发表机构
Fraunhofer Institute for Applied and Integrated Security（弗劳恩霍夫应用与集成安全研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对常用全Gram核的局限，提出可训练的多类量子核方法McQuack，通过特定矩阵替换实现训练样本数量线性缩放，经模拟和硬件评估，性能良好，还研究了模型可训练性及参数初始化重要性。
AI 中文摘要
核方法是机器学习中的强大工具，但常用的全Gram核面临三个关键限制：与训练集大小呈二次缩放、使用固定的不可训练核以及缺乏多类分类的内在公式。我们提出了McQuack，一种用于多类问题的可训练量子核方法，在训练样本数量上实现线性缩放。通过用可训练的样本到（类质心）保真度矩阵替换全训练集Gram矩阵来实现。我们在模拟以及两个IBM设备的124个量子比特上对超过150个数据集进行评估。模拟中McQuack优于现有“纯”量子基线，硬件推理结果与RBF核性能相似。最后研究模型可训练性，在多达13个量子比特的实验中未发现贫瘠高原迹象，并强调参数初始化对成功优化的重要性。
英文摘要
Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification. We present McQuack, a trainable quantum kernel method for multiclass problems that achieves linear scaling in the number of training samples. This is accomplished by replacing the full training-set Gram matrix with a trainable sample-to-(class-centroid) fidelity matrix. We evaluate the model in simulation and on 124 qubits of two IBM devices, across more than 150 datasets. In simulation, McQuack outperforms existing "pure" quantum baselines, while results from hardware inference -- obtained without training -- achieve performance similar to an RBF kernel. Finally, we study the trainability of the model and observe no evidence of barren plateaus in our experiments with up to 13 qubits, and highlight the importance of parameter initialization for successful optimization.
