields, from
scalars to SU(3) Yang-Mills, on quantum degrees of freedom and
controllably performing subsequent dynamical evolutions.