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An efficient geometric approach to quantum-inspired classifications.

Roberto Leporini1, Davide Pastorello2

  • 1Department of Economics, University of Bergamo, via dei Caniana 2, 24127, Bergamo, Italy. roberto.leporini@unibg.it.

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This summary is machine-generated.

This study introduces a geometric approach to enhance quantum-inspired classification, improving efficiency in space and time for quantum encoding. It enables accurate classifier comparison for multiple quantum state preparations.

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Area of Science:

  • Quantum Information Science
  • Machine Learning
  • Quantum Computing

Background:

  • Optimal measurements for discriminating quantum states are crucial for classification tasks.
  • Quantum-inspired classifiers, while promising, are often limited by classical computation.
  • Encoding feature vectors into quantum states (density operators) is key for quantum computing applications.

Purpose of the Study:

  • To develop a geometric approach for improving the efficiency of quantum-inspired classification.
  • To enable correct comparison of classifiers with multiple input quantum state preparations.
  • To introduce and evaluate nearest mean classification using various distance metrics.

Main Methods:

  • A novel geometric approach is applied to quantum encoding for classification.
  • Quantum-inspired classifiers (nearest mean, Helstrom state discrimination) are analyzed.
  • Bures distance, Hellinger distance, and Jensen-Shannon distance are used for nearest mean classification.

Main Results:

  • The geometric approach significantly improves classification efficiency in terms of space and time.
  • The method allows for accurate classifier performance comparison with varied quantum state inputs.
  • Nearest mean classification using Bures, Hellinger, and Jensen-Shannon distances shows competitive performance on benchmark datasets.

Conclusions:

  • The proposed geometric approach enhances quantum-inspired classification efficiency and comparability.
  • New distance metrics provide effective alternatives for nearest mean quantum classification.
  • This work contributes to the practical application of quantum-inspired machine learning algorithms.