Cancer remains a leading global cause of death, primarily driven by the uncontrolled proliferation of abnormal cells. Malignant tumors, such as carcinomas, originate from unchecked epithelial cell growth and produce growth factors like FGF and VEGF, which promote angiogenesis and tumor progression through heparanase-mediated degradation of heparan-sulfate proteoglycans. Chitosan and its derivatives have shown promise in inhibiting tumor growth and metastasis. This study aims to investigate newly synthesized sulfated chitosan oligomers as heparin mimics to inhibit heparanase, evaluating their cytotoxic effects on SH-SY5Y, HCT116, A549, and MDA-MB-231 cancer cell lines. Moreover, it seeks to leverage a variational quantum neural network (VQNN) to predict and validate cytotoxicity outcomes, integrating quantum computing methods into evaluating novel anticancer compounds. The VQNN algorithm was applied to analyze the anticancer effects of sulfated chitosan oligomers. Cytotoxicity data from wet lab experiments validated the model's predictive performance. The VQNN model demonstrated strong predictive capabilities in evaluating anticancer compounds. Specifically, it achieved a mean absolute error (MAE) of 6.5844, indicating a similar trend to the experimental results. Additionally, the model obtained an R2 value of 0.6020, reflecting a moderate level of correlation between predicted and observed outcomes. The results underscore the potential of integrating quantum-based machine learning models into cancer research. The VQNN effectively predicted experimental outcomes, showcasing its utility in assessing novel anticancer compounds. This approach could speed up drug discovery by streamlining the identification and optimization of therapeutic candidates. Furthermore, the findings support the ongoing development of quantum computing techniques for tackling complex biological challenges, contributing to innovative cancer treatment strategies that target tumor growth and angiogenesis.