New local stabilizer codes from local classical codes

• URL: http://arxiv.org/abs/2503.20717v1
• Date: Wed, 26 Mar 2025 16:53:36 GMT
• Title: New local stabilizer codes from local classical codes
• Authors: Lane G. Gunderman,
• Abstract summary: We discuss new local and low-weight stabilizer codes which are obtained from the recent progress in $2D$ local classical codes.<n>We construct codes with weight and qubit use count of $5$ while being able to protect the information with high distance, or greater logical count.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new local and low-weight stabilizer codes which are obtained from the recent progress in $2D$ local classical codes. Of note, we construct codes with weight and qubit use count of $5$ while being able to protect the information with high distance, or greater logical count. We also consider the Fibonacci code family which generates weight and qubit use count of $6$ while having parameters $[[O(l^3),O(l),\Omega(l)]]$. While other weight-reduction methods centered on lowering the weight without regard to locality, this work achieves very low-weight and geometric locality. This work is exhaustive over translated classical generators of size $3\times 3$ and up to size $17\times 17$ classical bit grids.

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