Logical operations

electric-magnetic anyon exchange / logical-frame automorphism measurement-based claimed

Level: topological Clifford frame · Cost: one three-round memory period; two periods close the anyon label frame

References: hastings2021dynamically

twist creation, transport, fusion, and braiding braiding claimed

Level: defect-mediated topological operations · Cost: schedule deformations along condensation lines plus repeated fault-tolerant measurements around moving twist endpoints

References: ellison2023twist

logical HZ on a cross-cap encoded qubit measurement-based claimed

Level: Clifford · Cost: one schedule period on a non-orientable cross-cap geometry, or a folded bilayer implementation of that geometry

References: kobayashi2024crosscap