Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their popularity and success as qubit arrays, there remains yet untapped potential beyond the two-level approximation. Being experimentally controllable with high fidelity, the higher excited states provide an important resource for hardware-efficient many-body quantum simulations, quantum error correction, and quantum information protocols.

In this talk, I will first present an theoretical and numerical framework for describing the effective unitary dynamics of highly excited states based on 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. In the second part, I will discuss transmons in a waveguide and show how their bosonic statistics enhances collective sub/superradiance compared to that of qubit array. Together with the long-lived coherence times and versatile engineering possibilities, superconducting quantum devices provide an exciting platform to explore and deepen understanding on open many-body quantum dynamics.