One of the fastest growing areas of interest in quantum computing is its use within machine learning methods, in particular through the application of quantum kernels. Despite this large interest, there exist very few proposals for relevant physical platforms to evaluate quantum kernels. In this article, we propose and simulate a protocol capable of evaluating quantum kernels using Hong–Ou–Mandel interference, an experimental technique that is widely accessible to optics researchers. Our proposal utilises the orthogonal temporal modes of a single photon, allowing one to encode multi-dimensional feature vectors. As a result, interfering two photons and using the detected coincidence counts, we can perform a direct measurement and binary classification. This physical platform confers an exponential quantum advantage also described theoretically in other works. We present a complete description of this method and perform a numerical experiment to demonstrate a sample application for binary classification of classical data.

中文翻译：

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通过 Hong-Ou-Mandel 干涉进行量子核评估


量子计算增长最快的领域之一是其在机器学习方法中的应用，特别是通过量子内核的应用。尽管人们对此兴趣浓厚，但评估量子内核的相关物理平台的提案却很少。在本文中，我们提出并模拟了一种能够使用红欧曼德尔干涉评估量子内核的协议，这是一种光学研究人员广泛使用的实验技术。我们的建议利用单个光子的正交时间模式，允许对多维特征向量进行编码。因此，通过干扰两个光子并使用检测到的重合计数，我们可以执行直接测量和二元分类。该物理平台具有指数量子优势，这在其他著作中也得到了理论上的描述。我们对该方法进行了完整的描述，并进行了数值实验来演示经典数据二元分类的示例应用程序。