<p>We derive a generalization error bound for quantum neural networks (QNNs) using the framework of dynamical Lie algebras (DLAs). By constructing covering numbers from the DLA structure and applying Rademacher complexity theory, we show that the generalization error bound scales as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \mathcal {O}(\sqrt{ \dim ( \mathfrak {g}) }) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <msqrt> <mrow> <mo>dim</mo> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">g</mi> <mo stretchy="false">)</mo> </mrow> </msqrt> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \mathfrak {g} \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">g</mi> </math></EquationSource> </InlineEquation> denotes the associated Lie algebra. Additionally, we establish an upper bound on the number of trainable parameters required to ensure this generalization property. Numerical experiments using the transverse-field Ising model confirm the validity of our theoretical findings and illustrate the effect of boundary conditions and training strategies on generalization. Our results highlight the importance of algebraic structure in the design and analysis of QNNs.</p>