In this talk, I will present novel strategies to approach the continuum limit of lattice gauge theories on quantum hardware by combining classically improved Hamiltonians with state-dependent quantum corrections. Specifically, we develop and analyze Kogut-Susskind-type Hamiltonians on honeycomb and hyper-honeycomb spatial lattices, which minimize plaquette operator complexity by involving only three-link vertices. These constructions are enhanced through quantum tadpole improvements, where we explore the emergence of spacetime-dependent renormalizations in real-time simulations, highlighting the need for coefficient updates that depend on the current quantum state. Together, these developments mark significant steps toward scalable and accurate quantum simulations of gauge theories.