SAT, MaxSAT, and SMT for QLDPC Distance Computation: A Large-Scale Empirical Study
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Quantum Physics arXiv:2606.12445 (quant-ph) [Submitted on 29 May 2026] Title:SAT, MaxSAT, and SMT for QLDPC Distance Computation: A Large-Scale Empirical Study Authors:Yu-Fang Chen, Seyed Mohammad Reza Jafari, Ching-Yi Lai View a PDF of the paper titled SAT, MaxSAT, and SMT for QLDPC Distance Computation: A Large-Scale Empirical Study, by Yu-Fang Chen and Seyed Mohammad Reza Jafari and Ching-Yi Lai View PDF HTML (experimental) Abstract:Exact distance computation for quantum LDPC (QLDPC) codes plays a central role in validating candidate fault-tolerant quantum-code constructions, yet the computational structure of this problem remains poorly understood. Despite substantial recent progress in QLDPC design, it remains unclear which algorithmic principles govern the practical scalability of exact distance computation and which classes of exact solvers are best suited to this task. To address these questions, we conduct a systematic study of SAT- and MaxSAT-based formulations for exact QLDPC distance computation across representative codes. We further compare these formulations against several established exact-distance approaches in order to better understand the algorithmic landscape of exact QLDPC distance computation. Our study challenges and refines several prevailing intuitions about exact QLDPC distance computation. First, despite the XOR-rich structure of QLDPC parity checks, practical scalability appears to be governed more by the handling of cardinality constraints and optimization bounds than by parity reasoning alone. Accordingly, XOR-aware reasoning does not provide a systematic advantage across our benchmark suite. Second, Brouwer-Zimmermann-style search, long regarded as the benchmark paradigm for exact distance computation in sparse classical codes, no longer maintains its traditional scalability advantage in the QLDPC setting. This finding challenges the expectation that techniques successful for sparse classical codes remain dominant for QLDPC codes. Third, substantial qualitative differences arise even among MaxSAT solvers themselves. Branch-and-bound MaxSAT significantly outperforms unsat-core-based MaxSAT on challenging benchmarks, demonstrating that solver architecture and optimization strategy play a decisive role in practical scalability. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT); Programming Languages (cs.PL) Cite as: arXiv:2606.12445 [quant-ph] (or arXiv:2606.12445v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12445 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yu-Fang Chen [view email] [v1] Fri, 29 May 2026 15:34:33 UTC (154 KB) Full-text links: Access Paper: View a PDF of the paper titled SAT, MaxSAT, and SMT for QLDPC Distance Computation: A Large-Scale Empirical Study, by Yu-Fang Chen and Seyed Mohammad Reza Jafari and Ching-Yi LaiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.IT cs.PL math math.IT References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)