  Magic state resources or non-stabilizerness quantify the beyond-Clifford
operations necessary for universal quantum computing. How rapidly are magic
resources generated by generic many-body dynamics under constraints of
locality? We address this problem by exploring magic spreading in brick-wall
random unitary circuits. Inspired by the algebraic structure of the Clifford
group, we propose a scalable measure of non-stabilizerness, the
Calderbank-Shor-Steane entropy, which generalizes the notion of stabilizer
entropy and mirrors its qualitative behavior. This metric enables the
investigation of non-stabilizerness dynamics for systems of up to N = 1024
qudits. Our main finding is that magic resources equilibrate on timescales
logarithmic in system size N, akin to anticoncentration and Hilbert space
delocalization measures, but differently from entanglement entropy. We
conjecture that our findings describe the phenomenology of non-stabilizerness
growth in a broad class of chaotic many-body systems.
