Hybrid Quantum Image Preparation via JPEG Compression

TL;DR

The paper addresses the quantum-cost burden of loading images for amplitude-encoded quantum image processing by marrying JPEG compression with QPIE, loading only quantized JPEG coefficients into a quantum register. It introduces two hybrids: JQPIE, which coherently decompresses via a block-encoded inverse quantization, and QF-JQPIE, which forgoes quantization and uses truncation in the DCT domain to enable a fully unitary, ancilla-free preparation. Statevector simulations on USC-SIPI/Kodak show substantial reductions in CX gate counts and circuit depth with preserved or even enhanced PSNR/SSIM fidelity, particularly for QF-JQPIE, which avoids probabilistic overhead entirely. The work establishes a practical baseline for resource-efficient quantum image loading and points to future extensions with alternative compression schemes and data-driven reversible transforms.

Abstract

We present a hybrid classical-quantum image preparation scheme that reduces the quantum implementation cost of image loading for quantum pixel information encoding (QPIE). The proposed method, termed JPEG-assisted QPIE (JQPIE), loads only the quantized JPEG coefficients into a quantum register, leading to substantial reductions in \texttt{CX} gate count and circuit depth while preserving reconstruction quality comparable to classical JPEG compression. We develop two variants of the hybrid strategy. The first realizes the complete JPEG decompression pipeline coherently by implementing inverse quantization via a block-encoded unitary operator. The second, referred to as \emph{quantization-free JQPIE} (QF-JQPIE), omits quantization altogether, thereby avoiding the probabilistic nature of block-encoded quantization. Numerical simulations on standard benchmark image datasets (USC--SIPI and Kodak) demonstrate that both variants achieve significant constant-factor reductions in \texttt{CX} gate count and circuit depth relative to direct QPIE loading, while maintaining high reconstruction quality as measured by PSNR and SSIM.

Figures (12)

• Figure 1: Classical pre-processing steps used in the hybrid JPEG pipeline. (a) Partitioning of an input image into non-overlapping $8\times8$ blocks $B_j$ for localized DCT processing; if the image dimensions are not multiples of eight, zero-padding is applied along the bottom and right edges. (b) Zigzag traversal pattern $\pi(k)$ defining the one-dimensional ordering of DCT coefficients within each $8\times8$ block, mapping frequency coordinates $(u,v)$ to sequence indices $k=8u+v$, with low-frequency components appearing first. The ordering begins with low-frequency coefficients (e.g., $\pi(0)=0,\pi(1)=1,\pi(2)=8,\pi(3)=16,\pi(4)=9,\ldots$), which dominate perceptual energy.
• Figure 2: The CR obtained from JPEG compression ($S=1$) across standard image datasets. Each point corresponds to a single grayscale image from one of the Aerials, Textures, Miscellaneous, and Kodak sets. Colors indicate image categories, marker shapes denote image resolutions, and crosses correspond to non-square images. While JPEG compression substantially reduces the number of active coefficients, most images remain exponentially dense in $n=\log_2 N$, with sparsity compatible with sparse quantum state preparation occurring only for highly structured or texture-dominated images.
• Figure 3: Global distribution of non-zero quantized DCT coefficients across zigzag positions. The histogram aggregates all images after partitioning into $8\times 8$ blocks and applying JPEG quantization with the standard luminance matrix ($S=1$). Each bar reports the normalized frequency with which a given zigzag index contains a non-zero coefficient. The strong concentration at low-frequency zigzag indices indicates that, while images may remain dense overall, the non-zero support within each block is predominantly confined to the first few zigzag positions.
• Figure 4: Quantum state preparation (QSP) stage for the proposed hybrid image preparation schemes. In both circuits, the data and index registers are initialized in the $\ket{0}$ state. (a) JQPIE. The state-preparation operator $\mathcal{P}$ loads the truncated, zigzag-ordered quantized DCT coefficients $\hat{Z}_j^{(r)}$ on the quantum registers. (b) QF-JQPIE. The same preparation structure is used to encode the truncated zigzag-ordered unquantized DCT coefficients $Z_j^{(r)}$.
• Figure 5: Quantum implementation of the block-encoded quantization matrix. (a) The ancilla qubit receives uniformly controlled rotations conditioned on the 6-bit index $k$. (b) Equivalent decomposition using the Möttönen construction mottonen2004transformation.