Metachecks in Bivariate Bicycle Codes: Syndrome Distance, Measurement Faults, and Repair Limits
Abstract
Faulty syndrome measurements can corrupt an otherwise correct quantum-error correction step. Bivariate bicycle (BB) codes contain dependent stabilizer checks, so every valid syndrome obeys additional parity constraints, or metachecks. We study how far this built-in redundancy can identify measurement faults and when the remaining ambiguity is unavoidable, while separately checking the code's logical structure. A logical decomposition is used as a preliminary safety check: it identifies a k/2-dimensional annihilator subspace and a k/2-dimensional colon quotient, and the minimum-weight logical need not be visible from the annihilator side alone. On the measurement side, translation symmetry partitions syndrome locations into classes that carry identical metacheck information. This gives an exact characterization of the leading single-fault ambiguity, a bound on how many fault locations can be distinguished, and a family-level repair limit when the encoded dimension stays bounded while the block length grows. Under a static-data assumption, the same calculation gives the minimum number of checks that must be remeasured to remove every single-fault ambiguity. Exact finite-code calculations illustrate both regimes: all single measurement faults are distinguishable in a 72-qubit BB code, whereas the 144-qubit Gross code merges its 72 syndrome locations into 36 indistinguishable pairs. In a 108-qubit example, one logical component first appears at weight 12 while the other contains a weight-10 logical. Sustained phenomenological experiments show that joint data--measurement decoding is more robust than a separated repair stage on the more ambiguous codes. The resulting tests apply to general two-block BB codes, including non-coprime periods and repeated-root cases.
Related
- Logical Operator Decomposition for Distance Analysis of Bivariate Bicycle Codes
- Spectral Theory of Semisimple Bivariate Bicycle Codes
- Existence and Characterization of Bivariate Bicycle Codes
- Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark
- Sequences of Bivariate Bicycle Codes from Covering Graphs
BibTeX
@misc{rowshan2026metachecks,
title = {{Metachecks in Bivariate Bicycle Codes: Syndrome Distance, Measurement Faults, and Repair Limits}},
author = {Mohammad Rowshan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39121},
eprint = {2609.39121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39121},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Metachecks in Bivariate Bicycle Codes: Syndrome Distance, Measurement Faults, and Repair Limits
AU - Mohammad Rowshan
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.39121
UR - https://arxiv.org/abs/2609.39121
AB - Faulty syndrome measurements can corrupt an otherwise correct quantum-error correction step. Bivariate bicycle (BB) codes contain dependent stabilizer checks, so every valid syndrome obeys additional parity constraints, or metachecks. We study how far this built-in redundancy can identify measurement faults and when the remaining ambiguity is unavoidable, while separately checking the code's logical structure. A logical decomposition is used as a preliminary safety check: it identifies a k/2-dimensional annihilator subspace and a k/2-dimensional colon quotient, and the minimum-weight logical need not be visible from the annihilator side alone. On the measurement side, translation symmetry partitions syndrome locations into classes that carry identical metacheck information. This gives an exact characterization of the leading single-fault ambiguity, a bound on how many fault locations can be distinguished, and a family-level repair limit when the encoded dimension stays bounded while the block length grows. Under a static-data assumption, the same calculation gives the minimum number of checks that must be remeasured to remove every single-fault ambiguity. Exact finite-code calculations illustrate both regimes: all single measurement faults are distinguishable in a 72-qubit BB code, whereas the 144-qubit Gross code merges its 72 syndrome locations into 36 indistinguishable pairs. In a 108-qubit example, one logical component first appears at weight 12 while the other contains a weight-10 logical. Sustained phenomenological experiments show that joint data--measurement decoding is more robust than a separated repair stage on the more ambiguous codes. The resulting tests apply to general two-block BB codes, including non-coprime periods and repeated-root cases.
ER -