Simulation and optimization are at the core of modern product design, from structural and fluid analysis to materials modelling and logistics planning. As problem sizes and accuracy requirements grow, classical solvers face mounting computational costs. Quantum computing offers new computational paradigms, but turning algorithmic advances into industrial practice remains an open challenge. This session brings together mathematicians, computational scientists and industry practitioners to explore how quantum and hybrid quantum-classical algorithms can address scientific computing problems of industrial relevance. Contributions will cover recent mathematical developments in quantum algorithms for linear systems, partial differential equations, optimization and sampling, as well as realistic use cases in aerospace, energy, automotive and manufacturing. The session will also look critically at resource requirements, error mitigation and the outlook for near-term (NISQ) versus fault-tolerant devices, with emphasis on rigorous benchmarking against state-of-the-art classical methods, data encoding and readout costs, and integration into existing simulation and HPC workflows. Topics: quantum algorithms for linear systems and PDEs; variational and hybrid quantum-classical methods; quantum optimization for industrial problems; quantum machine learning for simulation and surrogate modelling; error mitigation and resource estimation; benchmarking and quantum-HPC integration; industrial case studies.