Understanding the computational complexity of quantum many-body states
is a central challenge at the interface of quantum information,
condensed matter, and high-energy physics. While entanglement provides a
fundamental lens on many-body structure, it is now clear that it alone
does not fully capture the resources underlying quantum advantage. In
particular, broad classes of highly entangled states\u2014such as stabilizer
states and fermionic Gaussian states\u2014remain efficiently simulable on
classical computers. In this talk, I introduce a unified perspective on
many-body complexity based on resource theories that quantify deviations
from such classically tractable manifolds. I will first review the
concept of nonstabilizerness and its quantitative characterization via
the stabilizer R\u00e9nyi entropy, which provides an efficiently computable
and experimentally accessible measure of complexity beyond entanglement.
I will then focus on fermionic systems, where Gaussian states define a
natural notion of classical simulability. Building on recent work, I
will introduce measures of fermionic magic, with particular emphasis on
the fermionic antiflatness, an efficiently computable diagnostic of
non-Gaussianity based on Majorana correlation functions. I will discuss
how these measures behave in equilibrium and out-of-equilibrium
many-body systems, highlighting their ability to detect phase
transitions, characterize criticality, and quantify the growth of
complexity under dynamics. Overall, this framework provides a coherent
approach to probing quantum complexity in many-body systems, bridging
concepts from quantum information and many-body physics, and offering
new tools to analyze regimes relevant for quantum simulation and quantum
advantage.<\/p>\n","protected":false},"excerpt":{"rendered":"
Understanding the computational complexity of quantum many-body statesis a central challenge at the interface of quantum information,condensed matter, and high-energy physics. While entanglement provides afundamental lens on many-body structure, it is now clear that it alonedoes not fully capture the resources underlying quantum advantage. Inparticular, broad classes of highly entangled states\u2014such as stabilizerstates and fermionic […]<\/p>\n","protected":false},"author":3246,"featured_media":0,"template":"","class_list":["post-2541","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/2541","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/3246"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=2541"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}