Qingxin Yang

Qingxin Yang, Stefano Markidis

Order finding is the core subroutine of Shor's algorithm. On NISQ hardware, phase estimation output distributions are often distorted by noise, making correct order recovery difficult. We study recoverability in noisy order finding: given a measured precision-register distribution, when does standard classical post-processing still return the true order? We analyze 680 distributions from IBM quantum systems across problem instances and circuit settings. For each distribution, we apply continued-fraction post-processing with modular verification and define recoverability as whether the recovered order equals the true one. We characterize each distribution using four features: autocorrelation peak strength, normalized entropy, dominant verified mass fraction, and verified margin fraction. We evaluate these quantities using marginal feature comparisons, single-feature AUROC analysis, and multivariate tree-based classifiers. We use random-forest permutation importance to assess which quantities contribute distinct predictive information once the other features are known. To make classification behavior interpretable, we train a decision tree that exposes threshold rules for recoverable and non-recoverable distributions. We find that recoverability is strongly associated with residual comb-like structure in the measured distribution and the way verified probability mass is organized across candidate denominators. The dominant verified mass fraction is the strongest single-feature indicator of recoverability, and tree-based analysis shows it also provides the primary split in an interpretable threshold description. Some highly distorted distributions remain recoverable when one verified denominator dominates the post-processing mass, while some visibly structured distributions fail because classical post-processing favors an incorrect verified denominator.

Ruizhe Wang, Chunliang Hua, Tomakayev Shingys et al.

The photorealistic reconstruction and rendering of architectural scenes have extensive applications in industries such as film, games, and transportation. It also plays an important role in urban planning, architectural design, and the city's promotion, especially in protecting historical and cultural relics. The 3D Gaussian Splatting, due to better performance over NeRF, has become a mainstream technology in 3D reconstruction. Its only input is a set of images but it relies heavily on geometric parameters computed by the SfM process. At the same time, there is an existing abundance of raw 3D models, that could inform the structural perception of certain buildings but cannot be applied. In this paper, we propose a straightforward method to harness these raw 3D models to guide 3D Gaussians in capturing the basic shape of the building and improve the visual quality of textures and details when photos are captured non-systematically. This exploration opens up new possibilities for improving the effectiveness of 3D reconstruction techniques in the field of architectural design.

Yiling Liu, Qiegen Liu, Minghui Zhang et al.

To improve the compressive sensing MRI (CS-MRI) approaches in terms of fine structure loss under high acceleration factors, we have proposed an iterative feature refinement model (IFR-CS), equipped with fixed transforms, to restore the meaningful structures and details. Nevertheless, the proposed IFR-CS still has some limitations, such as the selection of hyper-parameters, a lengthy reconstruction time, and the fixed sparsifying transform. To alleviate these issues, we unroll the iterative feature refinement procedures in IFR-CS to a supervised model-driven network, dubbed IFR-Net. Equipped with training data pairs, both regularization parameter and the utmost feature refinement operator in IFR-CS become trainable. Additionally, inspired by the powerful representation capability of convolutional neural network (CNN), CNN-based inversion blocks are explored in the sparsity-promoting denoising module to generalize the sparsity-enforcing operator. Extensive experiments on both simulated and in vivo MR datasets have shown that the proposed network possesses a strong capability to capture image details and preserve well the structural information with fast reconstruction speed.