Quantum Process Realization of LDPC Code Dualities and Product Constructions

Quantum Physics [Submitted on 13 Mar 2026] Quantum Process Realization of LDPC Code Dualities and Product Constructions Shuhan Zhang, Deepak Aryal, Yi-Zhuang You We realize a broad class of code constructions, including Kramers-Wannier duality, tensor product, and check product, as quantum processes consisting of ancilla initialization, local unitaries, and projective measurements. Using ZX-calculus, we represent these transformations diagrammatically and provide a systematic algorithm for extracting quantum circuits. Central to our framework is the observation that the physical content of a classical LDPC code is captured by the operator algebra associated with its Tanner graph, and that code transformations correspond to maps between such algebras. Kramers-Wannier duality then admits a natural interpretation as gauging, while tensor and check products correspond to coupled-layer constructions in which interlayer coupling and projection implement a quotient on stacked operator algebras. Together, these results establish a unified framework connecting code transformations, quantum circuits, and mappings between distinct quantum phases of matter. Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2603.13538 [quant-ph]   (or arXiv:2603.13538v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.13538 Focus to learn more Submission history From: Yi-Zhuang You [view email] [v1] Fri, 13 Mar 2026 19:21:05 UTC (661 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.str-el 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?)