In this study, we initially investigate the application of a hybrid classical-quantum classifier (HCQC) for sentiment analysis, comparing its performance against the classical CPLEX classifier and the Transformer architecture. Our findings indicate that while the HCQC underperforms relative to the Transformer in terms of classification accuracy, but it requires significantly less time to converge to a reasonably good approximate solution. This experiment also reveals a critical bottleneck in the HCQC, whose architecture is partially undisclosed by the D-Wave property. To address this limitation, we propose a novel algorithm based on the algebraic decomposition of QUBO models, which enhances the time the quantum processing unit can allocate to problem-solving tasks.