In this talk, we study the propagation, entanglement, and entropy of quantum information using 3×3 and 4×4 arrays of superconducting qubits that emulate the two-dimensional (2D) hard-core Bose-Hubbard model. The 2D arrays feature site-selective, simultaneous control and readout of all qubits. We highlight several recent experimental demonstrations using these arrays, including quantum random walks, Anderson and Wannier-Stark localization, the differentiation between area-law and volume-law entanglement scaling in these lattices, Aharonov-Bohm caging, and the emulation of flat-bands in 1D chains. Time permitting, I will talk about recent improvements in control fidelity with fluxonium qubits at the 99.998% level for single-qubit gates.