Quantum Spectral Clustering: Comparing Parameterized and Neuromorphic Quantum Kernels

TL;DR

This paper compares quantum spectral clustering methods, including parameterized quantum kernels and neuromorphic quantum kernels, with classical kernels across various datasets, highlighting their relative performance in different regimes.

Contribution

It introduces a comparative analysis of quantum and neuromorphic kernels in spectral clustering, emphasizing their performance differences on datasets of varying dimensionality.

Findings

QLIF kernel outperforms pQK on small datasets like Iris.

pQK performs better on higher-dimensional datasets like SDSS.

Quantum kernels show potential advantages in high-dimensional regimes.

Abstract

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 (RBF) kernel. 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 \texttt{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 (\texttt{SDSS}), pQK performed better, indicating a possible advantage in higher-dimensional regimes.