Data for "Universality in the Anticoncentration of Chaotic Quantum Circuits"

We identify a universal functional form that governs anticoncentration in random quantum cir
cuits—one that holds across diverse circuit architectures and depths, and crucially remains valid
 even at finite system sizes and shallow depth. We support this claim through analytical results
 for ensembles of random tensor-network states and random-phase models. This compact, universal
 expression for the output bitstring probability distribution is fully characterized by just two fitting
 parameters, as validated through extensive numerical simulations. Our findings underscore the piv
otal role of finite-size and finite-depth effects in shaping anticoncentration and introduce a practical
 framework for benchmarking quantum devices using shallow circuits, thereby enabling validation of
 systems significantly larger than previously accessible.