Description
Understanding the emergence of computational complexity in quantum many-body systems is a central challenge in quantum information and condensed matter physics. While fermionic Gaussian states and operations define a class of classically simulable dynamics, non-Gaussianity plays an analogous role to magic in the qubit Clifford/non-Clifford framework—serving as the key resource that enables universal quantum computation and classical intractability. In this talk, I will introduce the fermionic antiflatness (FAF), a novel, efficiently computable measure of fermionic non-Gaussianity based on two-point Majorana correlators. The FAF vanishes only for fermionic Gaussian states and remains invariant under Gaussian operations.
I will demonstrate how this framework captures essential features of quantum complexity, from the structure of typical Haar-random states to critical phenomena in equilibrium systems and the dynamical buildup of non-Gaussianity in out-of-equilibrium settings.
