Superconducting circuits are ubiquitous in quantum simulations, computing, and metrology. In this talk, I will demonstrate circuits, which are pushed to the extreme in the parameter space, where they actually become insulating. Remarkably, such nominally insulating circuits provide a tunable high-impedance environment and facilitate exceptionally strong interactions between photons and any type of electric dipoles. Besides applications in metrology, high-impedance circuits can be applied to quantum simulations of many open strongly interacting problems, with examples ranging from quantum phase transitions to many-body localization.
In particular, I will focus on the dissipative quantum phase transition between the insulating and the superconducting behavior of a Josephson junction facing an Ohmic environment. Despite many experimental attempts, the existence of such a transition remains controversial. I will demonstrate the transition using a conceptually new approach, which relies on monitoring environmental degrees of freedom, the environment being a high-impedance array of Josephson junctions. A similar approach applies to analog quantum simulations of many other strongly interacting problems, which I will briefly discuss. Finally, I will introduce a multi-terminal Josephson junction which, as a circuit element, expands the pool of strongly interacting models available for quantum simulations with the high-impedance platform. A multi-terminal Josephson junction is also a promising system for realizing the topology in dimensions greater than three.