将经典核方法与量子计算结合，实现高精度点分类。
Hybrid model of the kernel method for quantum computers
- 融合经典核方法与量子内积算法，构建混合学习模型。
- 在99%测试样本中准确判断点是否位于圆内。
- 适合量子机器学习初学者及跨学科研究者参考。
量子机器学习有望引领智能数据处理的革命。本文提出一种基于经典核方法的混合学习方法，并开发了用于连续值向量内积计算的量子算法。为适应量子处理器的希尔伯特空间限制，对经典核方法进行了必要改进。以有限正方形区域内随机生成的点是否位于内部圆内的分类任务为测试案例，结果显示算法在99%的样本中正确识别，仅因半径略大于理想值存在微小偏差。核方法成功实现分类，内积算法亦有效利用量子资源完成计算。本工作为物理学家与计算机科学家提供了可访问的新型量子机器学习模型。
原文摘要 · Abstract (English)
The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the development of a quantum algorithm for the calculation of internal products between vectors of continuous values. In order for this to be possible, it was necessary to make adaptations to the classic kernel method, since it is necessary to consider the limitations imposed by the Hilbert space of the quantum processor. As a test case, we applied this new algorithm to learn to classify whether new points generated randomly, in a finite square located under a plane, were found inside or outside a circle located inside this square. It was found that the algorithm was able to correctly detect new points in 99% of the samples tested, with a small difference due to considering the radius slightly larger than the ideal. However, the kernel method was able to perform classifications correctly, as well as the internal product algorithm successfully performed the internal product calculations using quantum resources. Thus, the present work represents a contribution to the area, proposing a new model of machine learning accessible to both physicists and computer scientists.
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