Edge scrambling in Floquet code under coherent errors

Floquet code stores quantum information in the dynamically evolving logical space generated by measurements in a periodic sequence. When placed on an open manifold, the edge of a two-dimensional Floquet code, after each period, undergoes a non-trivial translation that cannot be realized in a purely one-dimensional measurement circuit of constant depth. In this work, we study the Floquet code subject to coherent errors and show that its edge can exhibit a transition from a non-scrambled phase featuring a translation after each cycle to a phase in which the edge qubits develop volume-law entanglement. We numerically demonstrate this transition in the Wen plaquette translation model under coherent errors described by Clifford unitary gates. Furthermore, we discuss the connection between the edge scrambling transition and the decoding transition in the Floquet memory on a torus.