Dequantizing quantum machine learning models using tensor networks

Abstract

Ascertaining whether a classical model can efficiently replace a given quantum model -- dequantization -- is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning~(VQML) models by employing the tensor network formalism, effectively identifying every VQML model as a subclass of matrix product state (MPS) model characterized by constrained coefficient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model's function class is dequantizable or not. Furthermore, we introduce an efficient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework.

arXiv comment15 + 14 pages, 8 + 9 figures

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• Potential and limitations of random Fourier features for dequantizing quantum machine learning
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• On the similarity of bandwidth-tuned quantum kernels and classical kernels
• Pitfalls when tackling the exponential concentration of parameterized quantum models
• A quantum eigenvalue solver based on tensor networks
• Adaptive Interpolating Quantum Transform: A Quantum-Native Framework for Efficient Transform Learning