Description
A mapping between a 2D lattice of qubits and a 2D lattice quadratic Hamiltonian of Majorana modes. This family also includes a super-compact fermionic encoding with a qubit-to-fermion ratio of \(1.25\) [2; Table I].Protection
The original code [1] can be converted via Clifford operations into codes whose distance runs up to \(7\) while preserving the code rate [3].Encoding
Tensor-network realization [4], extended to periodic boundary conditions and sectors of odd fermionic charge [5].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].
Member of code lists
Primary Hierarchy
Parents
2D bosonization code
Children
The BKSF code is a distance-two 2D bosonization code for a specific edge ordering [2].
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]
- Y.-A. Chen, A. V. Gorshkov, and Y. Xu, “Error-correcting codes for fermionic quantum simulation”, SciPost Physics 16, (2024) arXiv:2210.08411 DOI
- [4]
- 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
- [5]
- O. O’Brien, L. Lootens, and F. Verstraete, “Local Jordan-Wigner transformations and topological sectors on the torus”, Physical Review B 111, (2025) arXiv:2404.07727 DOI
Page edit log
- Victor V. Albert (2024-03-20) — most recent
Cite as:
“2D bosonization code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/2d_bosonization