AI 中文总结
本研究提出干涉式量子多项式混沌展开生成模型，用于量热计簇射模拟，其表达能力随电路深度增长，训练后模型违反经典生成模型的贝尔界限，可消除光滑生成器的尾部相关性限制。
AI 中文摘要
我们提出了量子多项式混沌展开，这是一种生成式算法，其中单个量子电路即为整个模型，我们用它来学习量热计图像。在经典混沌展开中，随机性是输入，而系数是拟合对象；此处随机性仍然是唯一输入，它以旋转角的形式进入电路，并在每个量子模块中被重新加载，因此每个测量得到的可观测量都是潜在变量的混沌展开，其阶数等于电路深度，而需要拟合的是门本身。因此，表达能力随深度增长而非随经典系数增长，输出之间的相关性仅由纠缠门产生，所有量子比特读取的单个潜在量子比特承载着数据的集体模式。电路与样本之间没有任何拟合的中间环节，因此关闭纠缠门是模型本身的一种设置，且可证明会产生独立输出，将学习到的相关性归因于单个门的操作成为一种测量手段。逐次选择两种测量基矢将归因细化为认证，且训练后的模型违反了所有具有局域响应的经典生成模型（无论其规模如何）所遵守的贝尔界限。我们在Geant4簇射数据上训练该模型，在超导处理器上执行相同电路并预先预测其精度损失，证明了每个通过期望值读取的光滑生成器的尾部相关性存在一个不可能定理，并确定了可消除该限制的电路基本单元。
英文摘要
We present the quantum polynomial chaos expansion, a generative algorithm in which a single circuit is the entire model, and we use it to learn calorimeter images. In a classical chaos expansion the randomness is the input and the coefficients are fitted. Here the randomness is still the only input, entering the circuit as rotation angles and re-uploaded at every block, so that each measured observable is a chaos expansion of the latent variables whose order equals the circuit depth, and what is fitted are the gate angles themselves. Expressivity therefore grows with depth rather than with classical coefficients, correlations between outputs arise only from entangling gates, and a single latent wire read by all qubits carries the collective mode of the data. Nothing fitted stands between the circuit and the sample, so switching the entanglers off is a setting of the model itself and provably yields independent outputs, and attribution of the learned correlations to individual gates becomes a measurement. Choosing between two measurement bases shot by shot sharpens attribution into certification, and the trained model violates the Bell bound obeyed by every classical generative model with local response, whatever its size. We train the model on Geant4 shower data, execute the identical circuit on a superconducting processor with its accuracy loss predicted in advance, prove a no-go theorem for the tail dependence of every smooth generator read out through expectation values, and identify the circuit primitive that removes this limit.
