量子去噪器中的奇偶基底：固定映射去噪网络的闭式基准
Parity Floors in Quantum Denoisers: A Closed-Form Benchmark for Fixed-Map Denoising Networks
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中文总结 AI 辅助
该研究提出CoupledPhaseTexture基准，证明深度1的RY+CNOT+Pauli-Z去噪网络存在奇偶基底，揭示奇偶性是限制固定量子特征映射去噪器性能的关键结构约束。
中文摘要 AI 辅助
固定量子特征映射正被越来越多地引入扩散去噪器，但标准图像基准无法揭示哪种结构约束限制了它们。我们提出CoupledPhaseTexture，这是一个具有解析热核噪声化的环面扩散基准，可分离奇偶性、扇区内近似和样本复杂度限制。对于深度为1的RY+CNOT+Pauli-Z家族，我们证明了无包含关系的奇偶基底：所有可达特征都是编码角度的偶函数，而贝叶斯去噪器的正弦分量是奇函数，因此超额风险恰好分为不可访问的奇数部分和扇区内残差。第一项是针对每个偶特征类的不可约的、噪声尺度解析的下界，对特征类无包含、线性或闭性假设。该障碍是噪声条件去噪目标的属性，而非静态可表示性：由于目标的奇偶性内容随噪声变化，奇偶基底在每个噪声尺度上被重新推导。在两种不同先验上，测量的超额主要由奇偶代理主导。高阶Z读出改善了偶扇区，但纠缠不会降低基底，重上传也无法可靠地消除它。经典控制证实缺陷是奇偶性而非量子性：仅余弦库会出现类似的基底，而添加正弦扇区则匹配参考。在测试的结构中，奇数读出和噪声耦合编码器无法匹配带正弦的经典库。这些结果为无需高效经典替代物的非经典数据访问或特征类提供了动机；它们并未确立任何一种足以实现量子优势。
英文摘要
Fixed quantum feature maps are increasingly inserted into diffusion denoisers, but standard image benchmarks do not reveal which structural constraint limits them. We introduce CoupledPhaseTexture, a torus-diffusion benchmark with analytic heat-kernel noising that separates parity, within-sector approximation, and sample-complexity limitations. For the depth-1 RY+CNOT+Pauli-Z family we prove a containment-free parity floor: all reachable features are even functions of the encoded angles while the sine components of the Bayes denoiser are odd, so the excess risk splits exactly into an inaccessible odd part and a within-sector residual. The first term is an irreducible, noise-scale-resolved lower bound holding for every even feature class, with no containment, linearity, or closedness assumption on the feature class. The obstruction is a property of the noise-conditioned denoising target rather than static representability: the floor is re-derived at each noise scale because the target's parity content changes with noise. The measured excess is dominated by the parity proxy on two distinct priors. Higher-order Z readouts improve the even sector, but entanglement does not lower the floor and re-uploading does not reliably close it. Classical controls confirm the deficit is parity rather than quantumness: a cosine-only bank is floored similarly, while adding the sine sector matches the reference. Among tested constructions, odd readouts and a noise-coupled encoder do not match the sine-carrying classical bank. These results motivate nonclassical data access or feature classes without efficient classical surrogates; they do not establish either as sufficient for quantum advantage.
