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].

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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
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Zoo Code ID: bosonization

Cite as:
“Bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bosonization
BibTeX:
@incollection{eczoo_bosonization, title={Bosonization code}, booktitle={The Error Correction Zoo}, year={2024}, 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.), 2024. https://errorcorrectionzoo.org/c/bosonization

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