用于零样本量子学习和贫瘠高原缓解的李代数子空间量化
Lie-Algebraic Subspace Quantization for Zero-Shot Quantum Learning and Barren-Plateau Mitigation
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中文总结 AI 辅助
研究针对贫瘠高原现象限制参数化量子电路可扩展性的问题，提出基于李代数子空间量化的分析框架，通过特定方法实现经典到量子参数转移及模型合并，实验验证了该方法在保真度和梯度分辨上的有效性。
中文摘要 AI 辅助
贫瘠高原现象严重限制了参数化量子电路（PQCs）的可扩展性。我们提出了一个用于零样本经典到量子参数转移和基于流形的模型合并的分析框架，无需量子端优化。我们的参数转移映射使用施蒂费尔子空间选择、最近酉极投影和对数生成器提取，将经典神经网络权重转换为低维量子演化。我们证明了一个子空间量化定理，通过几何截断和精确非酉性来界定重构误差，在近酉区域中后者变为二阶。以恒等为中心的架构自然地在恒等附近产生生成器，避免对数分支切割奇点并减轻初始化时的梯度集中。我们进一步推导了基于流形的模型合并的显式误差界，并表明相同的构造提供了一个热启动初始化，其活跃动力学仍局限于一个k维子空间。在IBM ibm_kobe上的实验表明，在k = 8时，赫林格保真度为0.987，而子空间梯度在高达128个物理量子比特时仍可分辨。
英文摘要
The barren plateau phenomenon severely limits the scalability of parameterized quantum circuits (PQCs). We present an analytical framework for zero-shot classical-to-quantum parameter transfer and manifold-based model merging without quantum-side optimization. Our parameter transfer map converts classical neural-network weights into low-dimensional quantum evolutions using Stiefel subspace selection, nearest-unitary polar projection, and logarithmic generator extraction. We prove a Subspace Quantization Theorem that bounds the reconstruction error by geometric truncation and exact non-unitarity, with the latter becoming second order in the near-unitary regime. Identity-centered architectures naturally produce generators near the identity, avoiding logarithm branch-cut singularities and mitigating initialization-time gradient concentration. We further derive an explicit error bound for manifold-based model merging and show that the same construction provides a warm-start initialization whose active dynamics remain confined to a k-dimensional subspace. Experiments on IBM ibm_kobe demonstrate Hellinger fidelity of 0.987 at k=8, while subspace gradients remain resolvable up to 128 physical qubits.
