Pairwise classification using quantum support vector machine with Kronecker kernel
Pairwise classification using quantum support vector machine with Kronecker kernel
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DOI：
10.1007/s42484-022-00082-0
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发表时间：
2022-08
影响因子：
4.8
通讯作者：
Taisei Nohara;Satoshi Oyama;I. Noda
中科院分区：
文献类型：
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作者：
Taisei Nohara;Satoshi Oyama;I. Noda
我们研究了使用Kronecker核进行配对分类的量子计算的潜在应用，并设计了一种应用基于Harrow-Hassidim-Lloyd （HHL）的量子支持向量机算法的方法。两两分类可用于预测数据之间的关系，并用于诸如链接预测和化学相互作用预测等问题。然而，在使用Kronecker核的两两分类中，当数据量很大时，计算核矩阵的Kronecker积是非常昂贵的。我们发现核矩阵的Kronecker积在量子计算中可以比在经典计算中更有效地在时间和空间上表示。我们还发现，将基于hll的量子支持向量机算法应用于Kronecker核矩阵，可以有效地训练成对分类器。在量子计算模拟器上对经典算法与带有Kronecker内核的量子支持向量机进行了对比实验，在某些情况下，对于相同的两两分类问题，后者的误分类率与前者几乎相同。这表明采用Kronecker核算法的量子支持向量机可以更高效、更可扩展地达到与经典算法相当的精度。这一发现为应用量子机器学习来预测大规模数据中的关系铺平了道路。
We investigated the potential application of quantum computing using the Kronecker kernel to pairwise classification and have devised a way to apply the Harrow-Hassidim-Lloyd (HHL)-based quantum support vector machine algorithm. Pairwise classification can be used to predict relationships among data and is used for problems such as link prediction and chemical interaction prediction. However, in pairwise classification using a Kronecker kernel, it is very costly to calculate the Kronecker product of the kernel matrices when there is a large amount of data. We found that the Kronecker product of kernel matrices can be represented more efficiently in time and space in quantum computing than that in classical computing. We also found that a pairwise classifier can be effectively trained by applying the HHL-based quantum support vector machine algorithm to the Kronecker kernel matrix. In an experiment comparing a classical algorithm with a quantum support vector machine with a Kronecker kernel run on a quantum computing simulator, the misclassification rate of the latter was almost the same as that of the former for the same pairwise classification problem in some cases. This indicates that a quantum support vector machine with a Kronecker kernel algorithm can achieve accuracy equivalent to that of the classical algorithm more efficiently and scalably. This finding paves the way for applying quantum machine learning to predicting relationships in large-scale data.