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Explore how Fourier analysis revolutionizes quantum machine learning through this 53-minute conference talk from the Quantum Techniques in Machine Learning (QTML) 2025 conference. Discover how the quantum Fourier transform enables the construction of massively scalable quantum machine learning models that can be trained entirely on classical hardware, supporting circuits with thousands of qubits and millions of parameters. Learn about universal generative machine learning models built in Fourier space that encode important biases present in nearly all datasets, and understand how these models can be successfully trained despite the theoretical existence of barren plateaus under random parameter initialization. Examine the empirical implementation of training algorithms on large, real-world datasets and gain insights into a new generative machine learning algorithm called generative bandlimiting that exploits known biases in the Fourier spectra of data. The presentation concludes with reflections on the overall direction of the quantum machine learning field, providing valuable perspectives on scalable approaches to quantum ML model development.
