Quantum Complexity and Stabilizer-State Expansions: From Pairing to Deformation in Fermionic Systems

arXiv:2610.31792v1 Announce Type: new Abstract: Understanding how collective phenomena such as pairing and deformation emerge in interacting fermionic systems, and how the correlations underlying them shape the resources required for their simulation, is a central challenge in many-body physics. We investigate various aspects of quantum complexity in a fermionic system exhibiting two main forms of collectivity, specifically deformation and pairing, through entanglement, non-stabilizerness, and fermionic non-Gaussianity. In the deformed phase, high entanglement coexists with low non-stabilizerness, while the superfluid pairing phase, by contrast, exhibits substantial multipartite entanglement and non-stabilizerness, together with maximal fermionic anti-flatness.