This paper proposes a Quantum Computational Intelligence (QCI) model integrated with Generative Artificial Intelligence (GAI) for Taiwanese/English language co-learning applications within human-machine interactions. The QCI model comprises two main phases: human-machine interaction and data processing for quantum circuit generation and real-world applications. During the human-machine interaction phase, a synergy between Human Intelligence (HI) and Machine Intelligence (MI) enables young students to gain familiarity with CI that converges with QCI. The second phase involves data processing, which encompasses stages of data preprocessing, analysis, and evaluation. The methodology is applied to two distinct applications: 1) Application 1 focuses on constructing a knowledge graph using the Ollama platform and the TAIDE model—a Trustworthy AI Dialogue Engine developed by the Taiwanese government based on the LLaMa 2 model. 2) Application 2 addresses the GAI images to text/voice, and text/voice to GAI images, depending on the type of Taiwanese/English data collected. Subsequently, the QCI model is refined through Particle Swarm Optimization (PSO) and Genetic Algorithm Neural Networks (GANN). Moreover, a Quantum Fuzzy Inference Mechanism (QFIM) is integrated to enhance the QCI model’s capability in creating a quantum circuit. The experimental results suggest that the QCI model significantly enhances human-machine collaboration. Looking forward, we plan to extend the QCI model to reach more young learners.