发表机构
Institute of Science Tokyo（东京科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子启发的张量网络电路作为可训练变换用于图像修复，其对角QFT松弛可逆且计算高效，通过无约束梯度相位优化学习，以更少参数达到优于固定变换并匹配大型酉架构的性能。
AI 中文摘要
本文引入了量子启发的张量网络电路作为图像修复的可训练变换。在所提出的架构中，对角量子傅里叶变换（QFT）松弛是可逆的，对于$N\times N$图像的计算成本为$O(N^2 \log N)$，通过其电路结构在训练过程中固有地保持最小相干性，从而无需显式的相干性惩罚。无约束的基于梯度的相位优化（无需黎曼优化）能够从随机采样的训练数据中高效学习，使学习到的变换能够泛化到通过固定采样掩码观测的测试图像。数值测试表明，学习到的模型优于固定变换和逐图像优化，同时匹配更大规模酉架构的性能，但参数数量却少得多。
英文摘要
This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting. Among the proposed architectures, the diagonal quantum Fourier transform (QFT) relaxation is invertible with $O(N^2 \log N)$ computational cost for $N\times N$ images, inherently preserving minimum coherence throughout training via its circuit structure and eliminating the need for explicit coherence penalties. Unconstrained gradient-based phase optimization (Riemannian-optimization free) enables efficient learning from randomly sampled training data, allowing the learned transform to generalize to test images observed through fixed sampling masks. Numerical tests show that the learned models outperform fixed transforms and per-image optimization while matching the performance of much larger unitary architectures, yet with far fewer parameters.
Comments5 pages, 3 figures, 1 table. Submitted to ICASSP 2027
