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 (QIP) 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.

翻译：在大数据与人工智能时代，数据量的持续增长以及对解决日益复杂计算挑战的需求，是提升数据存储、处理与分析效率的两大驱动力。量子图像处理是量子信息科学与图像处理之间的交叉学科领域，其通过利用量子计算的能力，有望缓解其中部分挑战。在本工作中，我们比较并考察了四种不同量子图像表示的压缩特性：即张量网络表示、柔性量子图像表示、新型增强量子表示以及量子概率图像编码。我们的模拟结果表明，FRQI 与 QPIE 相比 TNR 与 NEQR 实现了更高的图像信息压缩。此外，我们研究了二分类问题中准确率与内存之间的权衡，评估了基于 QImR 的量子核与经典线性核相比的性能。我们的结果表明，量子核能够提供相当的分类平均准确率，但所需的图像存储资源呈指数级减少。