Floquet logical operations act by transporting an encoded space through a sequence of code frames. They are not ordinary transversal gates on one fixed stabilizer block.
After each round, contracting the measured matching exposes an instantaneous toric frame. Composing the three frame changes around one period exchanges the toric anyons e and m. A logical winding string of electric character is transported to magnetic character, and vice versa.
The operation is protected because it is induced by a local path through topologically ordered frames. Its physical cost is continued execution of the memory schedule plus classical tracking of measurement outcomes and logical representatives. Two periods restore the anyon label. This is the first operation recorded in card.yaml.
Floquet Codes with a Twist introduces fermion-condensation lines whose endpoints are twists. Schedule deformations can create, move, fuse, and braid these endpoints while keeping two-body measurements and trivalent connectivity.
The logical action belongs to the topology of defect worldlines, but fault tolerance still requires repeated syndrome extraction around the moving defects. A static picture of twist locations does not specify hook errors, time separation, or decoder boundaries.
Floquet Codes and Phases in Twist-Defect Networks places these operations in a broader classification of phases and anyon permutations. The classification tells which automorphism is possible; it does not by itself provide the hardware resource count.
Kobayashi and Zhu place the honeycomb Floquet code on a non-orientable cross-cap. One schedule period acts as logical HZ on the single encoded qubit in their convention. Folding turns the nonlocal identification into a bilayer geometry.
This gate is not a property of the ordinary orientable torus instance. Its resource contract includes the cross-cap or folded bilayer connectivity, schedule, and decoder adapted to that geometry.
Automorphism codes describe a protected loop in the space of gapped Hamiltonians or code frames. Fixed-point path-integral circuits generalize the idea to broader non-chiral Abelian topological phases and can include non-Clifford ingredients. These frameworks explain how to design logical action, but applying them to the original honeycomb memory requires an explicit schedule and fault-tolerance analysis.
The fetch-verified sweep found no complete universal, fully benchmarked logical gate set for the unmodified planar Hastings-Haah honeycomb memory. Three nearby results must remain separate:
The card therefore records only the native anyon exchange, twist-defect processing, and cross-cap HZ, each with its own mechanism and geometry.
A complete operation certificate needs:
The current constructor certifies only the undeformed periodic memory.