Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing

Adiabatic quantum computing (AQC) is a promising quantum computing approach for discrete and often NP-hard optimization problems. Current AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for many machine learning and computer vision tasks. Despite requiring multiple measurements from the noisy AQC, current approaches only utilize the best measurement, discarding information contained in the remaining ones. In this work, we explore the potential of using this information for probabilistic balanced k-means clustering. Instead of discarding non-optimal solutions, we propose to use them to compute calibrated posterior probabilities with little additional compute cost. This allows us to identify ambiguous solutions and data points, which we demonstrate on a D-Wave AQC on synthetic and real data.