  Universal quantum computing requires nonstabilizer (magic) quantum states.
Quantifying the nonstabilizerness and relating it to other quantum resources is
vital for characterizing the complexity of quantum many-body systems. In this
work, we prove that a quantum state is a stabilizer if and only if all states
belonging to its Clifford orbit have a flat probability distribution on the
computational basis. This implies, in particular, that multifractal states are
nonstabilizers. We introduce multifractal flatness, a measure based on the
participation entropy that quantifies the wave-function distribution flatness.
We demonstrate that this quantity is analytically related to the stabilizer
entropy of the state and present several examples elucidating the relationship
between multifractality and nonstabilizerness. In particular, we show that the
multifractal flatness provides an experimentally and computationally viable
nonstabilizerness certification. Our work unravels the direct relation between
the nonstabilizerness of a quantum state and its wave-function structure.
