  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.
