Lifting an [n,k,d] Binary Linear Code to an $[[n,k,d]]$ Quantum Stabilizer Code
Abstract
The codeword stabilized (CWS) framework provides a systematic method for constructing quantum error correcting codes from a simple undirected graph and a classical code. When the underlying classical code is linear, the resulting quantum code is a stabilizer code. In this work, we investigate the conditions under which an arbitrary [n,k,d] classical binary linear code can be lifted to an $[[n,k,d]]$ quantum stabilizer code using the CWS framework. We analyze the random CWS code constructed from a given [n,k,d] binary linear code 𝒞 and an Erdős-Rényi random graph G(n, 1/2). We establish a lower bound on the probability that the resulting quantum code preserves the minimum distance d of the classical code. This probabilistic analysis yields a Gilbert-Varshamov-type condition on the n,k,d parameters of the classical code that guarantees the existence of a graph resulting in a quantum code with the same n,k,d parameters.
Related
- Harmonically lifting linear series from curves to K3 surfaces
- Lifting curved Kakeya sets to linear Kakeya sets
- Exact Convex Reformulations of Linear Neural Networks via Completely Positive Lifting
- Stabilizer entropy cones as self-dual slices of linear rank cones: a five-party gap and dependence on the local dimension
- Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum Codes
BibTeX
@misc{aswanth2026lifting,
title = {{Lifting an $[n,k,d]$ Binary Linear Code to an $[[n,k,d]]$ Quantum Stabilizer Code}},
author = {Thamadathil Aswanth and Navin Kashyap},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14192},
eprint = {2610.14192},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14192},
}
RIS
TY - UNPB
TI - Lifting an [n,k,d] Binary Linear Code to an $[[n,k,d]]$ Quantum Stabilizer Code
AU - Thamadathil Aswanth
AU - Navin Kashyap
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14192
UR - https://arxiv.org/abs/2610.14192
AB - The codeword stabilized (CWS) framework provides a systematic method for constructing quantum error correcting codes from a simple undirected graph and a classical code. When the underlying classical code is linear, the resulting quantum code is a stabilizer code. In this work, we investigate the conditions under which an arbitrary [n,k,d] classical binary linear code can be lifted to an $[[n,k,d]]$ quantum stabilizer code using the CWS framework. We analyze the random CWS code constructed from a given [n,k,d] binary linear code 𝒞 and an Erdős-Rényi random graph G(n, 1/2). We establish a lower bound on the probability that the resulting quantum code preserves the minimum distance d of the classical code. This probabilistic analysis yields a Gilbert-Varshamov-type condition on the n,k,d parameters of the classical code that guarantees the existence of a graph resulting in a quantum code with the same n,k,d parameters.
ER -