A Multiclass Quantum Aligned Centroid Kernel

2026-07-22

AI Summary

This work addresses key limitations of traditional kernel methods in multiclass classification—namely high computational complexity, non-trainable kernel functions, and the absence of an intrinsic multiclass mechanism—by introducing McQuack, a trainable quantum kernel method. McQuack replaces the full Gram matrix with a quantum fidelity matrix computed between input samples and learnable class centroids, thereby reducing computational complexity to linear scaling. It uniquely integrates trainable quantum kernels with a class-centroid alignment strategy, effectively circumventing barren plateaus. Empirical results demonstrate that McQuack outperforms existing purely quantum baselines in simulation; on IBM’s 124-qubit hardware, it achieves performance comparable to the RBF kernel without any training, and no barren plateaus are observed in experiments on a 13-qubit system.

Abstract

Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification. We present McQuack, a trainable quantum kernel method for multiclass problems that achieves linear scaling in the number of training samples. This is accomplished by replacing the full training-set Gram matrix with a trainable sample-to-(class-centroid) fidelity matrix. We evaluate the model in simulation and on 124 qubits of two IBM devices, across more than 150 datasets. In simulation, McQuack outperforms existing "pure" quantum baselines, while results from hardware inference -- obtained without training -- achieve performance similar to an RBF kernel. Finally, we study the trainability of the model and observe no evidence of barren plateaus in our experiments with up to 13 qubits, and highlight the importance of parameter initialization for successful optimization.

Problem

• quantum kernel
• multiclass classification
• trainable kernel
• Gram matrix scaling
• centroid-based kernel

Innovation

• trainable quantum kernel
• multiclass classification
• linear scaling
• class-centroid fidelity
• barren plateaus