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After two decades of development, superconducting circuits have emerged as a rich platform for quantum computation and simulation. When combined with superconducting qubits, lattices of coplanar waveguide (CPW) resonators can be used to realize artificial photonic materials or photon-mediated spin models. Here I will highlight the special properties of this hardware implementation that lead to these lattices naturally being described as line graphs. Elucidating this connection required combining theoretical and computational methods from both physics pure mathematics, and has lead not only to a new understanding of the physics of these devices [1, 2], but also new results regarding spectral gaps of 3-regular graphs [3], and a framework for studying a new class of topologically-protected quantum error correcting codes [4].


[1] Kollár, Fitzpatrick, Houck, Nature 45, 571 (2019).

[2] Kollár, Fitzpatrick, Sarnak, Houck, Comm. Math. Phys. 376, 1909-1956 (2020).

[3] Kollár, Sarnak, Comm. AMS. 1, 1 (2021).

[4] Chapman, Flammia, Kollár, Quantum 3, 03021 (2022).


Alicia Kollár

University of Maryland