Dynamics of Entanglement Stabilization in Driven-dissipative Superconducting Circuit Lattices

Superconducting transmon qubits have emerged as a promising platform for simulating many-body physics, due to their long coherence times, tunable interactions, and single-site controllability. Beyond unitary evolution, incoherent driven-dissipative processes can greatly enrich the many-body phenomena, including thermalization, diffusive transport, and the formation of non-equilibrium steady states. In this context, we develop a hardware-efficient approach to implement tunable engineered baths in superconducting circuit lattices. We experimentally demonstrate the generation and stabilization of entanglement in a two-site lattice with tunable local gain/loss baths. Furthermore, we investigate the dependence of stabilization dynamics on the initial states, which is attributable to different decay channels within the system. Finally, I will present our progress on extending this stabilization protocol to larger lattices. Our work paves the way for preparing non-equilibrium steady states and studying their properties with analog quantum simulators.