Reproduce “Quantum Machine Learning for Industrial Applications” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Léo Monbroussou
This PhD thesis from Sorbonne Université investigates the theoretical foundations of Quantum Machine Learning (QML) for industrial applications, focusing on trainability, expressivity, and classical simulability on near-term quantum devices. The research develops subspace-preserving QML algorithms, including a QCNN experimentally validated on a photonic platform, and establishes conditions for achieving polynomial quantum advantage while mitigating vanishing gradients.
Key insights
- Barren Plateaus can be avoided in Hamming-weight preserving circuits by operating within fixed Hamming-weight subspaces, with gradient variance scaling inversely to the subspace dimension, challenging prior conjectures.
- The novel 'State Injection' scheme enables linear optical circuits to overcome inherent controllability limitations and generate classically hard-to-estimate probabilities, despite a theoretical trade-off with state purity.
- For a quantum model to avoid dequantization by classical surrogates, its effective weight vector's L2-norm must be significantly larger than that of classical minimum norm least squares estimators.
- Analyzing VQCs as Fourier models reveals that frequencies with low redundancy can suffer from 'vanishing expressivity,' where their Fourier coefficients exhibit exponentially vanishing variance, even if the overall model variance is non-vanishing.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.