Numerical evidence against advantage with quantum fidelity kernels on classical data

Abstract

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well-aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential "flattening" of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well-approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data.

References in corpus (27)

• Quantum Machine Learning
• Supervised learning with quantum enhanced feature spaces
• Barren plateaus in quantum neural network training landscapes
• Quantum machine learning in feature Hilbert spaces
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The power of quantum neural networks
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Power of data in quantum machine learning
• Challenges and Opportunities in Quantum Machine Learning
• Quantum advantage in learning from experiments
• A rigorous and robust quantum speed-up in supervised machine learning
• Generalization in quantum machine learning from few training data
• Average-case complexity versus approximate simulation of commuting quantum computations
• Quantum machine learning beyond kernel methods
• Group-Invariant Quantum Machine Learning
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Statistical Mechanics of Support Vector Networks
• Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks
• Generalizable control for quantum parameter estimation through reinforcement learning
• Statistical mechanics of complex neural systems and high dimensional data
• Importance of Kernel Bandwidth in Quantum Machine Learning
• The theory of the quantum kernel-based binary classifier
• Quantum Kernel Methods for Solving Differential Equations
• Quantum Phase Recognition via Quantum Kernel Methods

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