Description
2D subsystem stabilizer code whose low-energy excitations realize the three-fermion anyon theory [1,3,4]. One version uses two qubits at each site [2], while other manifestations utilize a single qubit per site and only two-body interactions [1,5]. All are expected to be equivalent to each other via a local constant-depth Clifford circuit.
Parents
- Subsystem qubit stabilizer code
- Lattice subsystem code
- Abelian topological code — The 3F code is a subsystme code characterized by 3F topological order [2], which is chiral and modular.
Cousins
- Kitaev surface code — One version of the 3F subsystem code can be obtained from two copies of the square-lattice surface code by gauging out the anyons \(e_1m_1e_2\) and \(e_2m_2\) [2; Sec. 7.4].
- Three-fermion (3F) Walker-Wang model code — The (three-dimensional) 3F Walker-Wang model cluster-like state encodes the temporal gate operations on the (two-dimensional) 3F subsystem code into a third spatial dimension [6].
- 2D color code — The 2D color code is equivalent to two decoupled copies of the 3F code in the sense that the same anyon theory describes the low-energy excitations of both codes [8][7; Appx. B].
References
- [1]
- H. Bombin, M. Kargarian, and M. A. Martin-Delgado, “Interacting anyonic fermions in a two-body color code model”, Physical Review B 80, (2009) arXiv:0811.0911 DOI
- [2]
- T. D. Ellison et al., “Pauli topological subsystem codes from Abelian anyon theories”, Quantum 7, 1137 (2023) arXiv:2211.03798 DOI
- [3]
- E. Rowell, R. Stong, and Z. Wang, “On classification of modular tensor categories”, (2009) arXiv:0712.1377
- [4]
- H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes”, New Journal of Physics 14, 073048 (2012) arXiv:1103.4606 DOI
- [5]
- H. Bombin, “Topological subsystem codes”, Physical Review A 81, (2010) arXiv:0908.4246 DOI
- [6]
- S. Roberts and D. J. Williamson, “3-Fermion Topological Quantum Computation”, PRX Quantum 5, (2024) arXiv:2011.04693 DOI
- [7]
- M. S. Kesselring et al., “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum 2, 101 (2018) arXiv:1806.02820 DOI
- [8]
- Zhenghan Wang. private communication, 2017.
Page edit log
- Nathanan Tantivasadakarn (2024-03-26) — most recent
- Victor V. Albert (2021-12-29)
Cite as:
“Three-fermion (3F) subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/subsystem_three_fermion