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Updated: Apr 13, 2026
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Expressibility-induced Concentration of Quantum Neural Tangent Kernels
Li-Wei Yu1, Weikang Li2, Qi Ye2
1Nankai University, Chern Institute of Mathematics, Tianjin, 300071, CHINA.
Reports on Progress in Physics. Physical Society (Great Britain)
|October 3, 2024
Summary
High expressibility in quantum neural networks can cause quantum tangent kernel values to concentrate to zero, impacting training. This concentration issue persists even with local encoding, offering insights for quantum circuit design.
Area of Science:
- Quantum Machine Learning
- Theoretical Computer Science
Background:
- Quantum tangent kernel methods analyze quantum machine learning (QML) models in the infinite-width limit.
- These methods are crucial for designing quantum circuit architectures and understanding training error convergence in quantum neural networks.
Purpose of the Study:
- To investigate the relationship between the expressibility and value concentration of quantum tangent kernel models.
- To analyze the impact of global and local quantum encodings on kernel value concentration.
Main Methods:
- Rigorous mathematical proofs for global and local loss functions.
- Extensive numerical simulations to validate theoretical findings.
Main Results:
- High expressibility in global and local quantum encodings leads to exponential concentration of quantum tangent kernel values to zero for global loss functions.
- This concentration issue persists but is partially mitigated for local loss functions.
Conclusions:
- The concentration of quantum neural tangent kernels is a fundamental feature that cannot be avoided solely by using local encoding with high expressibility.
- Findings provide crucial insights for designing effective wide quantum variational circuit models.
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