Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Implementation and Realisation of Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering

Alonso Viladomat Jasso
* ,
Ark Kumar Modi
* ,
Roberto Ferrara
ORCID logo ,
Janis Noetzel
,
Christian Deppe
ORCID logo ,
Maximilian Schädler
,
Fred Fung
Version 1 : Received: 1 May 2023 / Approved: 2 May 2023 / Online: 2 May 2023 (03:59:17 CEST)
Version 2 : Received: 3 August 2023 / Approved: 4 August 2023 / Online: 7 August 2023 (09:56:16 CEST)
Version 3 : Received: 15 September 2023 / Approved: 18 September 2023 / Online: 19 September 2023 (04:33:13 CEST)

A peer-reviewed article of this Preprint also exists.

Viladomat Jasso, A.; Modi, A.; Ferrara, R.; Deppe, C.; Nötzel, J.; Fung, F.; Schädler, M. Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering. Entropy 2023, 25, 1361. Viladomat Jasso, A.; Modi, A.; Ferrara, R.; Deppe, C.; Nötzel, J.; Fung, F.; Schädler, M. Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering. Entropy 2023, 25, 1361.

Abstract

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 stereographic quantum analogue 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 inverse stereographic projection.

Keywords

Quantum K-Means; Quantum Machine Learning; Quantum Computing; K-Means Clustering; 6G Communication; Quadrature Amplitude Modulation; Quantum-Classical Hybrid Algorithms; Quantum-Inspired Algorithms

Subject

Physical Sciences, Quantum Science and Technology

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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