Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
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Quantum Physics arXiv:2606.25048 (quant-ph) [Submitted on 23 Jun 2026] Title:Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases Authors:Meng Sun, Zongyuan Wang, Nathanan Tantivasadakarn, Yu-An Chen View a PDF of the paper titled Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases, by Meng Sun and 3 other authors View PDF Abstract:Stabilizer codes provide exact lattice realizations of bosonic topological orders. In contrast, systematic stabilizer descriptions of intrinsically fermionic topological phases remain much less developed. In this work, we introduce Majorana-Pauli stabilizer codes, a class of exactly solvable fermionic lattice models whose stabilizers are built from both generalized Pauli operators and Majorana operators. As a main example, we construct an exactly solvable stabilizer realization of the fermionic toric code: an intrinsically fermionic $\mathbb Z_2$ topological order in $(2{+}1)$ dimensions, using $\mathbb Z_8$ Pauli operators coupled to Majorana modes. Within this stabilizer framework, the anyons, string operators, fusion rules, and braiding statistics all follow naturally from the stabilizer algebra. More broadly, we show that the fermionic toric code belongs to a duality web generated by anyon condensation and by gauging bosonic or fermion-parity symmetries. This web connects bosonic topological orders, symmetry-enriched topological phases, and both bosonic and fermionic symmetry-protected topological phases, all within a common stabilizer description. We further show that the construction extends to all Abelian fermionic topological orders with gapped boundaries and to all supercohomology fermionic SPT phases in $(2{+}1)$ dimensions. Going beyond Majorana operators, we introduce fermionic versions of the clock and shift operators and use them to construct an exact bosonization map for $\mathbb Z_D^F$ symmetries for $D$ even. Using this, we realize a stabilizer model for a nontrivial $\mathbb Z_8^F$ fermionic SPT phase with no free-fermion analog. Altogether, these results extend the stabilizer-code paradigm to a broad class of intrinsically fermionic phases bridging fermionic quantum many-body physics to quantum error correction. Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph) Cite as: arXiv:2606.25048 [quant-ph] (or arXiv:2606.25048v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.25048 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Meng Sun [view email] [v1] Tue, 23 Jun 2026 18:03:51 UTC (184 KB) Full-text links: Access Paper: View a PDF of the paper titled Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases, by Meng Sun and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.str-el math math-ph math.MP 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?)