The field of superconducting circuits has emerged as a rich platform for both quantum computation and quantum simulation. Due to the native strong qubit-photon interactions, these systems can be used to study dynamical phase transitions, many-body phenomena, and spin models in driven-dissipative systems. Temporal control can be used to implement synthetic dimensions and lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit. I will present data from two new experiments, one featuring qubits in an unconventional at-band lattice, and a second showing that static dissipation can be used to stabilize quasienergy states of a time-periodic Floquet Hamiltonian.