Description
A mapping that maps a \(D\)-dimensional lattice quadratic Hamiltonian of Majorana modes into a lattice of qubits. The resulting qubit code can realize various topological phases, depending on the initial Majorana-mode Hamiltonian and its symmetries.
A general mapping for quadratic Hamiltonians was constructed in Ref. [1], while others considered higher-order products of Majorana modes that correspond to symmetry constraints [2,3].
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Children
Cousin
- Three-fermion (3F) Walker-Wang model code — The 3F QCA encoder [4,5] can be extended to SPTs in higher dimensions based on an exact bosonization duality [6].
References
- [1]
- Y.-A. Chen, “Exact bosonization in arbitrary dimensions”, Physical Review Research 2, (2020) arXiv:1911.00017 DOI
- [2]
- W. Shirley, “Fractonic order and emergent fermionic gauge theory”, (2020) arXiv:2002.12026
- [3]
- N. Tantivasadakarn, “Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension: Emergent fermions in fracton topological order”, Physical Review Research 2, (2020) arXiv:2002.11345 DOI
- [4]
- J. Haah, L. Fidkowski, and M. B. Hastings, “Nontrivial Quantum Cellular Automata in Higher Dimensions”, Communications in Mathematical Physics 398, 469 (2022) arXiv:1812.01625 DOI
- [5]
- J. Haah, “Topological phases of unitary dynamics: Classification in Clifford category”, (2024) arXiv:2205.09141
- [6]
- L. Fidkowski, J. Haah, and M. B. Hastings, “A QCA for every SPT”, (2024) arXiv:2407.07951
Page edit log
- Victor V. Albert (2024-03-26) — most recent
Cite as:
“Bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bosonization