用奇异值分解压缩量子图像编码，大幅降低电路复杂度。
Schmidt Decomposition-Based Methods for Efficient Quantum Image Encoding
- 基于奇异值分解保留量子态关键纠缠结构，减少冗余计算。
- FRQI编码电路深度降低97%，重建均方误差仅0.27。
- 适合资源受限的当前量子硬件，提升实用效率。
在量子图像处理中，将经典图像数据编码为量子态是基础步骤，常用方法包括FRQI、QPIE和NEQR。但在真实量子硬件上，这些方法易导致门数多、电路深度大、量子比特消耗高，对噪声中等规模量子（NISQ）设备构成挑战。本文研究通过奇异值分解进行低秩近似，能否降低编码复杂度。该方法保留量子态中最显著的纠缠成分，使状态制备更高效同时保留大部分图像信息。我们对比了三种编码方式在原始形式与低秩近似下的表现，评估电路深度、CNOT门数量、均方误差（MSE）及重构图像视觉质量。结果表明，在精度与资源效率间存在明显权衡：FRQI模型实现97%的电路深度缩减，重建误差仅为约0.27，证明低秩技术在近期量子硬件上推进实用化量子图像处理的巨大潜力。
原文摘要 · Abstract (English)
In quantum image processing, a fundamental step is encoding classical image data into quantum states. This can be achieved using methods such as Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), and Novel Enhanced Quantum Representation (NEQR). However, on real quantum hardware, these encodings can quickly lead to circuits with many gates, large circuit depth, and high qubit usage, which is a problem for Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we investigate whether low-rank state approximation, formulated via Schmidt decomposition, can help reduce this complexity. The method keeps only the most significant parts of a quantum state's entanglement structure, making state preparation more efficient while preserving most of the image information. We compare the three encoding techniques in their original form and with low-rank approximation, evaluating metrics such as circuit depth, CNOT count, MSE, and visual quality of reconstructed images. The results reveal meaningful trade-offs between accuracy and resource efficiency, with the FRQI model achieving a 97 percent reduction in circuit depth while maintaining a near-perfect reconstruction (MSE of about 0.27). This demonstrates the potential of low-rank techniques for advancing practical quantum image processing on near-term hardware.
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