Quantum technologies have the potential to play a significant role in future technological and economic advancement. However, our understanding of the specific narratives and topics present in national quantum technology policies is limited, even though these policies are vital for shaping global strategies, progress, and responsible development in the field. In this study, we use narrative policy analysis together with computational topic modeling to examine 55 governmental documents from 24 countries, covering over a decade. Using BERTopic modeling and the Narrative Policy Framework, the results reveal that national initiatives primarily focus on technological leadership for security and economic prosperity, assessing technological readiness, and, to a lesser extent, commercialization, and societal impacts. Over time, we see a trend toward greater alignment in the prevalence of these narratives, with different themes beginning to be considered more equally. Nevertheless, the narrative surrounding responsible quantum development and societal implications remains the least represented. The study shows the strategic priorities of the analyzed countries and introduces an innovative method for analyzing policy texts. Based on the results, we recommend a balanced regulatory approach for quantum technologies that promotes ethical innovation, supports inclusive technological ecosystems, and encourages global collaboration. Furthermore, we caution that an excessive emphasis on leadership and competition may lead to isolated innovation systems that could hinder progress, cooperation, and joint efforts.