Data for figures requiring simulation (i.e. Figs 5-6, 8-12) in S.H. Pickering, B. Bertini Asymptotically Solvable Quantum Circuits (https://arxiv.org/abs/2602.24276). In cases where the figures correspond to a visualisation of a single 2d array (i.e. Figs 5-6) a single file containing the array is given with a corresponding name. In cases where the figures correspond to a subsets of data acquired over multiple simulations (i.e. Figs 8-12) the full datasets are given in folders named according to the figures. File names contain information on the parameters used in the simulation. For example "half_svn_2l=8_s=1_h=2pi-12.csv" indicates that the file contains values representing half of the SvN (von Neumann entropy) with 2l=8, s=1, h=2pi/12=pi/6. All files within folders corresponding to Figs. 9-12 contain 1d arrays representing von Neumann entropies at each timestep for the respective simulation. For Fig. 8 the data is arranged into 2d arrays where the vertical axis corresponds to the Rényi index 1-10 and the horizontal axis corresponds to the timestep.