aiqbench analysis
This theoretical study proposes a mechanism using flux-expulsion islands in fractional quantum Hall systems to transition from abelian to nonabelian anyonic states, which is critical for topological quantum computing. By leveraging superconducting islands to enlarge ground-state monodromy, the research offers a potential pathway to realizing experimentally elusive nonabelian statistics in 2D heterostructures. The work advances the mathematical physics underpinning fault-tolerant quantum information processing without relying on external AI or machine learning components.
FQH Liquids with Flux-Expulsion Islands allow Nonabelian Anyons
arXiv:2602.18748v2 Announce Type: replace-cross Abstract: The idea that topologically protected quantum states, such as anyons, may be attached to super/semiconductor heterostructures has received enormous attention, but experimental signatures in 1D systems remain elusive. Here we revisit theoretical underpinnings of anyons in 2D fractional quantum Hall (FQH) systems, whose signatures have been experimentally observed by independent groups. Invoking novel theorems about the Hopfion or $\mathbb{C}P^1$-model understood as flux quantization in 2-Cohomotopy, which retrodicts abelian FQH anyon properties in fine detail. Examining this theoretical model further, we find that islands of expelled (surplus) flux enlarge the ground-state monodromy from an abelian group to a (framed spherical) braid group, nonabelian for two or more islands, so that nonabelian anyonic states become topologically admissible; superconducting islands are one candidate realization of such flux expulsion.
Abstract:The idea that topologically protected quantum states, such as anyons, may be attached to super/semiconductor heterostructures has received enormous attention, but experimental signatures in 1D systems remain elusive. Here we revisit theoretical underpinnings of anyons in 2D fractional quantum Hall (FQH) systems, whose signatures have been experimentally observed by independent groups. Invoking novel theorems about the Hopfion or $\mathbb{C}P^1$-model understood as flux quantization in 2-Cohomotopy, which retrodicts abelian FQH anyon properties in fine detail. Examining this theoretical model further, we find that islands of expelled (surplus) flux enlarge the ground-state monodromy from an abelian group to a (framed spherical) braid group, nonabelian for two or more islands, so that nonabelian anyonic states become topologically admissible; superconducting islands are one candidate realization of such flux expulsion.
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Algebraic Topology (math.AT); Quantum Physics (quant-ph)
arXiv:2602.18748 [cond-mat.mes-hall]
(or arXiv:2602.18748v2 [cond-mat.mes-hall] for this version)
https://doi.org/10.1209/0295-5075/aea022 DOI(s) linking to related resources
Full text under the publisher's open licence · 157 words
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