Logical-Class Diagnostic Layer for Stabilizer Codes and Decoders via Supercharge Structures
Abstract
We develop a decoder-agnostic logical-class diagnostic layer for abelian Pauli stabilizer codes, motivated by fault-tolerant quantum computing. An ancilla fermionic register defines a nilpotent supercharge whose clean degree-zero harmonic sector is the code space. Projected-return blocks derived from graded commutators organize the recovery test of whether a decoder-selected correction preserves every encoded input for every error in a declared same-syndrome family; the passing syndromes form the certified faithful window. Demoting the supercharge to an exact binary diagnostic formulation classifies residuals modulo stabilizers, separating a check violation, a harmless stabilizer residual, and a syndrome-silent nontrivial logical action, with a two-sector form for CSS codes. Because the unknown fault cancels, the relative logical class of two record-compatible candidates is computable online. We verify the diagnostic formalisms on the Steane code and specify a static--circuit bridge audit protocol for the Gross bivariate-bicycle quantum low-density parity-check (qLDPC) code. The method supplements existing decoders without additional physical qubits for software use.
Related
- Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes
- The logical set of Gaussian states under the stabilizer subsystem decomposition
- Quantum Secret Sharing from CSS qLDPC Codes: Computable Access Structures, Accessible Logical Dimension, and Topology-Aware Network Cost
- Certified Non-Degenerate Maximum-Likelihood Benchmarking of Quantum LDPC Decoders
- Hardware-Efficient Reinforcement-Learned Scheduling for Quantum LDPC Decoders
BibTeX
@misc{lin2026logicalclass,
title = {{Logical-Class Diagnostic Layer for Stabilizer Codes and Decoders via Supercharge Structures}},
author = {Hai Lin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01360},
eprint = {2611.01360},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01360},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Logical-Class Diagnostic Layer for Stabilizer Codes and Decoders via Supercharge Structures
AU - Hai Lin
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01360
UR - https://arxiv.org/abs/2611.01360
AB - We develop a decoder-agnostic logical-class diagnostic layer for abelian Pauli stabilizer codes, motivated by fault-tolerant quantum computing. An ancilla fermionic register defines a nilpotent supercharge whose clean degree-zero harmonic sector is the code space. Projected-return blocks derived from graded commutators organize the recovery test of whether a decoder-selected correction preserves every encoded input for every error in a declared same-syndrome family; the passing syndromes form the certified faithful window. Demoting the supercharge to an exact binary diagnostic formulation classifies residuals modulo stabilizers, separating a check violation, a harmless stabilizer residual, and a syndrome-silent nontrivial logical action, with a two-sector form for CSS codes. Because the unknown fault cancels, the relative logical class of two record-compatible candidates is computable online. We verify the diagnostic formalisms on the Steane code and specify a static--circuit bridge audit protocol for the Gross bivariate-bicycle quantum low-density parity-check (qLDPC) code. The method supplements existing decoders without additional physical qubits for software use.
ER -