用于分类任务的基于三量子比特的神经量子核
Qutrit-Based Neural Quantum Kernels for Classification Tasks
AI总结：
研究聚焦三量子比特，将神经量子核扩展到量子位设置，系统研究关键设计选择。在四个基准数据集任务中，三量子比特NQKs大多优于QNN基线，能从增加特征和系统规模受益，酉表示影响性能，凸显基于量子位量子模型潜力。
AI中文摘要：
神经量子核（NQKs）通过预训练量子神经网络（QNN）构建量子核，并将训练后的电路用作任务适配嵌入。将此框架扩展到具有\(\mathrm{SU}(d)\)中局部酉矩阵的量子位，通过增加局部自由度提供了获得更丰富数据嵌入的自然途径，以及通过本质上的多能级量子系统进行多类分类的直接接口。在这项工作中，聚焦于三量子比特（\(d = 3\)），我们将NQKs扩展到量子位设置，并对关键设计选择进行了系统研究，包括编码特征数量、三量子比特数量、核构建（1对\(n\)和\(n\)对\(n\)）以及\(\mathrm{SU}(3)\)酉矩阵的参数化。在四个基准数据集上的二分类和三分类任务中，三量子比特NQKs在几乎所有考虑的设置下都优于相应的QNN基线，并且可以从增加特征预算和系统大小中受益，尽管这些增益的幅度可能会饱和，取决于数据集，并取决于所选的参数化。特别是，对\(\mathrm{SU}(3)\)参数化的消融表明，酉表示可以显著影响优化行为和分类器性能。这些发现突出了基于量子位的量子模型的潜力，不仅作为基于量子比特架构的直接推广，而且作为在量子机器学习中更好地利用复杂数据结构的有前途的手段。
英文摘要：
Neural quantum kernels (NQKs) construct quantum kernels by pretraining a quantum neural network (QNN) and subsequently reusing the trained circuit as a task-adapted embedding. Extending this framework to qudits, with local unitaries in $\mathrm{SU}(d)$, provides a natural route to richer data embeddings through the increased local degrees of freedom and a direct interface for multiclass classification via intrinsically multi-level quantum systems. In this work, focusing on qutrits ($d=3$), we extend NQKs to the qudit setting and perform a systematic study of key design choices, including the number of encoded features, the number of qutrits, the kernel construction (1-to-$n$ and $n$-to-$n$), and the parameterization of $\mathrm{SU}(3)$ unitaries. Across binary and three-class tasks on four benchmark datasets, qutrit NQKs improve over the corresponding QNN baselines in nearly all settings considered and can benefit from scaling both the feature budget and the system size, although the magnitude of these gains may saturate, is dataset-dependent, and depends on the chosen parameterization. In particular, an ablation over $\mathrm{SU}(3)$ parameterizations shows that the unitary representation can substantially impact both optimization behaviour and classifier performance. These findings highlight the potential of qudit-based quantum models not only as a straightforward generalization of qubit-based architectures, but also as a promising means to better exploit complex data structures in quantum machine learning.
