Also known as Compact encoding.
Description
A fermion-into-qubit code defined on regular tilings with maximum degree 4 whose stabilizers are associated with loops in the tiling. The code outperforms several other encodings in terms of encoding rate [1; Table I]. It has been extended for models with several modes per site [3].
Protection
Some single-qubit errors are detectable, with the rest inducing low-weight fermionic dephasing noise [4].
Parents
- Quantum error-transmuting code (QETC) — The DK code transmutes all single-qubit errors [5].
- Fermion-into-qubit code
Cousins
- XZZX surface code — The DK code encodes fermions into excitations of the Wen plaquette model [6].
- 2D color code — The DK code on several tilings resembles the 2D color code with some vertex qubits removed [7].
References
- [1]
- C. Derby et al., “Compact fermion to qubit mappings”, Physical Review B 104, (2021) arXiv:2003.06939 DOI
- [2]
- C. Derby and J. Klassen, “A Compact Fermion to Qubit Mapping Part 2: Alternative Lattice Geometries”, (2021) arXiv:2101.10735
- [3]
- L. Clinton et al., “Towards near-term quantum simulation of materials”, Nature Communications 15, (2024) arXiv:2205.15256 DOI
- [4]
- J. Bausch et al., “Mitigating Errors in Local Fermionic Encodings”, (2020) arXiv:2003.07125
- [5]
- D. Zhang and T. Cubitt, “Quantum Error Transmutation”, (2023) arXiv:2310.10278
- [6]
- R. W. Chien and J. D. Whitfield, “Custom fermionic codes for quantum simulation”, (2020) arXiv:2009.11860
- [7]
- Derby, Charles. Compact fermion to qubit mappings for quantum simulation. Diss. UCL (University College London), 2023.
Page edit log
- Victor V. Albert (2024-03-20) — most recent
Cite as:
“Derby-Klassen (DK) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/derby_klassen