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).

arXiv:2609.25251 [quant-ph]

(or arXiv:2609.25251v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.25251 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.