Non-stabilizerness and entanglement in (2 + 1)-dimensional SU(2) lattice gauge theory using tensor networks

This study investigates the quantum resources required to simulate (2+1)-dimensional SU(2) Hamiltonian lattice gauge theory. As quantum field theories are fundamental to nature, understanding the cost of their simulation on quantum hardware is a central challenge. The authors focus on non-stabilizerness, or magic—a quantum resource distinct from entanglement that quantifies the difficulty of classically simulating a quantum state. Using a dressed-site formulation with a hardcore-gluon truncation, the researchers employ matrix product states (MPS) to compute three facets of magic: the full stabilizer Rényi entropy (SRE), the non-local SRE, and a lower bound derived from the anti-flatness of the entanglement spectrum.

The paper establishes a stronger version of the sandwich relation for non-local magic, providing a rigorous lower bound based on the entanglement spectrum's anti-flatness. A primary contribution is the demonstration that non-local magic is an intrinsic property of the bipartition, invariant under site-local re-encodings that typically plague the full SRE. By simulating lattices up to 6x6, the authors show that non-local magic acts as a sharper, more bond-dimension-friendly probe of the gauge-matter delocalization crossover (occurring at g^2 ~ 1) than standard entanglement entropy or the full SRE. This allows researchers to identify critical physical transitions even when the underlying MPS ground state has not yet fully converged.

This work bridges the gap between quantum information theory and non-perturbative lattice gauge theory. By identifying non-local magic as a physically preferred diagnostic, the authors provide a practical tool for researchers to characterize the complexity of gauge theories. The findings suggest that the computational cost of simulating these theories is tied to the growth of magic, reinforcing the necessity of developing fault-tolerant quantum algorithms that can handle high-magic states as we approach the continuum limit.