Beyond Hard-Core Bosons in Transmon Arrays

Arrays of transmons have proven to be a viable medium for quantum information science and simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or, equivalently, hard-core boson model. With higher excited levels included, coupled naturally realize attractive Bose-Hubbard The dynamics model has been difficult study due unfavorable scaling dimensionality Hilbert space with system size. In this work, we present framework describing effective unitary highly-excited states based on high-order degenerate perturbation theory. This allows us describe various collective phenomena -- such bosons stacked onto single site behaving particle, edge-localization, longer-range interactions in unified, compact accurate manner. While our examples deal one-dimensional chains sake clarity, theory can readily applied more general geometries.