Abstract Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining exponential speed-up. Secondly, we propose a hybrid quantum-classical version for sparse solutions of LS-SVM. By encoding a large dataset into a quantum state, a much smaller transformed dataset can be extracted using quantum matrix toolbox, which is further processed in classical SVM. We also incorporate kernel methods into the above quantum algorithms, which uses both exponential growth Hilbert space of qubits and infinite dimensionality of continuous variable for quantum feature maps. The quantum LS-SVM exploits quantum properties to explore important themes for SVM such as sparsity and kernel methods, and stresses its quantum advantages ranging from speed-up to the potential capacity to solve classically difficult machine learning tasks.

中文翻译：

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量子增强最小二乘支持向量机：简化的量子算法和稀疏解

摘要 量子算法可以在不同方面增强机器学习。在这里，我们研究了量子增强最小二乘支持向量机 (LS-SVM)。首先，引入了一种使用连续变量辅助矩阵求逆的新型量子算法，以简化量子LS-SVM算法，同时保持指数加速。其次，我们为 LS-SVM 的稀疏解提出了一个混合量子经典版本。通过将大型数据集编码为量子态，可以使用量子矩阵工具箱提取更小的转换数据集，并在经典 SVM 中进一步处理。我们还将核方法结合到上述量子算法中，该算法使用量子位的指数增长希尔伯特空间和连续变量的无限维数来进行量子特征映射。