  The pursuit of superconducting-based quantum computers has advanced the
fabrication of and experimentation with custom lattices of qubits and
resonators. Here, we describe a roadmap to use present experimental
capabilities to simulate an interacting many-body system of bosons and measure
quantities that are exponentially difficult to calculate numerically. We focus
on the two-dimensional hard-core Bose-Hubbard model implemented as an array of
floating transmon qubits. We describe a control scheme for such a lattice that
can perform individual qubit readout and show how the scheme enables the
preparation of a highly-excited many-body state, in contrast with atomic
implementations restricted to the ground state or thermal equilibrium. We
discuss what observables could be accessed and how they could be used to better
understand the properties of many-body systems, including the observation of
the transition of eigenstate entanglement entropy scaling from area law
behavior to volume law behavior
