Lattice waveguide QED: many-body interactions by dissipation

In waveguide QED, superconducting qubits acting as artificial atoms are coupled to a 1D superconducting transmission line playing the role of common bath for the qubits. By controlling their effective separation, it is possible to engineer various types of dissipation-induced interactions between the qubits. In this talk, we consider the situation where multiple superconducting qubits are coupled to a lattice of~superconducting transmission lines. Depending on the choice of lattice, the qubits exhibit a rich variety of interactions. We present a Markovian master equation framework to describe these systems, and discuss results obtained for simple lattices.