Quantum spectral clustering: Comparing parameterized and neuromorphic quantum kernels

We compare a parameterized quantum kernel (pQK) with a quantum leaky integrate-and-fire (QLIF) neuromorphic computing approach that employs either the Victor–Purpura or van Rossum kernel in a spectral clustering task, as well as the classical radial basis function kernel. To our knowledge, this is the first study to employ quantum neuromorphic leaky integrate-and-fire neurons as kernel generators within a spectral clustering framework and to directly compare them against gate-based quantum fidelity kernels under identical conditions. Performance evaluation includes label-based classification and clustering metrics, as well as optimal number of clusters predictions for each dataset based on an elbow-like curve, as is typically used in K-means clustering. The pQK encodes feature vectors through angle encoding, with rotation angles scaled parametrically. Parameters are optimized through grid search to maximize kernel-target alignment, producing a kernel that reflects distances in the feature space. The quantum neuromorphic approach uses population coding to transform data into spike trains, which are then processed using temporal distance metrics. Kernel matrices are used as input into a classical spectral clustering pipeline prior to performance evaluation. For the synthetic datasets and Iris, the QLIF kernel typically achieves better classification and clustering performance than pQK. However, on higher-dimensional datasets, such as a preprocessed version of the Sloan Digital Sky Survey, pQK performed better, indicating better relative performance compared to QLIF in higher-dimensional regimes.