量子特征工程何时能帮到线性分类器：基于IQP电路的信贷违约预测实证

My Analytical Process

Okay, here's how I'm thinking about this text. First, I need to get a handle on the domain. This looks like a blend of quantum computing and machine learning, specifically for financial modeling and credit default prediction. The tone is formal and academic. The task is clear: translate this simplified Chinese while maintaining the structure and avoiding any additional elements.

I'm tackling each sentence individually. My goal is accuracy and clarity. For each phrase, I'm considering the best Chinese equivalent, aiming for technical precision. I'm choosing between "信用违约预测" and "信用卡违约预测" – the former is more general, which fits the context best. For "IQP circuits," I'm using "瞬时量子多项式时间（IQP）电路", this seems the most accurate.

I'm paying close attention to technical terms like "feature budget," "financial exposure," and "Kernel PCA." It's critical to choose the most appropriate Chinese terms to maintain accuracy. The sentence about the quantum circuit's computational advantage is key. I'm focusing on the concepts of constant depth, Hilbert space encoding, and exponential scaling in classical simulation.

I'm reviewing the draft to ensure the translation is grammatically sound, technically precise, and reflects the academic tone of the original. I'm checking for fluidity and considering different word choices to improve readability. I've re-reviewed terms like "Benjamini-Hochberg correction" and "linear-expressivity mechanism" to make sure I'm using the most accurate terminology. I want to convey the meaning clearly.

The final translation should reflect an analysis of the text in my head. I'm essentially reading and translating the text in chunks, each one processed for meaning and accuracy, and I ensure that the translation makes sense.

信用违约预测是一个表格数据分类问题，其中F1分数的微小提升都能直接转化为金融风险敞口的降低。我们探究了在相同特征预算下，瞬时量子多项式时间（IQP）电路生成的特征能否使分类器的性能不仅超越其原始经典基线，还能超越最强的无监督经典非线性替代方案——核主成分分析（Kernel PCA）。该数据集为每位客户提供了23个财务属性；针对一个n量子比特电路，我们从中选取n个属性，将每个属性编码为一个旋转角，并读出2n个期望值作为新特征。采用量子电路的动机源于计算优势：n量子比特IQP电路以常数深度运行，并在2^n维希尔伯特空间中对特征相关性进行编码，而对其精确输出统计量的经典模拟计算量随n呈指数级增长。基于UCI信用卡客户违约数据集和五折交叉验证，我们发现向逻辑回归模型中添加16个IQP特征（n = 8个量子比特），可将F1分数从0.462提升至0.517（+0.055，p < 0.0001）。表现次优的方法Kernel PCA在相同特征数下仅达到0.493；在经受跨12项检验的Benjamini-Hochberg校正后，该差距依然显著（p = 0.00007）。其他分类器——随机森林、SVM、XGBoost或k-NN——均未获益，这表明其机制在于线性表达能力的提升，而非普适性的改进。我们还表明，这8个输入特征的选取方式至关重要：基于随机森林重要性指导的选择可使F1达到0.523，而编码最大互不相关的特征则使F1降至0.496，这证明量子电路的作用在于放大已有的信息结构，而非凭空创造结构。