发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究变分量子电路中训练性与量子优势的冲突问题，提出堆叠线性组合酉门（S-LCU）变分量子线路，通过图形分析界定其损失景观方差，证明方差下界，层数l可权衡计算复杂度与成本集中率，为构建合适量子线路提供系统方法。
AI 中文摘要
变分量子电路在许多量子计算近期应用中处于核心地位，但越来越多证据表明训练性和量子优势从根本上存在冲突：表达能力足以抵抗高效经典模拟的量子线路往往呈现贫瘠高原现象，而能排除贫瘠高原的结构通常可经典模拟。我们提出堆叠线性组合酉门（S-LCU）作为变分量子线路，在贫瘠高原和经典可模拟性之间提供可调权衡。通过图形分析，我们界定了自由费米子S-LCU的损失景观方差，其元素为费米高斯酉门。我们证明方差下界为Ω(1/(nk³ᵏ))，使用最佳经典算法模拟成本为O(k²ᵏn³)，而量子门复杂度仅为O(lkn²)。层数l作为一个调节旋钮，可在计算复杂度和成本集中率之间进行权衡。这为从业者提供了一种系统方法，用于构建最适合其应用和硬件的具有复杂度-训练性权衡的量子线路。
英文摘要
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.
Comments19 pages
