Achieving Sub-Exponential Speedup in Gate-Based Quantum Computing for Quadratic Unconstrained Binary Optimization

Recent quantum-inspired methods based on the Simulated Annealing (SA) algorithm have shown strong potential for solving combinatorial optimization problems. However, Grover's algorithm [1] in gate-based quantum computing offers only a quadratic speedup, which remains impractical for large problem sizes. This paper proposes a hybrid approach that integrates SA with Grover's algorithm to achieve sub-exponential speedup, thereby improving its industrial applicability. In enzyme fermentation, variables such as temperature, stirring, wait time, pH, tryptophan, rice flour and so on are encoded by 625 binary parameters, defining the space of possible enzyme formulations. We aim to find a binary configuration that maximizes the active ingredient, formulated as a 625-bit QUBO which is generated by historical experiments and AI techniques. Minimizing the QUBO cost corresponds to maximizing the active ingredient. This case study demonstrates that our hybrid method achieves sub-exponential speedup through gate-based quantum computing.