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This theoretical work establishes that restricting the parameter space of quantum circuits can improve Rademacher complexity scaling, offering a potential statistical advantage over classical linear models with fewer training samples. While numerical experiments confirm these bounds, the results remain conditional on specific parameter norm scaling, indicating that practical quantum machine learning gains depend heavily on architectural constraints. The findings provide a crucial theoretical benchmark for evaluating the generalization capabilities of parameterized quantum circuits in data-limited regimes.

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Quantum Models Show Potential for Improved Scaling with Three Times Fewer Samples

Quantum ZeitgeistMay 29, 20265 min read

Can a quantum circuit with a million parameters reliably learn from limited data. New theoretical bounds demonstrate Rademacher complexity improves from $ \mathcal{O}(\frac{L^{\frac{3}{2}}}{\sqrt{M}}) $ to $ \mathcal{O}(\frac{L}{\sqrt{M}}) $ by restricting the circuit’s operational space. This suggests a potential statistical edge for certain quantum machine learning models over their classical counterparts.

Hiroshi Ohno, from the Institute for Quantum Computing and the Department of Physics and Astronomy, and colleagues have determined scaling bounds for Rademacher complexity relating to the number of parameters and training samples in parameterised quantum circuits generated by Pauli strings. The bounds are for the full parameter domain and for a restricted one. These results offer a key comparison with classical linear models, indicating a potential statistical advantage for quantum machine learning when parameter norms scale appropriately. Numerical experiments confirm the predicted scaling behaviour. Rademacher complexity, a crucial concept in statistical…

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