Utilizing and extending superconducting circuit toolbox to simulate analog quantum gravity

There has been considerable effort to simulate quantum gravity features in solid state systems, such as analog black holes or wormholes. However, superconducting circuits have so far received only limited attention in this regard. Moreover, for quantum superpositions of spacetime geometries – a concept that presents significant challenges in developing a consistent theory of quantum gravity – there currently exist no solid state blueprints. We here show how quantum circuit hardware can implement a variety of classical and quantum spacetime geometries on lattices, by both using established circuit elements and introducing new ones. We demonstrate the possibility of a metric sharply changing within a single lattice point, thus entering a regime where the spacetime curvature itself is trans-Planckian, and the Hawking temperature ill-defined. In fact, our approach suggests that stable, thermal event horizons are incompatible with strictly discrete lattice models. We thus propose to directly probe the evaporation of a wormhole by tracking the accumulation of charge and phase quantum fluctuations over short time scales, which are a robust signature even in the presence of a dissipative environment. Moreover, we present a loop-hole for the typical black/white hole ambiguity in lattice simulations: the existence of exceptional points in the dispersion relation allows for the creation of pure black (or white) hole horizons – at the expense of radically changing the interior wormhole dynamics. Finally, based on multistable Josephson junctions, we introduce the notion of quantum inductors: circuit elements that can be prepared in a superposition of different inductance values. Such inductors realise regions with a quantum superposition of analog spacetime. The entanglement of signals with the quantum spacetime can be probed by a type of delayed-choice experiment.