Distance-Finding Algorithms for Quantum Codes and Circuits

Quantum Physics [Submitted on 23 Mar 2026] Distance-Finding Algorithms for Quantum Codes and Circuits Mark Webster, Abraham Jacob, Oscar Higgott The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum computation, but calculating their distance is challenging with existing methods. We generally assess the performance of a quantum code under circuit level error models, and for such scenarios the circuit distance is an important consideration. Calculating circuit distance is in general more difficult than finding the distance of the corresponding code as the detector error matrix of the circuit is usually much larger than the code's check matrix. In this work, we benchmark a wide range of distance-finding methods for various classical and quantum code families, as well as syndrome-extraction circuits. We consider both exact methods (such as Brouwer-Zimmermann, connected cluster, SAT and mixed integer programming) and heuristic methods which have lower run-time but can only give a bound on distance (examples include random information set, syndrome decoder algorithms, and Stim undetectable error methods). We further develop the QDistEvol algorithm and show that it performs well for the quantum LDPC codes in our benchmark. The algorithms and test data have been made available to the community in the codeDistance Python package. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.22532 [quant-ph]   (or arXiv:2603.22532v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22532 Focus to learn more Submission history From: Mark Webster [view email] [v1] Mon, 23 Mar 2026 19:52:23 UTC (10,517 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)