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Super-compact fermion-to-qubit code[1]

Alternative names: Super-compact encoding.

Description

A 2D fermion-into-qubit encoding on the square lattice obtained from exact 2D bosonization by a finite-depth generalized local unitary Clifford circuit, followed by re-pairing of Majorana modes and a slight lattice deformation. The code uses \(1.25\) qubits per fermion, improving on the square-lattice compact encoding with ratio \(r=1.5\). Its fermion-parity, hopping, and stabilizer operators have weights \(1\)-\(2\), \(2\)-\(6\), and \(12\), respectively [1; Table I].

Cousin

  • Derby-Klassen (DK) code— On the square lattice, the super-compact code is obtained by further transforming the \(r=1.5\) compact/DK construction to qubit-fermion ratio \(1.25\) [1].

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
Parents
2D bosonization code
The super-compact code is obtained from exact 2D bosonization by finite-depth generalized local unitaries [1].
Super-compact fermion-to-qubit code

References

[1]
Y.-A. Chen and Y. Xu, “Equivalence between Fermion-to-Qubit Mappings in two Spatial Dimensions”, PRX Quantum 4, (2023) arXiv:2201.05153 DOI
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Zoo Code ID: super_compact

Cite as:
“Super-compact fermion-to-qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/super_compact
BibTeX:
@incollection{eczoo_super_compact, title={Super-compact fermion-to-qubit code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/super_compact} }
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Permanent link:
https://errorcorrectionzoo.org/c/super_compact

Cite as:

“Super-compact fermion-to-qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/super_compact

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