H-EFT-VA: An Effective-Field-Theory Variational Ansatz with Provable Barren Plateau Avoidance

Variational Quantum Algorithms (VQAs) are critically threatened by the Barren Plateau (BP) phenomenon. In this work, we introduce the H-EFT Variational Ansatz (H-EFT-VA), an architecture inspired by Effective Field Theory (EFT). By enforcing a hierarchical "UV-cutoff" on initialization, we theoretically restrict the circuit's state exploration, preventing the formation of approximate unitary 2-designs. We provide a rigorous proof that this localization guarantees an inverse-polynomial lower bound on the gradient variance: $Var[\partial θ] \in Ω(1/poly(N))$. Crucially, unlike approaches that avoid BPs by limiting entanglement, we demonstrate that H-EFT-VA maintains volume-law entanglement and near-Haar purity, ensuring sufficient expressibility for complex quantum states. Extensive benchmarking across 16 experiments -- including Transverse Field Ising and Heisenberg XXZ models -- confirms a 109x improvement in energy convergence and a 10.7x increase in ground-state fidelity over standard Hardware-Efficient Ansatze (HEA), with a statistical significance of $p < 10^{-88}$.