Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical fibre communication systems. Quantum nearest-neighbour clustering promises a speed-up over the classical algorithms, but the current embedding of classical data introduces inaccuracies, insurmountable slowdowns, or undesired effects. This work proposes the generalised inverse stereographic projection into the Bloch sphere as an encoding for quantum distance estimation in k nearest-neighbour clustering, develops an analogous classical counterpart, and benchmarks its accuracy, runtime and convergence. Our proposed algorithm provides an improvement in both the accuracy and the convergence rate of the algorithm. We detail an experimental optic fibre setup as well, from which we collect 64-Quadrature Amplitude Modulation data. This is the dataset upon which the algorithms are benchmarked. Through experiments, we demonstrate the numerous benefits and practicality of using the `quantum-inspired' stereographic k nearest-neighbour for clustering real-world optical-fibre data. This work also proves that one can achieve a greater advantage by optimising the radius of the inverse stereographic projection.