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].
Cousins
- Haah cubic code (CC)— Bosonization can be used to realize a Haah cubic code with an emergent fermion from a Majorana stabilizer code [2]. This code is shown to be distinct from the original code [4].
- Fibonacci fractal spin-liquid code— Bosonization can be used to realize a Fibonacci fractal spin-liquid code with an emergent fermion from a Majorana stabilizer code [2]. This code is shown to be distinct from the original code [4].
- X-cube model code— Bosonization can be used to realize a X-cube model code with an emergent fermion from a Majorana stabilizer code [2], but this model has the same stabilizer group as the original X-cube model [3].
- Three-fermion (3F) Walker-Wang model code— The 3F Walker-Wang QCA encoder [5,6] can be extended to SPTs in higher dimensions based on an exact bosonization duality [7].
Member of code lists
Primary Hierarchy
References
- [1]
- Y.-A. Chen, “Exact bosonization in arbitrary dimensions”, Physical Review Research 2, (2020) arXiv:1911.00017 DOI
- [2]
- 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
- [3]
- W. Shirley, “Fractonic order and emergent fermionic gauge theory”, (2020) arXiv:2002.12026
- [4]
- H. Song, N. Tantivasadakarn, W. Shirley, and M. Hermele, “Fracton Self-Statistics”, Physical Review Letters 132, (2024) arXiv:2304.00028 DOI
- [5]
- 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
- [6]
- J. Haah, “Topological Phases of Unitary Dynamics: Classification in Clifford Category”, Communications in Mathematical Physics 406, (2025) arXiv:2205.09141 DOI
- [7]
- L. Fidkowski, J. Haah, and M. B. Hastings, “A QCA for every SPT”, (2024) arXiv:2407.07951
Page edit log
- Nathanan Tantivasadakarn (2025-06-18) — most recent
- Victor V. Albert (2024-03-26)
Cite as:
“Bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/bosonization