提出可训练的量子核方法，实现多分类线性扩展，无需反向传播
A Multiclass Quantum Aligned Centroid Kernel
- 用样本到类别中心的保真度矩阵替代全量核矩阵
- 模拟与硬件实验均表现优于纯量子基线，124量子比特设备上接近RBF性能
- 无平坦山谷现象，初始化对优化成功至关重要
核方法在机器学习中功能强大，但常用全量核矩阵存在三大局限：(1) 训练集规模下呈二次增长；(2) 使用固定不可训练的核函数；(3) 缺乏内在的多分类形式。本文提出McQuack——一种可训练的量子核方法，用于多分类问题，实现训练样本数量上的线性扩展。通过将完整训练集核矩阵替换为可训练的样本-（类别中心）保真度矩阵实现此目标。我们在仿真环境及两台IBM设备（共124量子比特）上对模型进行了评估，覆盖超过150个数据集。仿真结果显示，McQuack优于现有“纯”量子基线；而硬件推理结果（未进行训练）性能接近径向基函数（RBF）核。最后，我们研究了模型可训练性，在最多13量子比特的实验中未发现平坦山谷现象，并强调参数初始化对优化成功的重要性。
原文摘要 · Abstract (English)
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.
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