Ball-Verstraete-Cirac (BVC) code[1,2] 

Also known as Verstraete-Cirac code, Auxiliary fermion code.


A 2D fermion-into-qubit encoding that builds upon the JW transformation encoding by eliminating the weight-\(O(n)\) \(X\)-type string at the expense introducing additional qubits. See [3; Sec. IV.B] for details.


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



  • Rotated surface code — An appropriately chosen stabilizer generator set for the BVC code contains the stabilizers of the rotated surface code [6].


R. C. Ball, “Fermions without Fermion Fields”, Physical Review Letters 95, (2005) arXiv:cond-mat/0409485 DOI
F. Verstraete and J. I. Cirac, “Mapping local Hamiltonians of fermions to local Hamiltonians of spins”, Journal of Statistical Mechanics: Theory and Experiment 2005, P09012 (2005) arXiv:cond-mat/0508353 DOI
Y.-A. Chen and Y. Xu, “Equivalence between Fermion-to-Qubit Mappings in two Spatial Dimensions”, PRX Quantum 4, (2023) arXiv:2201.05153 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
Derby, Charles. Compact fermion to qubit mappings for quantum simulation. Diss. UCL (University College London), 2023.
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“Ball-Verstraete-Cirac (BVC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.
@incollection{eczoo_bvc, title={Ball-Verstraete-Cirac (BVC) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Ball-Verstraete-Cirac (BVC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.