Frame Generation in Hilbert Space: Generative Interpolation of Measurement Data for Quantum Parameter Adaptation

Quantum Parameter Adaptation (QPA) has emerged as a promising approach for leveraging quantum neural networks (QNNs) to generate classical neural network (NN) parameters, enabling parameter-efficient fine-tuning of large language models (LLMs). However, the practical implementation of QPA is hindered by the need for an extremely large number of quantum measurement shots, posing a significant challenge in real-world quantum computing environments. To address this issue, this work introduces Generative Interpolation (GI), a method inspired by frame generation in video data, where missing measurement probabilities are interpolated using a neural network-based generative model. By treating quantum measurement probabilities as analogous to video frames, GI estimates unmeasured basis state probabilities, significantly reducing the required quantum measurements. Empirical results demonstrate that incorporating GI into QPA reduces the quantum measurement shot requirement to just $2.5\%$ of the original count while achieving superior fine-tuning performance. This method not only enhances QPA efficiency but also establishes a broader connection between classical deep learning techniques and quantum measurement reconstruction. The proposed generative framework has the potential to extend to variational quantum algorithms, offering a pathway toward reducing quantum measurement overhead in hybrid quantum-classical computing paradigms.