Exploring Asymmetric QEC Code Concatenation
Abstract
Concatenated quantum error-correcting codes have recently gained popularity because they improve the effective distance of a joint code without requiring the discovery of new codes with desirable parameters. A common building block for such studies is the $[[4,1,2]]$ Iceberg code, the smallest error-detecting code and therefore the one with the lowest resource overhead. However, it has an asymmetric number of X and Z checks, and concatenating it produces skewed logical error rates (LERs) between the X and Z observables. This asymmetry can be mitigated by Clifford-deforming the individual blocks of the concatenation, but the space of possible Hadamard deformations grows doubly exponentially with the number of concatenation levels. We formalize this deformation space and investigate it by proposing six concrete deformation strategies, which we compare under a code capacity (with and without bias) noise model using a concatenated maximum-likelihood soft-information decoder. Among the strategies we study, one one of them achieves near-identical X and Z LERs in a logical-memory experiment while simultaneously reducing the total LER (the sum of the X and Z error rates).
Related
- Stitched surface codes: planar concatenation through GHZ corridors
- A customizable explicit partitioned FSI coupling framework for Code_Saturne and Code_Aster
- PGGC: phase-gradient Gray code with temporal pattern sharing for 3D measurement
- Asymmetric frequency conversion and violation of Kirchhoff’s law of thermal radiation in phased Floquet metasurfaces
- Ultraviolet to infrared thermally driven SSPM and spatially asymmetric optical propagation in vdW NbOCl₂ nanosheets
BibTeX
@misc{sethi2026exploring,
title = {{Exploring Asymmetric QEC Code Concatenation}},
author = {Sayam Sethi and Maxwell Poster and Aditi Awasthi and Willers Yang and Joshua Viszlai and Jonathan Mark Baker},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25251},
eprint = {2609.25251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exploring Asymmetric QEC Code Concatenation
AU - Sayam Sethi
AU - Maxwell Poster
AU - Aditi Awasthi
AU - Willers Yang
AU - Joshua Viszlai
AU - Jonathan Mark Baker
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25251
UR - https://arxiv.org/abs/2609.25251
AB - Concatenated quantum error-correcting codes have recently gained popularity because they improve the effective distance of a joint code without requiring the discovery of new codes with desirable parameters. A common building block for such studies is the $[[4,1,2]]$ Iceberg code, the smallest error-detecting code and therefore the one with the lowest resource overhead. However, it has an asymmetric number of X and Z checks, and concatenating it produces skewed logical error rates (LERs) between the X and Z observables. This asymmetry can be mitigated by Clifford-deforming the individual blocks of the concatenation, but the space of possible Hadamard deformations grows doubly exponentially with the number of concatenation levels. We formalize this deformation space and investigate it by proposing six concrete deformation strategies, which we compare under a code capacity (with and without bias) noise model using a concatenated maximum-likelihood soft-information decoder. Among the strategies we study, one one of them achieves near-identical X and Z LERs in a logical-memory experiment while simultaneously reducing the total LER (the sum of the X and Z error rates).
ER -