量子增强最小二乘支持向量机：简化量子算法及稀疏解
Quantum-enhanced least-square support vector machine: simplified quantum algorithm and sparse solutions
摘要：
量子算法可以在不同方面增强机器学习。在这里，我们研究量子增强最小二乘支持向量机（LS-SVM）。首先，引入一种新的量子算法，使用连续变量来辅助矩阵求逆，以简化量子LS-SVM算法，同时保持指数加速。其次，我们提出了一个混合量子经典版本的稀疏解的LS-SVM。通过将一个大的数据集编码成一个量子态，可以使用量子矩阵工具箱提取一个小得多的转换后的数据集，这是在经典的SVM进一步处理。我们还将核方法结合到上述量子算法中，该算法使用量子比特的指数增长希尔伯特空间和量子特征映射的连续变量的无限维。量子LS-SVM利用量子特性来探索SVM的重要主题，如稀疏性和核方法，并强调其量子优势，从加速到解决经典困难机器学习任务的潜在能力。
英文摘要：
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.
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