Quantum computing faces a key challenge: efficiently encoding classical data and extracting results. EDF R&D’s ERMES department (Palaiseau) has explored Variational Quantum Algorithms (VQAs) for solving PDEs since 2021, reformulating finite element discretization and validating feasibility on quantum hardware [1,2]. While VQAs suit NISQ devices, they suffer from barren plateaus and poor scalability, unlike Fault-Tolerant algorithms such as HHL. This internship targets to transpose the VQA results in the data input bottlenecks via block encoding, representing classical data as unitary operations to improve expressivity and efficiency. The approach will be benchmarked on EDF’s HPC-based QPU emulator and the partners QPU, supporting scalability analysis and contributing to a long-term goal: quantum reformulation of non-linear PDEs, that constitutes a PhD proposal. [1] Donachie et al arXiv:2510.15645 [2] Rémond et al arXiv:2510.14746