Quantum SVM的实际应用改进：从理论到实践
Practical application improvement to Quantum SVM: theory to practice
摘要：
量子机器学习（QML）已经成为量子应用的一个重要领域，尽管有用的QML应用需要许多量子位。因此，我们的论文的目的是探索量子支持向量机（QSVM）算法的成功应用，同时平衡噪声中间尺度量子（NISQ）假设下的几个实际和技术考虑。对于NISQ下的量子支持向量机，我们使用量子特征映射将数据转换为量子态，并从这些量子态中构造支持向量机核，并与经典的径向基函数（RBF）核支持向量机进行了比较。由于数据集在某种意义上更加复杂或抽象，与QSVM相比，使用典型经典核的经典SVM导致精度较低，因为使用典型经典核的经典SVM不能容易地分离不同类别的数据。类似地，QSVM应该能够在更广泛的数据集上提供有竞争力的性能，包括“更简单”的数据情况，其中需要更平滑的决策边界以避免任何模型方差问题（即，过拟合）。为了弥合“经典外观”决策边界和复杂的量子决策边界之间的差距，我们建议利用一般的浅幺正变换来创建具有旋转因子的特征映射，以定义可调的量子核，并添加正则化来平滑分离超平面模型。我们在实验中表明，这使得QSVM的性能等同于SVM，无论数据集的复杂性如何，并且在一些常用的参考数据集上表现出色。
英文摘要：
Quantum machine learning (QML) has emerged as an important area for Quantum applications, although useful QML applications would require many qubits. Therefore our paper is aimed at exploring the successful application of the Quantum Support Vector Machine (QSVM) algorithm while balancing several practical and technical considerations under the Noisy Intermediate-Scale Quantum (NISQ) assumption. For the quantum SVM under NISQ, we use quantum feature maps to translate data into quantum states and build the SVM kernel out of these quantum states, and further compare with classical SVM with radial basis function (RBF) kernels. As data sets are more complex or abstracted in some sense, classical SVM with classical kernels leads to less accuracy compared to QSVM, as classical SVM with typical classical kernels cannot easily separate different class data. Similarly, QSVM should be able to provide competitive performance over a broader range of data sets including ``simpler'' data cases in which smoother decision boundaries are required to avoid any model variance issues (i.e., overfitting). To bridge the gap between ``classical-looking'' decision boundaries and complex quantum decision boundaries, we propose to utilize general shallow unitary transformations to create feature maps with rotation factors to define a tunable quantum kernel, and added regularization to smooth the separating hyperplane model. We show in experiments that this allows QSVM to perform equally to SVM regardless of the complexity of the data sets and outperform in some commonly used reference data sets.
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。
