Accurate and efficient drug-drug interaction extraction (DDIE) from the medical corpus is essential for pharmacovigilance, drug therapy and drug development. To solve the problems of unbalance dataset and lack of accurate manual annotations in DDIE, a cross-attention guided Siamese quantum BiGRU (CA-SQBG) is constructed to improve feature representation learning ability for DDIE. It mainly consists of two quantum BiGRUs (QBiGRUs) and a cross-attention, where two QBiGRUs are Siamese implemented in a variational quantum environment to learn the contextual semantic feature representation of drug pairs, cross-attention is employed to learn mutual information from the Siamese QBiGRUs, which in turn allows the two modules to extract DDI more collaboratively. Unlike BiGRU, Siamese QBiGRUs uses internal and external dependencies in quaternion algebra to map DDI correlations within and between multidimensional features, whereas BiGRU can only capture dependencies within sequences. CA-SQBG is evaluated on the DDIExtraction2013 dataset, and the results demonstrate that it can effectively capture the inter- and intra-dependencies within multimodal features with few parameters, using a small number of training samples, and is superior to the most advanced DDIE methods. CA-SQBG offers potential applications for quantum computing and Siamese networks in the field of DDIE. Code is available on https://github.com/xaycq/CA-SQBG.