Schreiber Type IIA Anyons (Rev #7, changes)

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An article that we are finalizing at CQTS:

• Topological Quantum Gates on
  FCIs with Bounded Quantum Geometry

  manuscript: pdf (Oct 11)

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Two-band 2D fractional Chern insulators (FCI) have recently been shown to in principle admit unusual anyon order associated with Bloch Hopfions localized in momentum-space. Here we show that bounding the integrated quantum metric along one primitive Brillouin-zone cycle may refine this topological order to $|C|$ distinct braiding observables, cyclically permuted by lattice translations, for Chern numbers $|C| \gt 1$ . The cyclic structure entails mildly nonabelian braiding phases and otherwise matches thebraiding phases and otherwise matches the spectral flow exhibited by the FCI’s hybrid Wannier states through the effective quantum Hall layers of Qi and Barkeshli, with the metric bound equivalently a bound on the states’ real-space spread. We give a classification of quantum gates in principle implementable on this topological order, among them we find the non-Clifford T-gate and the non-Clifford entangling CCZ-gate. This points to novel pathways to fault-tolerant quantum processes within the known orbital structure of FCIs, potentially informing experimental searches towards hardware for future topological quantum computers.

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• Based on:

  • Fractional Quantum Hall Anyons via the Algebraic Topology of Surplus Flux Quanta

  • Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

  • On the Derivation of Twisted K-Theory from M-Theory

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