增强量子机器学习：非线性光学再生核的威力
Enhancing Quantum Machine Learning: The Power of Non-Linear Optical Reproducing Kernels
AI总结：
本研究提出基于Kerr相干态构建的新型量子核特征空间，可通过物理参数调控曲率，在含噪声数据集和硬件上表现出更优性能，为量子机器学习提供了灵活鲁棒的新方案。
摘要：
在众多量子机器学习算法中，量子核方法已成为研究焦点，这主要得益于其与含噪声中等规模量子器件的兼容性，以及实现量子优势的潜力。该方法通过将数据非线性变换到由量子态构建的特征空间中运行，可执行分类和回归任务。本研究提出了一种利用Kerr相干态构建的新型特征空间，Kerr相干态是su(2)、su(1,1)相干态以及压缩态的推广。值得注意的是，该特征空间具有常曲率，根据Kerr参数的符号不同，可呈现球面几何和双曲几何两种形态。尤为突出的是，与这些相干态相关的物理参数能够调控特征空间的曲率。本研究采用将数据编码到Kerr相干态的相位和振幅中所得到的Kerr核，分析了从Moon到乳腺癌诊断的各类数据集。研究结果表明，Kerr相干态具有鲁棒性，这源于其适配不同超参数的灵活性，因此在含噪声数据集和硬件配置中均能提供更优的性能。
英文摘要：
Amidst the array of quantum machine learning algorithms, the quantum kernel method has emerged as a focal point, primarily owing to its compatibility with noisy intermediate-scale quantum devices and its promise to achieve quantum advantage. This method operates by nonlinearly transforming data into feature space constructed with quantum states, enabling classification and regression tasks. In this study, we present a novel feature space constructed using Kerr coherent states, which generalize su(2), su(1, 1) coherent states, and squeezed states. Notably, the feature space exhibits constant curvature, comprising both spherical and hyperbolic geometries, depending on the sign of the Kerr parameter. Remarkably, the physical parameters associated with the coherent states, enable control over the curvature of the feature space. Our study employs Kerr kernels derived from encoding data into the phase and amplitude of Kerr coherent states. We analyze various datasets ranging from Moon to breast cancer diagnostics. Our findings demonstrate the robustness of Kerr coherent states, attributed to their flexibility in accommodating different hyperparameters, thereby offering superior performance across noisy datasets and hardware setups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
