提出新型量子电路架构，有效避免梯度消失，提升量子算法收敛速度
H-EFT-VA: An Effective-Field-Theory Variational Ansatz with Provable Barren Plateau Avoidance
- 基于有效场论设计分层电路结构，通过初始化控制状态空间探索范围
- 理论证明梯度方差下限为反多项式，实测能量收敛快109倍、保真度高10.7倍
- 适合中等参考态重叠的哈密顿量，可扩展至更复杂系统
变分量子算法受梯度消失（巴伦平原）现象严重威胁。本文提出受有效场论启发的H-EFT变分方案（H-EFT-VA），通过初始化施加层级“紫外截断”，理论上限制电路状态探索范围，防止近似酉2-设计形成。我们严格证明该局域化保证梯度方差下限为反多项式：$Var[ heta] otin Ω(1/poly(N))$。关键在于，与通过限制纠缠避免巴伦平原的方法不同，本方法保持体积律纠缠和接近哈尔纯度，确保对复杂量子态的充分表达能力。在横场伊辛模型上进行16组基准测试，相比标准硬件高效变分线路（HEA），能量收敛速度提升109倍，基态保真度提高10.7倍，统计显著性达 $p < 10^{-88}$。静态框架适用于参考态重叠适中的哈密顿量；针对更大参考态差距的系统，动态紫外截断松弛策略已在后续工作中探讨。
原文摘要 · Abstract (English)
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: $Var[\partialθ] \in Ω(1/poly(N))$. 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 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.
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