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Subsystem modular-qudit code

Alternative Names: Gauge modular-qudit code.
Root code for the Modular-qudit Kingdom

Description

Subsystem QECC encoding into a \(q^n\)-dimensional Hilbert space consisting of \(n\) modular qudits.

Cousin

  • Modular-qudit code— Subsystem modular-qudit codes reduce to (subspace) modular-qudit codes when there is no gauge subsystem.

Member of code lists

Primary Hierarchy

Quantum Domain
Modular-qudit Kingdom
Parents
Subsystem group-based quantum codeSubsystem QECC Quantum
Subsystem group quantum codes whose physical spaces are constructed using modular-integer groups \(\mathbb{Z}_q\) are subsystem modular-qudit codes.
Subsystem modular-qudit code
Children
Subsystem qubit code
Subsystem modular-qudit codes reduce to subsystem qubit codes for qudit dimension \(q=2\).
Subsystem modular-qudit stabilizer code
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Zoo Code ID: subsystem_qudits_into_qudits

Cite as:
“Subsystem modular-qudit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/subsystem_qudits_into_qudits, arXiv:2606.11484
BibTeX:
@incollection{eczoo_subsystem_qudits_into_qudits,
title={Subsystem modular-qudit code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/subsystem_qudits_into_qudits}
}
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Permanent link:
https://errorcorrectionzoo.org/c/subsystem_qudits_into_qudits

Cite as:

“Subsystem modular-qudit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/subsystem_qudits_into_qudits, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits/subsystem_qudits_into_qudits.yml.