dorsal/arxiv
View SchemaH-EFT-VA: An Effective-Field-Theory Variational Ansatz with Provable Barren Plateau Avoidance
| Authors | Eyad I. B Hamid |
|---|---|
| Categories | |
| ArXiv ID | 2601.10479vv1 |
| URL | https://arxiv.org/abs/2601.10479 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
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: $Var[\partial \theta] \in \Omega(1/poly(N))$. 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 $p < 10^{-88}$.
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"abstract": "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\u0027s 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: $Var[\\partial \\theta] \\in \\Omega(1/poly(N))$. 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 $p \u003c 10^{-88}$.",
"arxiv_id": "2601.10479",
"authors": [
"Eyad I. B Hamid"
],
"categories": [
"quant-ph",
"cs.LG",
"math-ph",
"math.MP"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "H-EFT-VA: An Effective-Field-Theory Variational Ansatz with Provable Barren Plateau Avoidance",
"url": "https://arxiv.org/abs/2601.10479",
"version": "v1"
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