Testing of Hybrid Quantum-Classical K-Means for Nonlinear Noise Mitigation

Nearest-neighbour clustering is a powerful set of heuristic algorithms that find natural application in the decoding of signals transmitted using the $M$-Quadrature Amplitude Modulation (M-QAM) protocol. Lloyd et al. proposed a quantum version of the algorithm that promised an exponential speed-up. We analyse the performance of this algorithm by simulating the use of a hybrid quantum-classical implementation of it upon 16-QAM and experimental 64-QAM data. We then benchmark the implementation against the classical k-means clustering algorithm. The choice of quantum encoding of the classical data plays a significant role in the performance, as it would for the hybrid quantum-classical implementation of any quantum machine learning algorithm. In this work, we use the popular angle embedding method for data embedding and the SWAP test for overlap estimation. The algorithm is emulated in software using Qiskit and tested on simulated and real-world experimental data. The discrepancy in accuracy from the perspective of the induced metric of the angle embedding method is discussed, and a thorough analysis regarding the angle embedding method in the context of distance estimation is provided. We detail an experimental optic fibre setup as well, from which we collect 64-QAM data. This is the dataset upon which the algorithms are benchmarked. Finally, some promising current and future directions for further research are discussed.