3D bosonization code

3D bosonization code[1]

Description

A mapping that maps a 3D lattice quadratic Hamiltonian of Majorana modes into a lattice of qubits which realize a \(\mathbb{Z}_2\) gauge theory with a particular Gauss law.

Parent

Bosonization code

Cousins

3D fermionic surface code — The 3D fermionic surface code is the result of applying the 3D bosonization mapping to a trivial fermonic theory [2]. Twist defects in the 3D fermionic surface code take the form of Kitaev chains after the mapping [2,3].
Three-fermion (3F) Walker-Wang model code — The 3F QCA encoder [4,5] can be simplified using bosonization [6].

References

[1]: Y.-A. Chen and A. Kapustin, “Bosonization in three spatial dimensions and a 2-form gauge theory”, Physical Review B 100, (2019) arXiv:1807.07081 DOI
[2]: M. Barkeshli et al., “Codimension-2 defects and higher symmetries in (3+1)D topological phases”, SciPost Physics 14, (2023) arXiv:2208.07367 DOI
[3]: P. Webster and S. D. Bartlett, “Fault-tolerant quantum gates with defects in topological stabilizer codes”, Physical Review A 102, (2020) arXiv:1906.01045 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 and M. B. Hastings, “Pumping Chirality in Three Dimensions”, (2023) arXiv:2309.15903

Page edit log

Victor V. Albert (2024-03-26) — most recent

Cite as:

“3D bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/3d_bosonization

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fermion_into_qubit/bosonization/3d_bosonization.yml.