Comparison of C# and Qiskit Runtimes on K-Means Clustering

International literature suggests that quantum computers hold the potential for exponential speedup over classical computers, particularly for certain types of optimization problems. However, the practical application of quantum k-means is currently limited by the capabilities of available quantum hardware. As quantum technology improves and more efficient algorithms are developed, quantum k-means may offer advantages for larger datasets and high-dimensional data. This essay presents a comparative study of the k-means clustering algorithm implemented in two runtime environments, C# and Qiskit, with a focus on investigating the potential existence of quantum supremacy for a defined problem. The experiment involves randomly generated data and data tables of different sizes and dimensions. The classical approach utilizes a brute-force enumeration method, while the quantum approach employs a quadratic programming algorithm on a quantum computer using Qiskit. Results show that for small problem sizes, the classical brute-force approach exhibits superior runtime performance compared to the quantum approach. However, the study highlights the challenges in achieving quantum supremacy, as the performance of quantum computers is highly dependent on machine capabilities and qubit numbers.