A taxonomy is a hierarchical graph containing knowledge to provide valuable insights for various web applications. However, the manual construction of taxonomies requires significant human effort. As web content continues to expand at an unprecedented pace, existing taxonomies risk becoming outdated, struggling to incorporate new and emerging information effectively. As a consequence, there is a growing need for dynamic taxonomy expansion to keep them relevant and up-to-date. Existing taxonomy expansion methods often rely on classical word embeddings to represent entities. However, these embeddings fall short of capturing hierarchical polysemy, where an entity's meaning can vary based on its position in the hierarchy and its surrounding context. To address this challenge, we introduce QuanTaxo, a quantum-inspired framework for taxonomy expansion that encodes entities in a Hilbert space and models interference effects between them, yielding richer, context-sensitive representations. Comprehensive experiments on five real-world benchmark datasets show that QuanTaxo significantly outperforms classical embedding models, achieving substantial improvements of 12.3% in accuracy, 11.2% in Mean Reciprocal Rank (MRR), and 6.9% in Wu & Palmer (Wu&P) metrics across nine classical embedding-based baselines.