Quantum–Classical Hybrid Architecture for Solving the Muskat–Leverett Model
Beimbet Daribayev, Aksultan Mukhanbet, Erlan Makhmut, Nurtugan Azatbekuly, Timur Imankulov · IET Quantum Communication · 2025
ABSTRACT Hybrid quantum–classical architectures demonstrate significant potential for efficiently solving complex physical models. This study focuses on developing and implementing a hybrid quantum–classical algorithm to solve the Muskat–Leverett model by reformulating it as a system of linear equations. By expressing the Muskat–Leverett model in matrix form , we enable the application of quantum algorithms. We leverage classical computational platforms (CPU and GPU) alongside quantum computing to efficiently solve the model, achieving competitive accuracy and demonstrating potential for scalability compared to traditional methods. The Harrow–Hassidim–Lloyd algorithm and the variational quantum linear solver were utilised to design quantum circuits and variational ansatz. The study evaluates quantum solutions with classical optimisation, variational methods, fully classical solutions on graphical processors and purely quantum solutions. Experimental results show that the hybrid architecture, utilising cuQuantum and CUDA‐Q, achieves up to 6.42× faster execution compared to CPU implementations and provides a comparable speedup to GPU‐based solvers. When applied for large‐scale problems, the hybrid approach is also ∼10× faster than standard quantum simulators. Key factors, such as qubits, optimisers and cost functions, were analysed to determine optimal parameters. These results highlight the advantages of hybrid architecture in accelerating and optimising numerical solutions for complex physical models.