Analysis of Quantum Image Representations for Supervised Classification

TL;DR

The paper addresses the challenge of efficiently representing and classifying images on quantum hardware by comparing four quantum image representations (TNR, FRQI, NEQR, QPIE) for compression and their use in quantum-kernel-based supervised classification. It implements quantum kernels via state overlaps and evaluates performance on MNIST and Fashion-MNIST after resizing images to 16×16, finding that FRQI and QPIE achieve stronger compression while maintaining comparable accuracy to a classical linear kernel, with substantial memory savings. The work connects tensor-network concepts (e.g., MPS) to quantum encoding and discusses information-theoretic trade-offs governing compression and learnability, highlighting practical bottlenecks such as data-loading costs. Overall, the results guide the design of memory-efficient quantum image representations for downstream classification and point to future directions including RGB extensions and hardware experiments under noise.

Abstract

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.

Figures (8)

• Figure 1: Example real-ket indexing for an image with $2^2 \times 2^2$ pixels
• Figure 2: A typical image in the framework of tensor networks
• Figure 3: A $2\times 2$frqi image. The angles $\theta_i$, with $i = 0, 1, 2, 3$, at the center of each pixel encode the grays intensity of the corresponding pixels in the angle representation, while the 2-bit strings in the lower-right corner identify the positions in the image in binary representation.
• Figure 4: A $2\times 2$neqr image. The $8$-bit strings at the center of each pixel and the $2$-bit strings in the lower-right corner encode, respectively, the gray intensity and the positions of the pixels in the image.
• Figure 5: A $2\times 2$qpie image. The amplitudes $c_i$, with $i = 0, 1, 2, 3$, at the center of each pixel encode the grays intensity of the corresponding pixels, while the 2-bit strings in the lower-right corner label the pixel positions in the image in binary representation.