Analysis of quantum image representations for supervised classification

In the era of big data and artificial intelligence, the increasing volume of data and the demand to solve more and more complex computational challenges are two driving forces for improving the efficiency of data storage, processing, and analysis. Quantum image processing is an interdisciplinary field between quantum information science and image processing, which has the potential to alleviate some of these challenges by leveraging the power of quantum computing. In this work, we compare and examine the compression properties of four different quantum image representations (QImRs): namely, tensor network representation (TNR), flexible representation of quantum image (FRQI), novel enhanced quantum representation (NEQR), and quantum probability image encoding (QPIE). Our simulations show that FRQI and QPIE perform a higher compression of image information than TNR and NEQR. Furthermore, we investigate the trade-off between accuracy and memory in binary classification problems, evaluating the performance of quantum kernels based on QImRs compared to the classical linear kernel. Our results indicate that quantum kernels provide comparable classification average accuracy but require exponentially fewer resources for image storage.