Long-lived fluxon excitations can be trapped inside a superinductor ring, which can be realized with a long array of Josephson junctions, one of which offers the input/ output path for the magnetic flux . The superinductor ring can be separated into smaller loops by a periodic sequence of Josephson junctions in the quantum regime, thereby allowing fluxons to tunnel between neighboring loops. This model is dual to that of two-leg ladder bosons, which have a rich phase diagram depending on flux and density . By tuning the Josephson coupling, and implicitly the tunneling probability amplitude of fluxons, a wide class of 1D tight-binding lattice models may be implemented and populated with a stable number of fluxons. In this context, fluxons are lattice bosons with repulsive interactions. We illustrate this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the 1-fluxon subspace, which hosts a symmetry protected topological phase with fractionally charged bound states at the edges . This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.
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