Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
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 ℤ2 topological order in (2+1) dimensions, using ℤ8 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 or ungauging bosonic or fermionic symmetries. This web connects bosonic topological orders, symmetry-enriched topological (SET) phases, and both bosonic and fermionic symmetry-protected topological (SPT) phases, all within a common stabilizer description. We extend this construction to all Abelian fermionic topological orders with gapped boundaries and to fermionic SPT phases whose fully gauged theories are Abelian. Going beyond Majorana operators, we introduce fermionic versions of the clock and shift operators and use them to construct an exact bosonization map for ℤDF symmetries for D even. Using this, we realize a stabilizer model for a nontrivial ℤ8F 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.
Related
- Classification of order-two T-duality orbifolds at the SO(12) free fermionic point
- Non-invertible SPT phases from fusion rings via Tannaka duality
- Topological Quantum Spin Liquids in a Ladder with Majorana fermions and p-wave Superconductivity
- Provable circuit-level thresholds for non-abelian topological phases
- On a topological duality for Stonean Hilbert algebras
BibTeX
@misc{sun2026majoranapauli,
title = {{Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases}},
author = {Meng Sun and Zongyuan Wang and Nathanan Tantivasadakarn and Yu-An Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.25048},
eprint = {2606.25048},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25048},
}
RIS
TY - UNPB
TI - Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
AU - Meng Sun
AU - Zongyuan Wang
AU - Nathanan Tantivasadakarn
AU - Yu-An Chen
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.25048
UR - https://arxiv.org/abs/2606.25048
AB - 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 ℤ_2 topological order in (2+1) dimensions, using 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 or ungauging bosonic or fermionic symmetries. This web connects bosonic topological orders, symmetry-enriched topological (SET) phases, and both bosonic and fermionic symmetry-protected topological (SPT) phases, all within a common stabilizer description. We extend this construction to all Abelian fermionic topological orders with gapped boundaries and to fermionic SPT phases whose fully gauged theories are Abelian. Going beyond Majorana operators, we introduce fermionic versions of the clock and shift operators and use them to construct an exact bosonization map for ℤ_D^F symmetries for D even. Using this, we realize a stabilizer model for a nontrivial 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.
ER -