傅里叶壁垒：为何公共表格数据集无法实现量子优势以及量子优势所在的经过验证的方法
The Fourier Wall: Why Public Tabular Datasets Refuse Quantum Advantage, and a Certified Recipe for Where It Lives
浏览论文内容
中文总结 AI 辅助
研究公共表格数据集中量子机器学习模型常输于经典基线的原因，提出傅里叶壁垒概念及SPECTRA两层证书方法，通过工业智能电表数据等验证，为表格数据中量子优势候选者的识别、设计和部署提供实用方法。
中文摘要 AI 辅助
在公共表格基准测试中，量子机器学习（QML）模型通常输给精心调优的经典基线。我们认为这是数据集的结构属性，而非当前模型的局限。由于角度编码量子神经网络是部分傅里叶级数，只有当目标频谱同时满足离格、相互作用阶至少为三、高频、由近乎独立的特征支持且密集到无法实际枚举时，才会产生真正的优势。我们将不满足这些条件称为傅里叶壁垒。我们将这些条件转化为SPECTRA，这是一种两层证书：无模拟器的结构筛选，然后使用配对自举置信界对匹配的量子模型和五个调优的经典孪生模型进行决定性比较。在工业智能电表数据上，SPECTRA正确拒绝了实际的峰值负荷目标，梯度提升树在该目标上的验证ROC-AUC达到0.999。在由相互作用量子过程生成标签的相同实际能量阶段，动力学匹配的量子模型达到0.994，而最佳通用经典基线为0.699，当其相互作用耦合被消除时则降至随机水平。精确的经典模拟器在小宽度时与量子模型相当，但评估成本呈指数级增长，估计硬件交叉点在13 - 19个位点附近。这些结果为在表格数据中识别、设计和部署量子优势候选者提供了实用方法。
英文摘要
Across public tabular benchmarks, quantum machine-learning (QML) models usually lose to carefully tuned classical baselines. We argue that this is a structural property of the datasets rather than merely a limitation of current models. Because an angle-encoded quantum neural network is a partial Fourier series, a genuine advantage can arise only when the target spectrum is simultaneously off-grid, of interaction order at least three, high-frequency, supported by near-independent features, and dense beyond practical enumeration. We call the failure to satisfy these conditions the Fourier wall. We operationalize the conditions as SPECTRA, a two-tier certificate: a simulator-free structural screen followed by a decisive comparison between a matched quantum model and five tuned classical twins using paired-bootstrap confidence bounds. On industrial smart-meter data, SPECTRA correctly refuses the real peak-load target, for which gradient-boosted trees reach a held-out ROC-AUC of 0.999. On the same real energy phases with labels generated by an interacting quantum process, the dynamics-matched quantum model reaches 0.994 versus 0.699 for the best generic classical baseline, and collapses to chance when its interaction couplings are ablated. An exact classical simulator ties the quantum model at small width but incurs measured exponential evaluation cost, with an estimated hardware crossover near 13-19 sites. These results provide a practical recipe for identifying, engineering, and deploying quantum-advantage candidates in tabular data.
