Bravyi-Kitaev superfast (BKSF) code

Bravyi-Kitaev superfast (BKSF) code[1]

Alternative Names: Loop-stabilized fermion simulation (LSFS) code.

Description

A single-error-detecting fermion-into-qubit encoding defined on a 2D qubit lattice whose stabilizers are associated with loops in the lattice. For the square-lattice edge ordering used in Ref. [2], the BKSF logical operators coincide with exact 2D bosonization on the dual lattice after relabeling \(X\) and \(Y\). The code can be generalized to a single error-correcting code (i.e., with distance three) on graphs of degree \(\geq 6\) [3].

Protection

The code can detect single-qubit errors [4]. 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 \(< 6\) [3].

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Union stabilizer (USt) codeQECC Quantum

Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Fermion-into-qubit code

Bosonization codeQLDPC Lattice stabilizer Stabilizer Hamiltonian-based Qubit QECC Quantum

2D bosonization codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum

Majorana loop stabilizer code (MLSC)

Parents

Majorana loop stabilizer code (MLSC)

The BKSF code can be thought of as a particular MLSC [4].

Bravyi-Kitaev superfast (BKSF) code

References

[1]: S. B. Bravyi and A. Yu. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002) arXiv:quant-ph/0003137 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]: 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
[4]: 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

Page edit log

Victor V. Albert (2026-06-08) — most recent
Victor V. Albert (2024-03-20)

Cite as:

“Bravyi-Kitaev superfast (BKSF) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bksf, arXiv:2606.11484

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