Viladomat Jasso Alonso, Modi Ark, Ferrara Roberto, Deppe Christian, Nötzel Janis, Fung Fred, Schädler Maximilian
Theoretical Quantum System Design Group, Chair of Theoretical Information Technology, Technical University of Munich, 80333 Munich, Germany.
Institute for Communications Engineering, TUM School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany.
Entropy (Basel). 2023 Sep 20;25(9):1361. doi: 10.3390/e25091361.
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 -means clustering promises a speed-up over the classical -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 -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.
最近邻聚类是一种简单却强大的机器学习算法，在经典光纤通信系统中的信号解码方面有着自然的应用。量子均值聚类有望比经典均值算法更快；然而，由于经典数据的嵌入会引入不准确性和速度减慢，目前已证明它在解码光纤信号时无法实现这种加速。尽管对于含噪声中等规模量子（NISQ）实现仍未实现指数级加速，但这项工作提出了广义逆立体投影，作为在k近邻聚类中用于量子距离估计的改进的布洛赫球嵌入方法，这使我们能够更接近经典性能。我们还使用广义逆立体投影来开发一种类似的经典聚类算法，并对其解码实际实验光纤通信数据的准确性、运行时间和收敛性进行基准测试。这种提出的“量子启发式”算法在准确性和收敛速度方面相对于均值算法都有改进。因此，这项工作有两个主要贡献。首先，我们提出将广义逆立体投影到布洛赫球作为量子机器学习算法的更好嵌入方法；在此，我们以聚类正交幅度调制光纤信号的问题为例。其次，作为受第一个贡献启发的纯经典贡献，我们提出并基准测试了使用广义逆立体投影和球心来聚类光纤信号，表明优化半径会在准确性和收敛速度方面带来持续改进。
