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Subsystem homological code

Alternative names: Subsystem generalized surface code.

Description

A subsystem CSS code that is a subsystem version of the homological code, defined on cellulations of manifolds in arbitrary dimensions. Gauge-group generators are of lower weight than the stabilizers of the corresponding surface code, enabling fault-tolerant syndrome extraction with simpler circuits. The stabilizer group may contain generators of unbounded weight, distinguishing these codes from stabilizer codes with bounded-weight generators for which some logical qubits were re-assigned to be gauge qubits.

Cousin

  • Homological code— Subsystem homological codes are subsystem versions of homological codes, with gauge-group generators of lower weight than the corresponding surface-code stabilizers.

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Subsystem qubit codeSubsystem QECC Quantum
Subsystem qubit stabilizer codeSubsystem QECC Quantum
Subsystem CSS codeSubsystem QECC Quantum
Parents
Subsystem CSS code
QLDPC subsystem codeSubsystem QECC Quantum
Subsystem homological code
Children
3D subsystem surface code
Subsystem hyperbolic surface code
Subsystem rotated surface code
Subsystem surface code
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Zoo Code ID: subsystem_higher_dimensional_surface

Cite as:
“Subsystem homological code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/subsystem_higher_dimensional_surface
BibTeX:
@incollection{eczoo_subsystem_higher_dimensional_surface, title={Subsystem homological code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/subsystem_higher_dimensional_surface} }
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Permanent link:
https://errorcorrectionzoo.org/c/subsystem_higher_dimensional_surface

Cite as:

“Subsystem homological code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/subsystem_higher_dimensional_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/topological/surface/subsystem_higher_dimensional_surface.yml.