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Bosonization code[13]

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].

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
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Zoo Code ID: bosonization

Cite as:
“Bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/bosonization
BibTeX:
@incollection{eczoo_bosonization, title={Bosonization code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bosonization} }
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Permanent link:
https://errorcorrectionzoo.org/c/bosonization

Cite as:

“Bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/bosonization

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fermion_into_qubit/bosonization/bosonization.yml.