H-EFT-VA: An Effective-Field-Theory Variational Ansatz with Provable Barren Plateau Avoidance
This addresses a critical bottleneck for quantum computing researchers by providing a method to avoid barren plateaus while maintaining expressibility, though it is incremental as it builds on existing variational ansatz frameworks.
The paper tackled the Barren Plateau problem in Variational Quantum Algorithms by introducing the H-EFT-VA ansatz, which achieved a 109x improvement in energy convergence and a 10.7x increase in ground-state fidelity over standard methods in benchmarks.
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 $p < 10^{-88}$.