  While Quantum Machine Learning (QML) is an exciting emerging area, the
accuracy of the loss function still needs to be improved by the number of
available qubits. Here, we reformulate the QML problem such that the
approximation error (representation power) does not depend on the number of
qubits. We prove that a classical-to-quantum transfer learning architecture
using a Variational Quantum Circuit (VQC) improves the representation and
generalization (estimation error) capabilities of the VQC model. We derive
analytical bounds for the approximation and estimation error. We show that the
architecture of classical-to-quantum transfer learning leverages pre-trained
classical generative AI models, making it easier to find the optimal parameters
for the VQC in the training stage. To validate our theoretical analysis, we
perform experiments on single-dot and double-dot binary classification tasks
for charge stability diagrams in semiconductor quantum dots, where the related
empirical results support our theoretical findings. Our analytical and
empirical results demonstrate the effectiveness of classical-to-quantum
transfer learning architecture in realistic tasks. This sets the stage for
accelerating QML applications beyond the current limits of available qubits.
