Fermionic Magic Resources of Quantum Many-Body Systems

Abstract: Understanding the computational complexity of quantum states is a central challenge in quantum many-body physics. In qubit systems, fermionic Gaussian states can be efficiently simulated on classical computers and thus provide a natural baseline for assessing quantum complexity. In this talk, based on [arXiv:2506.00116], I will briefly introduce the idea of magic state resource theories and then focus on a framework for quantifying fermionic magic resources, also known as fermionic non-Gaussianity. I will describe the algebraic structure of the fermionic commutant and introduce fermionic antiflatness (FAF)—an efficiently computable and experimentally accessible measure of non-Gaussianity with a clear physical interpretation in terms of Majorana fermion correlation functions. I will argue that FAF detects phase transitions, reveals universal features of critical points, and identifies special solvable points in many-body systems. Extending to out-of-equilibrium settings, I will show that fermionic magic resources proliferate in highly excited eigenstates, and I will describe the growth and saturation of FAF under ergodic dynamics, emphasizing how conservation laws and locality constrain the increase of non-Gaussianity during unitary evolution. The main goal of this talk is to present fermionic non-Gaussianity—alongside entanglement and non-stabilizerness—as a resource relevant not only for foundational studies but also for experimental platforms aiming at quantum advantage.