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The pursuit of superconducting-based quantum computers has advanced thefabrication of and experimentation with custom lattices of qubits andresonators. Here, we describe a roadmap to use present experimentalcapabilities to simulate an interacting many-body system of bosons and measurequantities that are exponentially difficult to calculate numerically. We focuson the two-dimensional hard-core Bose-Hubbard model implemented as an array offloating transmon qubits. We describe a control scheme for such a lattice thatcan perform individual qubit readout and show how the scheme enables thepreparation of a highly-excited many-body state, in contrast with atomicimplementations restricted to the ground state or thermal equilibrium. Wediscuss what observables could be accessed and how they could be used to betterunderstand the properties of many-body systems, including the observation ofthe transition of eigenstate entanglement entropy scaling from area lawbehavior to volume law behavior

Realizing the two-dimensional hard-core Bose-Hubbard model with superconducting qubits