Image Similarity Quantum Algorithm and Its Application in Image Retrieval Systems

The measurement of image similarity represents a fundamental task within the domain of image processing, enabling the application of sophisticated computational techniques to ascertain the degree of similarity between two images. To enhance the performance of these similarity measurement algorithms, the academic community has investigated a range of quantum algorithms. Notably, the swap test-based quantum inner product algorithm (ST-QIP) has emerged as a pivotal method for computing image similarity. However, the inherent destructive nature of the swap test necessitates multiple quantum state evolutions and measurements, which leads to consumption of quantum resources and prolonged computational time, ultimately constraining its practical applicability. To address these limitations, this study introduces an advanced quantum inner product algorithm based on amplitude estimation (AE-QIP) designed to compute image similarity. This innovative approach circumvents the repetitive measurement processes associated with the swap test, thereby optimizing the utilization of quantum resources and substantially enhancing the algorithm's performance. We conducted experiments using a quantum simulator to implement the AE-QIP algorithm and evaluate its effectiveness in the image retrieval tasks. It is found that the AE-QIP algorithm achieves comparable precision to the ST-QIP algorithm while exhibiting significant reductions in qubit consumption and average processing time. Additionally, our findings suggest that increasing the number of ancillary qubits can further enhance the accuracy of the AE-QIP algorithm. Overall, within the acceptable error thresholds, the AE-QIP algorithm exhibits enhanced efficiency relative to the ST-QIP algorithm. However, significant further research is needed to address the challenges involved in optimizing the performance of quantum retrieval systems as a whole.