Absence of Localization in Two-Dimensional Clifford Circuits

We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using graphs methods from percolation theory, we prove the dimensional setting that some local operators grow at ballistic rate, which implies absence of localization. In contrast, one-dimensional model displays strong form localization characterized by emergence left right-blocking walls locations. provide additional insights complementing our analytical results numerical simulations operator spreading entanglement growth, show (presence) two-dimension (one-dimension). Furthermore, unveil spectral factor unitary two-dimensional circuits behaves like quasi-free fermions chaotic single particle dynamics, an exponential ramp persists till times scaling linearly size system. Our work sheds light on nature disordered, dynamics its relationship to fully quantum dynamics.