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McQuack introduces a trainable quantum kernel method for multiclass classification that overcomes the quadratic scaling limits of traditional full-Gram matrices by utilizing sample-to-centroid fidelity. Evaluated on up to 124 qubits across IBM hardware and simulations, the approach demonstrates linear scalability and avoids barren plateaus in small-scale experiments without requiring training during inference. This work advances practical quantum machine learning architectures by integrating classical optimization techniques with quantum feature maps for specific classification tasks.
A Multiclass Quantum Aligned Centroid Kernel
arXiv:2607.19782v1 Announce Type: new 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.
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.
Quantum Physics (quant-ph); Machine Learning (cs.LG)
arXiv:2607.19782 [quant-ph]
(or arXiv:2607.19782v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.19782 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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