Geometric phases in unitary and non-unitary radical Floquet dynamics

We demonstrate that under the honeycomb Floquet code of Hastings and Haah all trajectories acquire a nontrivial geometric phase, independent of measurement outcomes. This Pancharatnam phase is the Berry phase of a continuous geodesic evolution between individual post-measurement states; however its value is topological, being a consequence of the automorphism. In the particular case of the honeycomb code, such geodesic paths are in the equivalence class of the radical chiral Floquet unitary, a non-equilibrium topological phase that has been deeply explored. In this way, the honeycomb code constitutes a fixed point of the radical chiral Floquet phase. We discuss the implications for stability as well as the boundary signatures of the nontrivial bulk in the code.