When Noisy Quantum Order Finding Remains Recoverable for Shor's Algorithm
Year: 2026
Type: conference-paper
Abstract: Order finding is the core subroutine of Shor’s algorithm. On NISQ hardware, its 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 collected from IBM quantum systems across multiple problem instances and circuit settings. For each distribution, we apply continued-fraction post-processing with modular verification and define recoverability as a binary outcome according to whether the recovered order equals the true one. We then 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 further use random-forest permutation importance to assess which quantities contribute distinct predictive information once the other features are known. To make the resulting classification behavior interpretable, we also train a decision tree that exposes threshold rules for recoverable and non-recoverable distributions. We find that recoverability is strongly associated with both 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 the tree-based analysis shows that 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.
Authors: Qingxin Yang, Stefano Markidis
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7166661262