  We propose an architecture based on superconducting qubits and resonators for
the implementation of a variety of exotic lattice systems, such as spin and
Hubbard models in higher or fractal dimensions and higher-genus topologies.
Spin systems are realized naturally using qubits, while superconducting
resonators can be used for the realization of Bose-Hubbard models. Fundamental
requirements for these designs, such as controllable interactions between
arbitrary qubit pairs, have recently been implemented in the laboratory,
rendering our proposals feasible with current technology.
