A Fast Quantum Image Compression Algorithm based on Taylor Expansion

TL;DR

The paper addresses the challenge of balancing compression quality and data size in image storage by leveraging a hybrid quantum–classical model. It introduces Fast QIC, an enhanced quantum image compression method that uses block-wise encoding, parameterized quantum circuits, and a first-order Taylor expansion to drastically reduce iterations while maintaining low loss, achieving up to a $86\%$ reduction in iterations for high-resolution images. Key contributions include a neighbor-aware update rule for adjacent blocks, a Taylor-based update scheme with a Moore–Penrose inverse for fast parameter adjustments, and a compact $W_{\text{chain}}+ZXZ$ variational ansatz to minimize circuit depth. Experiments on Lenna and Cameraman demonstrate improved efficiency and scalability, suggesting this approach can be a practical pathway for quantum-assisted image processing as quantum hardware advances.

Abstract

With the increasing demand for storing images, traditional image compression methods face challenges in balancing the compressed size and image quality. However, the hybrid quantum-classical model can recover this weakness by using the advantage of qubits. In this study, we upgrade a quantum image compression algorithm within parameterized quantum circuits. Our approach encodes image data as unitary operator parameters and applies the quantum compilation algorithm to emulate the encryption process. By utilizing first-order Taylor expansion, we significantly reduce both the computational cost and loss, better than the previous version. Experimental results on benchmark images, including Lenna and Cameraman, show that our method achieves up to 86\% reduction in the number of iterations while maintaining a lower compression loss, better for high-resolution images. The results confirm that the proposed algorithm provides an efficient and scalable image compression mechanism, making it a promising candidate for future image processing applications.

Figures (4)

• Figure 1: Overview of quantum image compression/decompression procedures.
• Figure 2: The architecture of fast QIC, $\text{get}(i,j)$ take the blocks $i,j$, then apply $\text{vec}\;\circ\;\text{norm}\;(\ldots)$ to return corresponding quantum state $|\psi\rangle_{i,j}$ (a) Looping through all blocks generated from the image $\mathcal{I}$ (b) The compilation algorithm inside each loop (c) A 3-qubit $W_{\text{chain}}+XYZ$ ansatz as $U(\bm\theta^{(t)})$.
• Figure 3: The ratio (data size) between compressed image and original image. The dotted line is $\text{ratio}=1$, at this line, the compressed image and the original image's size are equal. Both axes are plotted on a logarithmic scale.
• Figure 4: Experiment's result on (a) Lenna image and (b) Cameraman image. The investigated properties include (1) average cost value, (2) average minimal number of iterations, and (3) "Transferred" percent. We experimented with two images: Lenna and Cameraman. The original size of these images is $256\times256$ which is scaled as $8\times8, 16\times 16,\ldots$ and $128\times 128$. The fast method and the naive method's result are presented as normal (----) and dotted lines ([0.5ex]0.4cm0.5pt0.5mm), respectively.