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We study the Hamiltonian lattice Yang-Mills theory based on spin networksthat provide a useful basis to represent the physical states satisfying theGauss law constraints. We focus on $\mathrm{SU}(2)$ Yang-Mills theory in$(2+1)$ dimensions. Following the string-net model, we introduce aregularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theorybased on the $q$ deformation, which respects the (discretized) $\mathrm{SU}(2)$gauge symmetry as quantum group, i.e., $\mathrm{SU}(2)_k$, and enablesimplementation of the lattice Yang-Mills theory both in classical and quantumalgorithms by referring to those of the string-net model. Using the regularizedHamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scarsare nonthermal energy eigenstates arising in the constrained quantum many-bodysystems. We find that quantum scars from zero modes, which have been found inabelian gauge theories arise even in a nonabelian gauge theory. We also showthe spectrum of a single-plaquette model for SU(2)$_k$ and SU(3)$_k$ with naivecutoff and that based on the $q$-deformation to discuss cutoff dependence ofthe formulation.

String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory