Fluxonium can be modeled using only three circuit elements: a Josephson junction, a capacitor, and an inductor all connected in parallel. Despite such circuit simplicity, when the three circuit parameters are chosen appropriately, fluxonium's spectrum can be quite rich, involving very different transition frequencies and efficiencies, a useful feature for quantum information applications. Most importantly, one needs an unusual combination of a large inductance L and a small capacitance C, such that impedance **(L/C)^1/2** is on the order of resistance quantum (26.5 kOhm); most conventional circuit impedances are limited by the vacuum impedance (377 Ohm). In fluxonium, such a large and compact inductance (often referred to as "superinductance") is successfully achieved using a chain of Josephson junctions with parameters chosen to minimize quantum phase slip and standing wave resonances.
In this talk, I will introduce circuit quantum electrodynamics (QED) with fluxonium qubits and present our first experiments at UMD. I will also discuss the potential of high-impedance circuits for creating ultra-compact resonators for quantum technology development, exploring utlrastrong coupling QED, and simulating quantum impurity physics.