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Generalization in quantum machine learning from few training data.

Matthias C Caro1,2, Hsin-Yuan Huang3,4, M Cerezo5,6

  • 1Department of Mathematics, Technical University of Munich, Garching, Germany. caro@ma.tum.de.

Nature Communications
|August 22, 2022
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Summary
This summary is machine-generated.

Quantum machine learning (QML) models generalize well even with limited data. This study shows generalization error improves when fewer gates are optimized, speeding up quantum computing applications and enabling state classification with minimal training data.

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Area of Science:

  • Quantum Computing
  • Machine Learning
  • Artificial Intelligence

Background:

  • Modern quantum machine learning (QML) involves optimizing parameterized quantum circuits on training data for generalization.
  • Assessing QML generalization performance with limited training data is crucial for practical applications.

Purpose of the Study:

  • To comprehensively study the generalization performance of QML models trained on limited data.
  • To establish theoretical bounds on generalization error based on the number of trainable gates and optimized gates.
  • To explore the implications for quantum computing industry applications and state classification tasks.

Main Methods:

  • Theoretical analysis of generalization error scaling with the number of trainable gates (T).
  • Derivation of improved generalization error bounds when only a subset of gates (K << T) are significantly optimized.
  • Application of QML models to classify quantum states across a phase transition.

Main Results:

  • Generalization error in QML models with T trainable gates scales at worst as O(sqrt(T/N)).
  • When only K << T gates are substantially changed during optimization, generalization error improves to O(sqrt(K/N)).
  • Quantum convolutional neural networks require very small datasets for classifying quantum states across phase transitions.

Conclusions:

  • QML models can achieve good generalization performance even with a limited number of training data points (N).
  • The findings suggest significant speedups in compiling unitaries for the quantum computing industry.
  • The study injects optimism into QML by guaranteeing good generalization from few training data points.