Quantum

Lifting an $[n,k,d]$ Binary Linear Code to an $[[n,k,d]]$ Quantum Stabilizer Code

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Briefings

A new arXiv preprint (arXiv:2610.14192v1) proposes lifting arbitrary classical binary linear codes to quantum stabilizer codes via the CWS framework. The study analyzes the probability of preserving the minimum distance $d$ using an Erdős-Rényi random graph, establishing a Gilbert-Varshamov-type condition for code parameters. The research provides a probabilistic lower bound on this preservation probability, offering a systematic method for constructing codes with specific $n,k,d$ parameters.

Key points

• The CWS framework allows constructing quantum stabilizer codes from a classical code and an Erdős-Rényi random graph.
• An arXiv preprint (arXiv:2610.14192v1) investigates the conditions for lifting $[n,k,d]$ binary linear codes to $[[n,k,d]]$ quantum codes.

Context

This research addresses the systematic construction of quantum error correcting codes from classical codes, specifically utilizing the CWS framework to analyze distance preservation probabilities.

Limitations

The evidence is a single arXiv preprint (arXiv:2610.14192v1) with no peer review or experimental validation. The probabilistic analysis provides a lower bound on preservation probability but does not guarantee success for all cases. The study relies on theoretical analysis of random graphs and classical code parameters without empirical data or additional background context.

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