Novel Enhanced Unsupervised Quantum Clustering Algorithm

Abstract

Every day, humans generate approximately 2.5 billion gigabytes of new data. While this data is crucial in applications such as drug development and cybersecurity, it is mostly unstructured and unlabeled which makes it difficult to process effectively. Businesses and governments alike solve this problem by using machine learning algorithms to characterize the data and make decisions with it. However, conventional machine learning processes consume excessive computational resources and time: one of the most prominent, K-means clustering, has an approximate time complexity of O(n^2), where n is the input data size. This quadratic time complexity causes scalability problems with large datasets. In this project, I have created an improved, more scalable clustering algorithm by leveraging quantum computation. The approach (new Q-means) involves an Angle Embedding Feature Map, an d-dimensional SWAP Test, and a dynamic, threshold distance-based termination criteria. After implementing this algorithm using the IBM Qiskit SDK, the new Q-means algorithm was run several times on different dimensional datasets. On an average, the new Q-means performed 18% better than the K-means algorithm based on the Adjusted Rand Index. In terms of the simulation execution time, the new Q-means was about six times faster than the existing Q-means due to a multi-threaded implementation and faster convergence. The time complexity of the new Q-means without a Quantum Random Access Memory (QRAM) is O(n^2). While the existing Q-means algorithm, which utilizes QRAM, has a time complexity of O(n(log n)^p), the time complexity of the new Q-means with QRAM is significantly better—O(n).