The efficient solution of large-scale sparse linear systems remains a cornerstone of scientific computing, including computational fluid dynamics. Traditional solvers often face scalability challenges due to memory constraints and computational complexity. In this work, we present a novel approach to integrate quantum-inspired tensor network methods into the sparse linear solver Spliss. By leveraging the expressive power of tensor networks we represent the solution space in a compressed, low-rank format that captures essential correlations. This quantum-based compression enables adaptive, hierarchical preconditioning and efficient iterative updates within Spliss’s framework. Our hybrid approach bridges classical sparse linear algebra with quantum-inspired data representation, opening new pathways for scalable, high-precision solutions to large-scale problems using quantum algorithms. This work establishes a foundation for future integration of quantum algorithms and tensor network techniques into mainstream scientific computing tools.