提出可调训练性的量子电路结构，平衡计算复杂度与优化难度。
Stacking the Deck: Tunable Trainability in Stacked LCUs
- 用堆叠的酉矩阵组合设计可调节的变分电路
- 证明损失曲面方差下界为Ω(1/(nk³l))，模拟成本为O(k²ln³)
- 适合需要权衡硬件限制与优化性能的研究者使用
变分量子电路是近期量子计算应用的核心，但训练性与量子优势存在根本矛盾：表达能力强的电路易陷入平坦区，而能避免平坦区的结构往往可被经典算法高效模拟。本文提出堆叠线性酉组合（S-LCU）作为变分电路，可在平坦区与经典可模拟性之间实现可调平衡。通过图示分析，我们给出了自由费米子S-LCU的损失曲面方差边界，其元素为费米子高斯酉矩阵。证明方差下界为Ω(1/(nk³l))，经典模拟成本为O(k²ln³)，而量子门复杂度仅为O(lkn²)。层数l作为单一调控参数，可权衡计算复杂度与代价集中速率，为实际应用提供系统化构建方法。
原文摘要 · Abstract (English)
Variational quantum circuits have been central to many proposed near-term applications of quantum computing, but a growing body of evidence suggests that trainability and quantum advantage are fundamentally at odds: ansätze expressive enough to resist efficient classical simulation tend to exhibit barren plateaus, while structures that provably rule out barren plateaus typically render them classically simulable. We propose a stacked linear combination of unitaries (S-LCU) as a variational ansatz which provides a tunable trade-off between barren plateaus and classical simulability. Using a diagrammatic analysis, we bound the loss-landscape variance of the Free Fermion S-LCU, whose elements are fermionic Gaussian unitaries. We prove a variance lower bound of $Ω(1/(n k^{3l}))$, with a simulation cost of $O(k^{2l} n^3)$ using the best known classical algorithm, compared to a quantum gate complexity of only $O(lkn^2)$. The number of layers $l$ serves as a single dial that trades computational complexity against the rate of cost concentration. This offers practitioners a systematic method for constructing ansätze with a complexity-trainability trade-off that best suits their application and hardware.
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