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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. 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].

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 codeQLDPC Lattice stabilizer Stabilizer Hamiltonian-based Qubit QECC Quantum
Majorana loop stabilizer code (MLSC)Fermion-into-qubit Stabilizer Hamiltonian-based Qubit QECC Quantum
Parents
Majorana loop stabilizer code (MLSC)
The BKSF code can be thought of as a particular MLSC [3].
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]
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
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Zoo Code ID: bksf

Cite as:
“Bravyi-Kitaev superfast (BKSF) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bksf
BibTeX:
@incollection{eczoo_bksf, title={Bravyi-Kitaev superfast (BKSF) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bksf} }
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Permanent link:
https://errorcorrectionzoo.org/c/bksf

Cite as:

“Bravyi-Kitaev superfast (BKSF) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bksf

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