Quantum machine learning beyond kernel methods

Abstract

Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.

10+10 pages, 14 figures; significant changes in the main text, corrections in the numerical simulations

References in corpus (15)

• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• Variational Quantum Algorithms
• A Quantum Approximate Optimization Algorithm
• Noisy intermediate-scale quantum (NISQ) algorithms
• The effect of data encoding on the expressive power of variational quantum machine learning models
• A rigorous and robust quantum speed-up in supervised machine learning
• Information-theoretic bounds on quantum advantage in machine learning
• Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning
• Supervised quantum machine learning models are kernel methods
• Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces
• One qubit as a Universal Approximant
• Quantum machine learning of large datasets using randomized measurements
• Structural risk minimization for quantum linear classifiers
• The Inductive Bias of Quantum Kernels
• Encoding-dependent generalization bounds for parametrized quantum circuits

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