Quantum-Accelerated Solution of the Two-Dimensional Frank–Kamenetskii Nonlinear Combustion Problem Using Newton– Quantum Linear Solver Methods on EuroHPC Quantum Computers
Poyraz Koçak Y. (Yürütücü), Yıldız H., Uzal E.
Diğer Ülkelerdeki Özel Organizasyonlar Tarafından Desteklenmiş Proje, 2026 - 2026
- Proje Türü: Diğer Ülkelerdeki Özel Organizasyonlar Tarafından Desteklenmiş Proje
- Başlama Tarihi: Eylül 2026
- Bitiş Tarihi: Aralık 2026
Proje Özeti
The Frank–Kamenetskii equation is a fundamental nonlinear reaction–diffusion model widely used to investigate thermal explosion phenomena in combustion science, chemical engineering, heat transfer, and reactive transport processes. While one-dimensional formulations can be solved efficiently using conventional numerical techniques, extending the problem to two-dimensional domins substantially increases the computational cost because each Newton iteration requires the solution of a large sparse Jacobian linear system. Consequently, the Frank–Kamenetskii equation provides an ideal benchmark for evaluating hybrid quantum–classical algorithms for nonlinear partial differential equations. The objective of this project is to develop and evaluate a hybrid quantum–classical framework for solving the two-dimensional Frank–Kamenetskii problem on EuroHPC quantum computing infrastructures. The proposed methodology combines the Newton's method with Quantum Algorithms for solving linear system, including the Variational Quantum Linear Solver (VQLS) and the Harrow–Hassidim–Lloyd (HHL) algorithm. During each Newton iteration, the Jacobian matrix generated from the finite difference discretization will be encoded into quantum circuits and executed on real quantum hardware available through the EuroHPC Quantum Access Programme. The proposed framework builds upon our previous work, in which the one-dimensional Frank–Kamenetskii problem was successfully solved using hybrid quantum–classical techniques in the simulation environment. In this project, the methodology will be extended to twodimensional nonlinear PDEs, enabling the investigation of scalability, numerical stability, quantum resource requirements, and execution performance on real quantum computers. To ensure rigorous validation, the proposed quantum approach will be systematically benchmarked against well-established classical numerical methods, including analytical solutions (where available), finite difference discretization, collocation methods, and the conventional Newton–Raphson solver. Comparisons will focus on numerical accuracy, convergence behaviour, computational efficiency, scalability, and quantum resource utilization. The expected outcome of this project is a comprehensive benchmark demonstrating the feasibility and current capabilities of hybrid quantum algorithms for solving large-scale nonlinear engineering problems. The resulting software framework and performance analysis will contribute to the development of practical quantum scientific computing and provide a foundation for future quantum-enabled simulations of nonlinear partial differential equations on EuroHPC quantum infrastructures.