Derby-Klassen (DK) code[1,2] 

Also known as Compact encoding.


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].


Some single-qubit errors are detectable, with the rest inducing low-weight fermionic dephasing noise [4].



  • 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].


C. Derby et al., “Compact fermion to qubit mappings”, Physical Review B 104, (2021) arXiv:2003.06939 DOI
C. Derby and J. Klassen, “A Compact Fermion to Qubit Mapping Part 2: Alternative Lattice Geometries”, (2021) arXiv:2101.10735
L. Clinton et al., “Towards near-term quantum simulation of materials”, Nature Communications 15, (2024) arXiv:2205.15256 DOI
J. Bausch et al., “Mitigating Errors in Local Fermionic Encodings”, (2020) arXiv:2003.07125
D. Zhang and T. Cubitt, “Quantum Error Transmutation”, (2023) arXiv:2310.10278
R. W. Chien and J. D. Whitfield, “Custom fermionic codes for quantum simulation”, (2020) arXiv:2009.11860
Derby, Charles. Compact fermion to qubit mappings for quantum simulation. Diss. UCL (University College London), 2023.
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Zoo Code ID: derby_klassen

Cite as:
“Derby-Klassen (DK) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.
@incollection{eczoo_derby_klassen, title={Derby-Klassen (DK) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Derby-Klassen (DK) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.