Circuit-QED Lattice System with Flexible Connectivity and Gapped Flat Bands for Photon-Mediated Spin Models

Quantum spin models are ubiquitous in solid-state physics, but classical simulation of them remains extremely challenging. Experimental testbed systems with a variety of spin-spin interactions and measurement channels are therefore needed. One promising potential route to such testbeds is provided by microwave-photon-mediated interactions between superconducting qubits, where native strong light-matter coupling enables significant interactions even for virtual-photon-mediated processes. In this approach, the spin-model connectivity is set by the photonic mode structure, rather than the spatial structure of the qubit. Lattices of coplanar-waveguide (CPW) resonators have been demonstrated to allow extremely flexible connectivities and can therefore host a huge variety of photon-mediated spin models. However, large-scale CPW lattices with nontrivial band structures have never before been successfully combined with superconducting qubits. Here we present the first such device featuring a quasi-1D CPW lattice with multiple transmon qubits. We demonstrate that superconducting-qubit readout and diagnostic techniques can be generalized to this highly multimode environment and observe the effective qubit-qubit interaction mediated by the bands of the resonator lattice. This device completes the toolkit needed to realize CPW lattices with qubits in one or two Euclidean dimensions, or negatively curved hyperbolic space, and paves the way to driven-dissipative spin models with a large variety of connectivities.