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Ark Modi, Alonso Viladomat Jasso, Roberto Ferrara, Christian Deppe, Janis Noetzel, Fred Fung, Maximilian Schaedler

In the context of optical signal processing, quantum and quantum-inspired machine learning algorithms have massive potential for deployment. One of the applications is in error correction protocols for the received noisy signals. In some scenarios, non-linear and unknown errors can lead to noise that bypasses linear error correction protocols that optical receivers generally implement. In those cases, machine learning techniques are used to recover the transmitted signal from the received signal through various estimation procedures. Since quantum machine learning algorithms promise advantage over classical algorithms, we expect that optical signal processing can benefit from these advantages. In this review, we survey several proposed quantum and quantum-inspired machine learning algorithms and their applicability with current technology to optical signal processing.

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Ark Modi, Alonso Viladomat Jasso, Roberto Ferrara, Christian Deppe, Janis Noetzel, Fred Fung, Maximilian Schaedler

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.

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Alonso Viladomat Jasso, Ark Modi, Roberto Ferrara, Christian Deppe, Janis Noetzel, Fred Fung, Maximilian Schaedler

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.

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