Reproduce “Potential and limitations of random Fourier features for dequantizing quantum machine learning” 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
Ryan Sweke, Erik Recio-Armengol, Sofiene Jerbi, Elies Gil-Fuster, Bryce Fuller, Jens Eisert, Johannes Jakob Meyer
A collaboration between IBM Quantum, Freie Universität Berlin, and ICFO rigorously defines the conditions under which Random Fourier Features (RFF) can efficiently dequantize the training process of variational quantum machine learning (QML) models for regression, demonstrating that efficient classical simulation depends on the frequency spectrum's concentration and alignment with structured sampling distributions.
Key insights
- Efficient RFF-based dequantization of QML is highly conditional, depending critically on the specific PQC architecture, the regression problem, and the chosen re-weighting strategy for the kernel.
- For RFF to be efficient, the frequency spectrum of the optimal PQC function must be sufficiently concentrated and well-aligned with an efficiently sampleable probability distribution derived from the re-weighted kernel.
- The choice of re-weighting impacts both the ability to efficiently sample RFF and the magnitude of key theoretical quantities like the kernel integral operator norm and the RKHS norm of the QML functions.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.