Histogram-Driven Amplitude Embedding for Qubit-Efficient Quantum Image Compression

Abstract

This work introduces a compact and hardwareefficient method for compressing color images using near-term quantum devices. The approach segments the image into fixedsize blocks (“bixels”), and computes the total intensity within each block. A global histogram with B bins is then constructed from these block intensities, and the normalized square roots of the bin counts are encoded as amplitudes into an $n$-qubit quantum state, where $n=\left\lceil\log _{2} B\right\rceil$. Amplitude embedding is performed using PennyLane and executed on real IBM Quantum hardware. The resulting state is measured to reconstruct the histogram, enabling approximate recovery of block intensities and full-image reassembly. The method maintains a constant qubit requirement based solely on the number of histogram bins, independent of the image's resolution. By adjusting $B$, users can control the trade-off between fidelity and resource usage. Empirical results demonstrate high-quality reconstructions using as few as $\mathbf{5}-\mathbf{7}$ qubits, significantly outperforming conventional pixel-level encodings in terms of qubit efficiency, and validating the method's practicality for current NISQ-era quantum systems.