Band Engineering and Graph-Theoretic Connections in Circuit QED*

The field of circuit QED has emerged as a rich platform for both quantum com- putation and quantum simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit [1] capable of realizing non-Eucliudean geometries [2] and unconventional unit cells [3]. Combined with strong qubit-photon interactions, these systems can be used to study dynamical phase transitions, many-body phenomena, and spin models in driven-dissipative systems. Furthermore, the one-dimensional waveguide nature of these resonators permit the creation of unique devices which host photons in curved spaces, gapped flat bands, and novel forms of qubit-qubit interaction. I will show that graph theory is the natural language for describing these microwave photonic systems and how it can be used to understand the types of devices that can be achieved [3], as well as how the physics of these types of devices connects to open problems in other fields such as quantum error correction and pure mathematics [4,5].

[1] D. Underwood et al., Phys. Rev. A 86, 023837 (2012)

[2] A. J. Kollár et al., Nature 571, 45 (2019)

[3] A. J. Kollár et al., Comm. Math. Phys. 376,1909 (2019)

[4] A. J. Kollár, P. Sarnak, Comm. Amer. Math. Soc. 1,1 (2021)

[5]. A. C. Chapman, S. T. Flammia, Quantum 4, 278 (2020), A. C. Chapman, S.

T. Flammia, A. J. Kollár, In Preparation (2021)