Within the realm of advanced code retrieval, existing methods have primarily relied on intricate matching and attention-based mechanisms. However, these methods often lead to computational and memory inefficiencies, posing a significant challenge to their real-world applicability. To tackle this challenge, we propose a novel approach, the Hyperbolic Code QA Matching (HyCoQA). This approach leverages the unique properties of Hyperbolic space to express connections between code fragments and their corresponding queries, thereby obviating the necessity for intricate interaction layers. The process commences with a reimagining of the code retrieval challenge, framed within a question-answering (QA) matching framework, constructing a dataset with triple matches characterized as \texttt{}. These matches are subsequently processed via a static BERT embedding layer, yielding initial embeddings. Thereafter, a hyperbolic embedder transforms these representations into hyperbolic space, calculating distances between the codes and descriptions. The process concludes by implementing a scoring layer on these distances and leveraging hinge loss for model training. Especially, the design of HyCoQA inherently facilitates self-organization, allowing for the automatic detection of embedded hierarchical patterns during the learning phase. Experimentally, HyCoQA showcases remarkable effectiveness in our evaluations: an average performance improvement of 3.5\% to 4\% compared to state-of-the-art code retrieval techniques.