A central challenge in quantum many-body physics is to understand when quantum states can be efficiently simulated on classical computers, and when they possess genuine computational power. In the qubit setting, this distinction is captured by the resource theory of magic—non-stabilizerness beyond Clifford circuits. In fermionic systems, the natural analogue of stabilizer states are fermionic Gaussian states, which admit efficient classical simulation. 

In our work, we develop a framework to quantify departures from Gaussianity, which we term fermionic magic resources. At the heart of this framework is a new measure—fermionic antiflatness (FAF)—that is both efficiently computable and experimentally accessible. 
FAF detects non-Gaussian correlations directly from two-point Majorana fermion correlators, giving it a clear physical interpretation. We show that FAF not only identifies quantum phase transitions and critical points in equilibrium settings, but also reveals how non-Gaussian resources grow in highly excited eigenstates and under ergodic dynamics. This framework provides experimental probes of many-body states and fresh theoretical insights into quantum many-body physics.