  Quantum simulation can be implemented in pure digital or analog ways, each
with their pros and cons. By taking advantage of the universality of a digital
route and the efficiency of analog simulation, hybrid digital-analog approaches
can enrich the possibilities for quantum simulation. We use a unique hybrid
approach to experimentally perform a quantum simulation of phase-controlled
dynamics resulting from a closed-contour interaction (CCI) within certain
multi-level systems in superconducting quantum circuits. Due to symmetry
constraints, such systems cannot host an inherent CCI. Nevertheless, by
assembling analog modules corresponding to their natural evolutions and
specially designed digital modules constructed from standard quantum logic
gates, we can bypass such constraints and realize an effective CCI in these
systems. Based on this realization, we demonstrate a variety of related and
interesting phenomena, including phase-controlled chiral dynamics, separation
of chiral enantiomers, and a new mechanism to generate entangled states based
on CCI.
