Abstract

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