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 on the Transverse Field Ising Model confirms a 109x improvement in energy convergence and a 10.7x increase in ground-state fidelity over standard Hardware-Efficient Ansätze (HEA), with statistical significance of $p < 10^{-88}$. The static framework is most effective for Hamiltonians with moderate reference-state overlap; extension to systems with larger reference-state gaps is addressed through dynamic UV-cutoff relaxation strategies explored in concurrent work.
| Comments: | v2: Expanded Section III with explicit circuit architecture description. Added Section IV.F to discuss static initialization limitations and reference-state dependence. Abstract and conclusion updated to scope TFIM results and cite concurrent work on dynamic extensions. 8 pages, 5 figures, Appendix |
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG); Mathematical Physics (math-ph) |
| Cite as: | arXiv:2601.10479 [quant-ph] |
| (or arXiv:2601.10479v2 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2601.10479 arXiv-issued DOI via DataCite |
From: Eyad Hamid [view email]
[v1]
Thu, 15 Jan 2026 15:01:16 UTC (343 KB)
[v2]
Thu, 23 Apr 2026 07:28:02 UTC (352 KB)
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