Practical Quantum K-Means Clustering: Performance Analysis and Applications in Energy Grid Classification

In this work, we aim to solve a practical use-case of unsupervised clustering that has applications in predictive maintenance in the energy operations sector using quantum computers. Using only cloud access to quantum computers, we complete thorough performance analysis of what some current quantum computing systems are capable of for practical applications involving nontrivial mid-to-high-dimensional datasets. We first benchmark how well distance estimation can be performed using two different metrics based on the swap-test, using angle and amplitude data embedding. Next, for the clustering performance analysis, we generate sets of synthetic data with varying cluster variance and compare simulation to physical hardware results using the two metrics. From the results of this performance analysis, we propose a general, competitive, and parallelized version of quantum <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-means clustering to avoid some pitfalls discovered due to noisy hardware and apply the approach to a real energy grid clustering scenario. Using real-world German electricity grid data, we show that the new approach improves the balanced accuracy of the standard quantum <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-means clustering by 67.8&#x0025; with respect to the labeling of the classical algorithm.