Finite-group gauge theories on lattices as Hamiltonian systems with constraints

In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite groups, in order to show how they can be interpreted as Hamiltonian system with constraints, analogous what happens classical (continuous) (field) theories. As interpretation is not usually explored literature that discusses/introduces concept lattice theory, some recent works have been exploring models support kind quantum computation, use to, for example, geometric view one class these models: Kitaev Quantum Double Models.