  Chern-Simons theory is a topological quantum field theory with numerous
applications in condensed matter and high-energy physics, including the study
of anomalies, fermion/boson dualities, and the fractional quantum Hall effect.
In this work, a Hamiltonian lattice formulation for 2+1D compact
Maxwell-Chern-Simons theory is derived. We analytically solve this theory and
demonstrate that the mass gap in the continuum limit matches the well-known
continuum formula. Our formulation preserves topological features such as the
quantization of the Chern-Simons level, the degeneracy of energy eigenstates,
and the non-trivial properties of Wilson loops. This work lays the groundwork
for future Hamiltonian-based simulations of Maxwell-Chern-Simons theory on
classical and quantum computers.
