Rademacher Complexity Bounds for Parameterized Quantum Circuits Generated by Pauli Strings

In this study, we analyze the Rademacher complexity ${\mathcal{R}}_M$ of a parameterized unitary whose generators are chosen from $n$-qubit Pauli strings. Although generalization bounds for quantum machine learning models have been studied in several settings, explicit Rademacher-complexity bounds for parameterized unitaries generated by Pauli strings remain less transparent. We derive simple scaling bounds in terms of the number of parameters $L$ and the number of training samples $M$: $\mathcal{O}(\frac{L^{\frac{3}{2}}}{\sqrt{M}})$ for the full parameter domain and $\mathcal{O}(\frac{L}{\sqrt{M}})$ for a restricted parameter domain. Furthermore, we compare the obtained results with those for a classical linear model class and suggest a potential statistical-complexity advantage when the norms of both the input and the parameter in the classical model scale with the number of parameters. Numerical experiments provide qualitative evidence consistent with the predicted scaling.