发表机构
Rice University; Ken Kennedy Institute at Rice University（莱斯大学; 莱斯大学肯·肯尼迪研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究变分量子算法训练问题，提出恒等配对渐进深度训练方法，通过添加特定块对解决初始化冲击，证明可达集饱和定理，实现可训练性超越可表达性，降低总门成本。
AI 中文摘要
变分量子算法（VQAs）是近期量子计算的主导范式，但其训练对电路深度、初始化和诸如贫瘠高原等景观病态敏感。我们研究了渐进深度训练（PDT），它是一种分层课程，在添加新层之前先训练浅电路，并识别出一个基本障碍：硬件高效量子近似中的固定纠缠门（CNOT）会导致初始化冲击，即添加新层时的能量尖峰。我们提出了恒等配对渐进深度训练（IP - PDT），它添加正向/反向块对，每个块对由一个标准旋转 + CNOT块及其反向组成，在初始化时组合为恒等。由于相邻的CNOT环抵消，有效电路仅保留由过参数化局部旋转包围的单个纠缠层。我们证明了一个简单的可达集饱和定理：在这种构造下，变分流形仅在首次引入后纠缠器旋转时精确扩展一次然后饱和；所有后续深度增加仅提供单量子比特酉的纯过参数化。尽管有这种饱和，旋转参数的渐进添加仍可继续改善优化结果——我们称之为可训练性超越可表达性。我们将IP - PDT形式化为嵌套流形上的连续方法，在接受规则下证明单调能量保证，并通过谱隙不等式将能量误差与基态保真度联系起来。详细的资源分析表明，IP - PDT通过消除大多数CNOT门，实现了比两个基线更低的总门成本。
英文摘要
Variational Quantum Algorithms (VQAs) are a leading paradigm for near-term quantum computing, yet their training suffers from sensitivity to circuit depth, initialization, and landscape pathologies such as barren plateaus. We study \emph{progressive depth training} (PDT) -- a layerwise curriculum that trains a shallow circuit before appending new layers -- and identify a fundamental obstacle: fixed entangling gates (CNOTs) in hardware-efficient ansätze cause \emph{initialization shock}, an energy spike when new layers are added. We propose \emph{identity-paired progressive depth training} (IP-PDT), which appends forward/inverse block pairs -- each consisting of a standard rotation$+$CNOT block followed by its reverse -- that compose to the identity at initialization. Because the adjacent CNOT rings cancel, the effective circuit retains only \textit{a single entangling layer} surrounded by \textit{overparameterized local rotations}. We prove a simple \textit{Reachable Set Saturation Theorem}: under this construction the variational manifold expands exactly once (when post-entangler rotations are first introduced) and then \emph{saturates}; all subsequent depth increases provide pure overparameterization of single-qubit unitaries. Despite this saturation, progressive addition of rotation parameters can continue to improve optimization outcomes -- a phenomenon we term \emph{trainability beyond expressibility}. We formalize IP-PDT as a continuation method on nested manifolds, prove monotone energy guarantees under an acceptance rule, and connect energy error to ground-state fidelity through spectral-gap inequalities. A detailed resource analysis shows that IP-PDT achieves lower total gate cost than both baselines by eliminating most CNOT gates.
Comments49 pages
