Description
Group-based code realizing a 3D topological order rendered by a Dijkgraaf-Witten gauge theory. The corresponding anyon theory is defined by a finite group \(G\) and a Type-IV group cocycle \(\omega\). Canonical TQD models [1,2] and other formulations whose ground states are in the same phase are all defined on group-valued qudits .
Boundaries and excitations have been studied in Refs. [5–7]. Gapped boundaries are classified by a subgroup \(K \subseteq G\) and a particular three-cochain [5]. Generalizations of Ocneanu's tube algebras [8,9] can be used to characterize excitations, which are described by the tube algebra of the category \(\text{Vec}^{\omega}(G)\) [10,11].
Cousin
- Twisted quantum double (TQD) code— The TQT model can be thought of as a 3D version of the TQD model.
Member of code lists
Primary Hierarchy
References
- [1]
- A. Mesaros and Y. Ran, “Classification of symmetry enriched topological phases with exactly solvable models”, Physical Review B 87, (2013) arXiv:1212.0835 DOI
- [2]
- S. Jiang, A. Mesaros, and Y. Ran, “Generalized Modular Transformations in(3+1)DTopologically Ordered Phases and Triple Linking Invariant of Loop Braiding”, Physical Review X 4, (2014) arXiv:1404.1062 DOI
- [3]
- J. C. Wang and X.-G. Wen, “Non-Abelian string and particle braiding in topological order: ModularSL(3,Z)representation and(3+1)-dimensional twisted gauge theory”, Physical Review B 91, (2015) arXiv:1404.7854 DOI
- [4]
- Y. Wan, J. C. Wang, and H. He, “Twisted gauge theory model of topological phases in three dimensions”, Physical Review B 92, (2015) arXiv:1409.3216 DOI
- [5]
- H. Wang, Y. Li, Y. Hu, and Y. Wan, “Gapped boundary theory of the twisted gauge theory model of three-dimensional topological orders”, Journal of High Energy Physics 2018, (2018) arXiv:1807.11083 DOI
- [6]
- A. Bullivant and C. Delcamp, “Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases”, Journal of High Energy Physics 2021, (2021) arXiv:2006.06536 DOI
- [7]
- J. Huxford, D. X. Nguyen, and Y. B. Kim, “Twisted Lattice Gauge Theory: Membrane Operators, Three-loop Braiding and Topological Charge”, (2024) arXiv:2401.13042
- [8]
- Ocneanu, Adrian. "Chirality for operator algebras." Subfactors (Kyuzeso, 1993) 39 (1994).
- [9]
- A. Ocneanu, “Operator Algebras, Topology and Subgroups of Quantum Symmetry – Construction of Subgroups of Quantum Groups –”, Advanced Studies in Pure Mathematics 235 DOI
- [10]
- A. Bullivant and C. Delcamp, “Tube algebras, excitations statistics and compactification in gauge models of topological phases”, Journal of High Energy Physics 2019, (2019) arXiv:1905.08673 DOI
- [11]
- T. Bartsch, M. Bullimore, and A. Grigoletto, “Representation theory for categorical symmetries”, (2023) arXiv:2305.17165
Page edit log
- Victor V. Albert (2025-09-25) — most recent
Cite as:
“Twisted quantum triple (TQT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/tqt