AI 中文总结
该研究提出MPS模拟框架用于图像超分辨率的ANO-VQC，突破态矢模拟限制。通过GPU运行时基准测试、键维度扫描及Fashion-MNIST SR训练，表明MPS可扩展可控，能完成特定规模输入的特征提取，是研究大规模量子算法的实用工具。
AI 中文摘要
这项工作提出了一种矩阵乘积态（MPS）模拟框架，用于图像超分辨率（SR）中的自适应非局部可观测量变分量子电路（ANO-VQC），突破了态矢模拟的实际限制。在单个NVIDIA RTX 4070 GPU上的运行时基准测试表明，在测试的浅电路设置下，MPS能完成高达16×16像素（256量子比特）单个输入的ANO-VQC前向特征提取，而态矢模拟在6×6输入（36量子比特）时遇到内存瓶颈，精确张量网络（Exact TN）收缩在超过12×12输入（144量子比特）时计算上不切实际。对于固定的7×7输入（49量子比特），对深度L = 1到L = 4进行键维度扫描表明，所需的MPS键维度随电路深度增加。以Exact TN收缩为参考，近乎精确一致所需的键维度从L = 1时的χ = 2增加到L = 4时的χ = 16。最后，使用χ = 16对7×7到28×28的Fashion-MNIST SR进行训练表明，在测试深度中，浅L = 1模型实现了最低损失和最佳的LPIPS、PSNR和SSIM。这些结果突出了MPS作为ANO-VQC图像SR的可扩展和可控模拟后端以及研究大规模量子算法的实用工具。
英文摘要
This work presents a matrix product state (MPS) simulation framework for adaptive non-local observable variational quantum circuits (ANO-VQCs) in image super-resolution (SR) beyond the practical limits of statevector simulation. Runtime benchmarks on a single NVIDIA RTX 4070 GPU show that, under the tested shallow-circuit setting, MPS completes ANO-VQC forward feature extraction for individual inputs up to 16 x 16 pixels (256 qubits), whereas statevector simulation encounters a memory bottleneck at 6 x 6 inputs (36 qubits) and exact tensor-network (Exact TN) contraction becomes computationally impractical beyond 12 x 12 inputs (144 qubits). For a fixed 7 x 7 input (49 qubits), a bond-dimension sweep over depths L = 1 to L = 4 shows that the required MPS bond dimension increases with circuit depth. Using Exact TN contraction as the reference, the bond dimension required for near-exact agreement increases from chi = 2 at L = 1 to chi = 16 at L = 4. Finally, 7 x 7 to 28 x 28 Fashion-MNIST SR training with chi = 16 shows that the shallow L = 1 model achieves the lowest loss, lowest LPIPS, and highest PSNR and SSIM among the tested depths. These results highlight MPS as a scalable and controllable simulation backend for ANO-VQC image SR and as a practical tool for studying large-scale quantum algorithms.
