Scalable Tensor Network Simulation for Quantum-Classical Dual Kernel

TL;DR

This paper introduces a scalable tensor network framework for simulating quantum kernels, enabling evaluation of large quantum-classical dual kernels with up to 784 qubits, demonstrating improved classification performance and stability over classical and quantum kernels.

Contribution

The authors develop a scalable tensor network method for quantum kernel simulation, allowing large-scale evaluation of quantum-classical dual kernels and revealing their advantages in stability and performance.

Findings

Quantum-classical dual kernel outperforms single kernels in classification tasks.

Dual kernel remains stable as feature dimensionality increases.

Quantum contributions dominate at lower feature counts, classical at higher.

Abstract

This paper presents an efficient and scalable tensor network framework for quantum kernel circuit simulation, alleviating practical costs associated with increasing qubit counts and data size. The framework enables systematic large-scale evaluation of a linearly mixed quantum-classical dual kernel of up to 784 qubits. Using Fashion-MNIST, the classification performance of the test dataset is compared between a classical kernel, a quantum kernel, and the quantum-classical dual kernel across the feature dimensions from 2 to 784, with a one-to-one mapping between encoded features and qubits. Our result shows that the quantum-classical dual kernel consistently outperforms both single-kernel baselines, remains stable as the dimensionality increases, and mitigates the large-scale degradation observed in the quantum kernel. Analysis of the learned mixing weights indicates that quantum contributions dominate below 128 features, while classical contributions become increasingly important beyond 128, suggesting that the classical kernel provides a stabilizing anchor against concentration effects and hardware noise while preserving quantum gains at lower dimensions.