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

Cousins

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”, (2022) arXiv:2205.09141
[6]
L. Fidkowski and M. B. Hastings, “Pumping Chirality in Three Dimensions”, (2023) arXiv:2309.15903
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Zoo Code ID: 3d_bosonization

Cite as:
“3D bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/3d_bosonization
BibTeX:
@incollection{eczoo_3d_bosonization, title={3D bosonization code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/3d_bosonization} }
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Permanent link:
https://errorcorrectionzoo.org/c/3d_bosonization

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.