Bravyi-Kitaev superfast (BKSF) code[1]
Also known as Loop-stabilized fermion simulation (LSFS) code.
Description
An single error-detecting fermion-into-qubit encoding defined on 2D qubit lattice whose stabilizers are associated with loops in the lattice. The code can be generalized to a single error-correcting code (i.e., with distance three) on graphs of degree \(\geq 6\) [2].
Protection
The code can detect single-qubit errors [3]. A generalized BKSF code has distance 3 on a graph with degree \(\geq 6\), while original BKSF code cannot correct single-qubit errors on graphs of degree \(< 6\) [2].
Parents
- Majorana loop stabilizer code (MLSC) — The BKSF code can be thought of as a particular MLSC [3].
- 2D bosonization code — The BKSF code is a distance-two 2D bosonization code for a specific edge ordering [4].
References
- [1]
- S. B. Bravyi and A. Yu. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002) arXiv:quant-ph/0003137 DOI
- [2]
- K. Setia, S. Bravyi, A. Mezzacapo, and J. D. Whitfield, “Superfast encodings for fermionic quantum simulation”, Physical Review Research 1, (2019) arXiv:1810.05274 DOI
- [3]
- Z. Jiang, J. McClean, R. Babbush, and H. Neven, “Majorana Loop Stabilizer Codes for Error Mitigation in Fermionic Quantum Simulations”, Physical Review Applied 12, (2019) arXiv:1812.08190 DOI
- [4]
- Y.-A. Chen and Y. Xu, “Equivalence between Fermion-to-Qubit Mappings in two Spatial Dimensions”, PRX Quantum 4, (2023) arXiv:2201.05153 DOI
Page edit log
- Victor V. Albert (2024-03-20) — most recent
Cite as:
“Bravyi-Kitaev superfast (BKSF) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bksf