Recommendation has become especially crucial during the COVID-19 pandemic as a significant number of people rely on online shopping from home. Existing recommendation algorithms, designed to address issues like cold start and data sparsity, often overlook the time constraints of users. Specifically, users expect to receive recommendations for products of interest in the shortest possible time. To address this challenge, we propose a novel collaborative filtering recommendation algorithm that leverages the advantages of quantum computing circuits based on data reconstruction. This approach allows for the rapid identification of users similar to the target user, thereby improving recommendation speed. In our method, we utilize the information of known users to linearly reconstruct that of the target users, forming a relational matrix. Subsequently, we employ \(l_{2,1}-\) norm and \(l_{1}-\) norm to sparsely constrain the relationship matrix, deducing the weight of each known user. The final step involves providing similar recommendations to target users based on these weights. Furthermore, we implement the proposed algorithm using a quantum circuit, enabling exponential acceleration. The final weight matrix is derived from the quantum state outputted by the circuit. The speed of this process is theoretically demonstrated in detail. Experimental results indicate that our algorithm outperforms state-of-the-art methods in terms of root mean squared error (RMSE), mean absolute error (MAE) and normalized discounted cumulative gain (NDCG). Compared to state-of-the-art comparison algorithms, the proposed algorithm achieves the fastest recommendation speed across eight public datasets.