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.
 N. A. Masluk, I. M. Pop, A. Kamal, Z. K. Minev, and M. H. Devoret, Phys. Rev. Lett. 109, 137002 (2012).
 E. Orignac and T. Giamarchi, Phys. Rev. B 64, 144515 (2001) ; A. Petrescu and K. Le Hur, Phys. Rev. Lett. 111, 150601 (2013) ; M. Piraud, F. Heidrich-Meisner, I. P. McCulloch, S. Greschner, T. Vekua, and U. Schollwllwock, Phys. Rev. B 91, 140406 (2015) ; A. Petrescu, M. Piraud, G. Roux, I. P. McCulloch, and K. Le Hur, Phys. Rev. B 96, 014524 (2017).
 R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976) ; W. P. Su, J. R. Schrie-er, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).