Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.

内核方法在机器学习中具有广泛的应用。最近，量子计算与内核理论之间的联系已经正式建立，这为量子技术提供了机会，以增强各种现有的机器学习方法。我们提出了一种基于距离的量子分类器，其分类器基于训练和测试数据之间的量子状态保真度。可以使用量子电路系统地定制量子内核，以将内核提升到任意幂并为每个训练数据分配任意权重。在给定特定输入状态的情况下，我们的协议通过交换测试电路并随后进行两个单量子位测量，计算量子并行中量子数据保真度的加权功率总和，而与数据数量无关，仅需要恒定的重复次数即可。我们还表明，我们的分类器等效于测量Helstrom算子的期望值，从中可以得出众所周知的最佳量子态判别。我们通过经典模拟，逼真的噪声模型和使用IBM量子云平台的原理验证实验，证明了分类器的性能。