Speaker
Description
Classical simulations play a central role in many-body quantum physics, from lattice gauge theories to strongly correlated systems, yet their computational cost varies dramatically across different regimes. In this talk, I will discuss how the complexity of simulating quantum many-body systems can be understood in terms of physical resources carried by quantum states.
I will first review tensor network methods, focusing on matrix product states, and explain how entanglement entropy—via area laws—controls their efficiency in one dimension. I will then argue why entanglement alone is not sufficient to characterize classical simulability, highlighting the special role of stabilizer states and introducing stabilizer Rényi entropy as a measure of non-Clifford complexity.
Finally, I will present recent results on fermionic many-body systems, where highly entangled Gaussian states remain efficiently simulable. I will show how fermionic non-Gaussianity, quantified by fermionic antiflatness, emerges as a key resource governing the classical complexity of fermionic simulations.