Alternative names: Anisotropic lineon code.
Description
A type-I fracton code obtained by gauging [2–11] a 3D paramagnet with planar subsystem symmetries in two directions. In that construction, the gauge charges are lineons and the flux excitations are also lineons moving in the same direction, yielding the anisotropic lineon model [2; Sec. 4.1.2].Gates
The code admits a cup product structure and admits a logical CZ gate from physical CZ gates [12].Cousins
- Plaquette Ising code— The two-foliated fracton code is a hypergraph product of the repetition code and the plaquette Ising code on a square lattice with periodic boundary conditions [12].
- Repetition code— The two-foliated fracton code is a hypergraph product of the repetition code and the plaquette Ising code on a square lattice with periodic boundary conditions [12].
- Symmetry-protected topological (SPT) code— Gauging a 3D paramagnet with planar subsystem symmetries in two directions yields the anisotropic lineon model; each symmetry charge becomes a lineon gauge charge, while certain pairs become planons [2; Sec. 4.1.2].
Primary Hierarchy
Generalized homological-product qubit CSS codeQLDPC Qubit Generalized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Hypergraph product (HGP) codeQLDPC CSS Generalized homological-product Lattice stabilizer Stabilizer Hamiltonian-based Qubit QECC Quantum
Parents
The two-foliated fracton code is a hypergraph product of the repetition code and the plaquette Ising code on a square lattice with periodic boundary conditions [12].
The two-foliated fracton code is a foliated type-I fracton code.
Two-foliated fracton code
References
- [1]
- W. Shirley, K. Slagle, and X. Chen, “Fractional excitations in foliated fracton phases”, Annals of Physics 410, 167922 (2019) arXiv:1806.08625 DOI
- [2]
- W. Shirley, K. Slagle, and X. Chen, “Foliated fracton order from gauging subsystem symmetries”, SciPost Physics 6, (2019) arXiv:1806.08679 DOI
- [3]
- M. Levin and Z.-C. Gu, “Braiding statistics approach to symmetry-protected topological phases”, Physical Review B 86, (2012) arXiv:1202.3120 DOI
- [4]
- J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, “Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems”, Physical Review X 5, (2015) arXiv:1407.1025 DOI
- [5]
- S. Vijay, J. Haah, and L. Fu, “Fracton topological order, generalized lattice gauge theory, and duality”, Physical Review B 94, (2016) arXiv:1603.04442 DOI
- [6]
- D. J. Williamson, “Fractal symmetries: Ungauging the cubic code”, Physical Review B 94, (2016) arXiv:1603.05182 DOI
- [7]
- L. Bhardwaj, D. Gaiotto, and A. Kapustin, “State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter”, Journal of High Energy Physics 2017, (2017) arXiv:1605.01640 DOI
- [8]
- A. Kubica and B. Yoshida, “Ungauging quantum error-correcting codes”, (2018) arXiv:1805.01836
- [9]
- K. Dolev, V. Calvera, S. S. Cree, and D. J. Williamson, “Gauging the bulk: generalized gauging maps and holographic codes”, Journal of High Energy Physics 2022, (2022) arXiv:2108.11402 DOI
- [10]
- T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes I. Gauging and dualities”, (2023) arXiv:2310.16032
- [11]
- D. J. Williamson and T. J. Yoder, “Low-overhead fault-tolerant quantum computation by gauging logical operators”, (2024) arXiv:2410.02213
- [12]
- N. P. Breuckmann, M. Davydova, J. N. Eberhardt, and N. Tantivasadakarn, “Cups and Gates I: Cohomology invariants and logical quantum operations”, (2025) arXiv:2410.16250
Page edit log
- Victor V. Albert (2025-01-16) — most recent
Cite as:
“Two-foliated fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/two_foliated