Machine learning and quantum computing are two technologies that are causing a paradigm shift in the performance and behavior of certain algorithms, achieving previously unattainable results. Machine learning (kernel classification) has become ubiquitous as the forefront method for pattern recognition and has been shown to have numerous societal applications. While not yet fault-tolerant, Quantum computing is an entirely new method of computation due to its exploitation of quantum phenomena such as superposition and entanglement. While current machine learning classifiers like the Support Vector Machine are seeing gradual improvements in performance, there are still severe limitations on the efficiency and scalability of such algorithms due to a limited feature space which makes the kernel functions computationally expensive to estimate. By integrating quantum circuits into traditional ML, we may solve this problem through the use of quantum feature space, a technique that improves existing Machine Learning algorithms through the use of parallelization and the reduction of the storage space from exponential to linear. This research expands on this concept of the Hilbert space and applies it for classical machine learning by implementing the quantum-enhanced version of the K nearest neighbors algorithm. This paper first understands the mathematical intuition for the implementation of quantum feature space and successfully simulates quantum properties and algorithms like Fidelity and Grover's Algorithm via the Qiskit python library and the IBM Quantum Experience platform. The primary experiment of this research is to build a noisy variational quantum circuit KNN (QKNN) which mimics the classification methods of a traditional KNN classifier. The QKNN utilizes the distance metric of Hamming Distance and is able to outperform the existing KNN on a 10-dimensional Breast Cancer dataset.

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QEML（量子增强机器学习）：使用量子计算来增强 ML 分类器和特征空间

机器学习和量子计算这两种技术正在导致某些算法的性能和行为发生范式转变，从而实现以前无法实现的结果。机器学习（内核分类）作为模式识别的前沿方法已经无处不在，并已被证明具有众多社会应用。虽然还不是容错的，但量子计算是一种全新的计算方法，因为它利用了叠加和纠缠等量子现象。虽然当前的机器学习分类器（如支持向量机）的性能正在逐步提高，但由于特征空间有限，使得估计核函数的计算成本很高，因此此类算法的效率和可扩展性仍然存在严重限制。通过将量子电路集成到传统机器学习中，我们可以通过使用量子特征空间来解决这个问题，这是一种通过使用并行化和将存储空间从指数减少到线性来改进现有机器学习算法的技术。这项研究扩展了希尔伯特空间的这一概念，并通过实现 K 最近邻算法的量子增强版本将其应用于经典机器学习。本文首先了解了实现量子特征空间的数学直觉，并通过Qiskit python库和IBM Quantum Experience平台成功模拟了Fidelity和Grover's Algorithm等量子特性和算法。本研究的主要实验是建立一个噪声变分量子电路 KNN（QKNN），它模仿传统 KNN 分类器的分类方法。QKNN 利用汉明距离的距离度量，能够在 10 维乳腺癌数据集上优于现有的 KNN。