Charge-4e superconductor with parafermionic vortices: A path to universal topological quantum computation

Topological superconductors (TSCs) provide a promising route to fault-tolerant quantum information processing. However, the canonical Majorana platform based on 2e TSCs remains computationally constrained. In this work, we find a 4e TSC that overcomes these constraints by combining a charge-4e condensate with an Abelian chiral mathbb{Z}₃ topological order in an intertwined fashion. Remarkably, this 4e TSC can be obtained by proliferating vortex-antivortex pairs in a stack of two 2e p+ip TSCs, or by melting a ν=2/3 quantum Hall state. Specific to this TSC, the hc/(4e) fluxes act as charge-conjugation defects in the topological order, whose braiding with anyons transmutes anyons into their antiparticles. This symmetry enrichment leads to mathbb{Z}₃ parafermion zero modes trapped in the elementary vortex cores, which naturally encode qutrits. Braiding the parafermion defects alone generates the full many-qutrit Clifford group. We further show that a simple single-probe interferometric measurement enables topologically protected magic-state preparation, promoting Clifford operations to a universal gate set. Importantly, the non-Abelian excitations in the 4e TSC are confined to externally controlled defects, making them uniquely identifiable and amenable to controlled creation and motion with superconducting-circuit technology. Our results establish hierarchical electron aggregation as a complementary principle for engineering topological quantum matter with enhanced computational power.