RESUMEN
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 k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed 'quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.
RESUMEN
In this paper, we analyze the construction of identification codes. Identification codes are based on the question: "Is the message I have just received the one I am interested in?", as opposed to Shannon's transmission, where the receiver is interested in not only one, but any, message. The advantage of identification is that it allows rates growing double exponentially in the blocklength at the cost of not being able to decode every message, which might be beneficial in certain applications. We focus on a special identification code construction based on two concatenated Reed-Solomon codes and have a closer look at its implementation, analyzing the trade-offs of identification with respect to transmission and the trade-offs introduced by the computational cost of identification codes.