Flux-tunable regimes and supersymmetry in twisted cuprate heterostructures

Van der Waals assembly allows for the creation of Josephson junctions in an atomically sharp interface between two exfoliated Bi2Sr2CaCu2O8+δ (Bi-2212) flakes that are twisted relative to each other. In a narrow range of angles close to 45 ° , the junction exhibits a regime where time-reversal symmetry can be spontaneously broken, and it can be used to encode an inherently protected qubit called flowermon. In this work, we investigate the physics emerging when two such junctions are integrated in a superconducting quantum interference device circuit threaded by a magnetic flux. We show that the flowermon qubit regime is maintained up to a finite critical value of the magnetic field, and, under appropriate conditions, it is protected against both charge and flux noise. For larger external fluxes, the interplay between the inherent twisted d-wave nature of the order parameter and the external magnetic flux enables the implementation of different artificial atoms, including a flux-biased protected qubit and a supersymmetric quantum circuit.