SDP bounds on quantum codes: rational certificates

Quantum Physics [Submitted on 20 Mar 2026] SDP bounds on quantum codes: rational certificates Gerard Anglès Munné, Felix Huber A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum linear programming bounds. However, floating-point inaccuracies prevent the extraction of rigorous non-existence proofs from the numerical methods. Here, we address this by providing rational infeasibility certificates for a range of quantum codes. Using a clustered low-rank solver with heuristic rounding to algebraic expressions, we can improve upon 18 upper bounds on the maximum size of n-qubit codes with 6 \leq n \leq 19. Our work highlights the practicality and scalability of semidefinite programming for quantum coding bounds. Comments: 16 Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2603.19901 [quant-ph]   (or arXiv:2603.19901v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.19901 Focus to learn more Submission history From: Gerard Anglès Munné [view email] [v1] Fri, 20 Mar 2026 12:33:38 UTC (125 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT 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?)