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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.06963 |
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| _version_ | 1866912987286077440 |
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| author | Shi, Zhengyan Darius Han, Zhaoyu Raghu, Srinivas Vishwanath, Ashvin |
| author_facet | Shi, Zhengyan Darius Han, Zhaoyu Raghu, Srinivas Vishwanath, Ashvin |
| contents | 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 single-probe interferometric measurement enables topologically protected magic-state preparation, promoting Clifford operations to a universal gate set. Because the non-Abelian modes are bound to flux defects, they can, in principle, be externally controlled using superconducting circuit-based technology. More broadly, our results highlight hierarchical electron aggregation, the formation and condensation of higher-charge electron clusters, as a design principle for topological quantum matter with increased computational capability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06963 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Charge-$4e$ superconductor with parafermionic vortices: A path to universal topological quantum computation Shi, Zhengyan Darius Han, Zhaoyu Raghu, Srinivas Vishwanath, Ashvin Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics 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 single-probe interferometric measurement enables topologically protected magic-state preparation, promoting Clifford operations to a universal gate set. Because the non-Abelian modes are bound to flux defects, they can, in principle, be externally controlled using superconducting circuit-based technology. More broadly, our results highlight hierarchical electron aggregation, the formation and condensation of higher-charge electron clusters, as a design principle for topological quantum matter with increased computational capability. |
| title | Charge-$4e$ superconductor with parafermionic vortices: A path to universal topological quantum computation |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2602.06963 |