Variational System Identification (VSI) provides a physics-informed framework for discovering governing partial differential equations from data by exploiting weak-form representations and sparse operator selection. Classical VSI has been applied to reaction–transport systems arising in biological migration–proliferation dynamics, wound healing, mechanochemical coupling, and damage evolution [1, 2, 3]. However, extending VSI to high-dimensional settings is fundamentally limited by the scaling of weak-form operator evaluation, finite-element assembly, and the computational complexity of large-scale sparse linear algebra. This work introduces Quantum Variational System Identification (QVSI), a quantum extension of VSI that leverages quantum linear algebra and quantum finite element methods to enable scalable inference of reaction–transport PDEs beyond classical limits. Building on the QuFEM framework[4], weak-form operators are assembled directly within quantum circuits using element-level oracles, avoiding explicit construction of global system matrices. Quantum block-encodings and variational quantum solvers are then used to efficiently evaluate inner products and identify sparse governing operators. By integrating variational system identification with quantum finite element assembly, QVSI provides a principled pathway for PDE discovery in high-dimensional reaction–transport systems relevant to biology, materials, and multiscale continuum physics. [1] Srivastava, S., & Garikipati, K. (2024). Pattern formation in dense populations studied by inference of nonlinear diffusion-reaction mechanisms. International Journal for Numerical Methods in Engineering, 125 (12). https://doi.org/10.1002/nme.7475 [2] Srivastava, S., Kinnunen, P. C., Wang, Z., Kenneth, K. Y. H., Humphries, B. A., Chen, S., Linderman, J. J., Luker, G. D., Luker, K. E., & Garikipati, K. (2025). Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells. PLOS Computational Biology, 21 (10), 1–27. https://doi.org/10.1371/journal.pcbi.1013607 [3] Livingston, E., Srivastava, S., Holber, J., Mourad, H. M., & Garikipati, K. (2026). Inference of phase field fracture models. Journal of the Mechanics and Physics of Solids, 209, 106495. https://doi.org/https://doi.org/10.1016/j.jmps.2025.106495 [4] Alkadri, A. M., Kharazi, T. D., Whaley, K. B., & Mandadapu, K. K. (2025). A Quantum Algorithm for the Finite Elem