Data of the publication "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<br> random graphs and methods from percolation theory, we prove in the two-dimensional (2D) setting that<br> some local operators grow at a ballistic rate, which implies the absence of localization. In contrast, the<br> one-dimensional model displays a strong form of localization, characterized by the emergence of left- and<br> right-blocking walls in random locations. We provide additional insights by complementing our analytical results with numerical simulations of operator spreading and entanglement growth, which show the<br> absence (presence) of localization in two dimensions (one dimension). Furthermore, we unveil how the<br> spectral form factor of the Floquet unitary in 2D circuits behaves like that of quasifree fermions with<br> chaotic single-particle dynamics, with an exponential ramp that persists up to times scaling linearly with<br> the size of the system. Our work sheds light on the nature of disordered Floquet Clifford dynamics and<br> their relationship to fully chaotic quantum dynamics.