2D bosonization code[1,2] 

Description

A mapping between a 2D lattice of qubits and a 2D lattice quadratic Hamiltonian of Majorana modes. The original code [1] can be converted via Clifford operations into codes whose distance runs up to \(7\) while preserving the code rate [2]. This family also includes a super-compact fermionic encoding with a qubit-to-fermion ratio of \(1.25\) [2; Table I].

Encoding

Tensor-network realization [3], extended to periodic boundary conditions and sectors of odd fermionic charge [4].

Parent

Child

Cousins

  • Jordan-Wigner transformation code — The 2D bosonization code can be converted into chains of JW-transformed qubits by a linear-depth circuit [2; Fig. 24].
  • Kitaev honeycomb code — While the Kitaev honeycomb model is bosonic, a fermion-into-qubit mapping is useful for solving and understanding the model. This fermion-into-qubit encoding that can be converted to a 2D bosonization code by converting to a relabeled square lattice and performing single-qubit rotations [1][2; Sec. IV.B].

References

[1]
Y.-A. Chen, A. Kapustin, and Đ. Radičević, “Exact bosonization in two spatial dimensions and a new class of lattice gauge theories”, Annals of Physics 393, 234 (2018) arXiv:1711.00515 DOI
[2]
Y.-A. Chen and Y. Xu, “Equivalence between Fermion-to-Qubit Mappings in two Spatial Dimensions”, PRX Quantum 4, (2023) arXiv:2201.05153 DOI
[3]
S. K. Shukla, T. D. Ellison, and L. Fidkowski, “Tensor network approach to two-dimensional bosonization”, Physical Review B 101, (2020) arXiv:1909.10552 DOI
[4]
O. O’Brien, L. Lootens, and F. Verstraete, “Local Jordan-Wigner transformations on the torus”, (2024) arXiv:2404.07727
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Zoo Code ID: 2d_bosonization

Cite as:
“2D bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/2d_bosonization
BibTeX:
@incollection{eczoo_2d_bosonization, title={2D bosonization code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/2d_bosonization} }
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Cite as:

“2D bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/2d_bosonization

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fermion_into_qubit/bosonization/2d_bosonization.yml.