Engineering Qubit-Qubit Interactions in Circuit QED Lattices

The inherent strong coupling between microwave resonators and superconducting qubits available in the circuit QED architecture makes it possible to use the spectrum of multimode photonic environments to engineer qubit-qubit interactions. Previously, one-dimensional cavity arrays and modulated waveguides have been used to induce exponentially-localized interactions [1,2].
Lattices of coplanar waveguide resonators realize artificial photonic materials that provide a tailored environment for with versatile control [3]. Qubits in these lattices experience a photon-mediated flip-flop interaction, which takes on different forms depending on the structure of the lattice, giving rise to a direct hardware-level implementation of a graph-like spin model with connections determined by the microwave resonator network. Here we present results towards realizing a larger variety interactions, such as frustrated interactions, in which different terms compete and favor different configurations, allowing a spin model to exhibit memory, and hyperbolic interactions, which lead to rapid growth of connectivity and efficient connections.

[1] N. M. Sundaresan et al., Phys. Rev. X 9, 011021 (2019).
[2] V. S. Ferreira et al., arXiv:2001.03240 (2020).
[3] A. J. Kollár et al., Nature 45, 571 (2019).