Dissipative Stabilization and Characterization of Strongly Correlated States in Superconducting Circuit Lattices

Superconducting circuits offer a powerful platform for studying many-body physics and realizing exotic quantum phases of matter. Beyond conventional Hamiltonian simulation, controlled dissipation can be introduced through parametric coupling between superconducting qubits and their lossy readout resonators. We design tunable particle drain and source baths, apply them to a Bose-Hubbard lattice formed by arrays of transmon qubits, and dissipatively stabilize strongly correlated many-body states. We further discuss how collective dissipation expands this toolbox and can lead to new dynamical and steady-state phenomena. To characterize the resulting states, we implement robust shadow estimation protocols capable of extracting correlations and many-body observables with provable resilience to readout and control imperfections. Together, these results demonstrate an integrated framework for the dissipative preparation and reliable characterization of many-body quantum states in superconducting analog quantum simulators.