A research team from Shanghai Jiao Tong University has developed cuLoRADS, a GPU-accelerated semidefinite programming solver that dramatically boosts the efficiency of solving large-scale semidefinite programming problems. The team achieved this through a combination of design strategies: exploiting the low-rank structure inherent in the problems, restructuring core computational workflows, and leveraging sparsity to optimize storage. On a single NVIDIA H100 GPU, the solver can handle problems involving matrices with tens of millions of dimensions in just 10 seconds to one minute—far outpacing traditional CPU-based solvers. The solver successfully resolved a fundamental quantum ordering search problem that had remained open for 18 years, determining that the maximum searchable list size for 5 queries is 7,265. The team also provided the relevant mathematical proof, laying a theoretical foundation for low-rank strategies. These results have potential applications in areas such as quantum algorithm complexity research, calculating ground-state energies of molecules in quantum chemistry, and real-time trajectory planning for embodied intelligent robots—demonstrating the significant advantages of co-designing algorithms and hardware. However, the solver is only suitable for large-scale semidefinite programming problems whose constraint data are sufficiently sparse or admit compact operator representations; its advantages diminish on dense, unstructured problems that require high-rank factor representations.