Metric Self-Dual Completion and Optimal Additive Hardness for Quantum and Graph-State Distance

arXiv:2609.22669 · quant-ph, cs.CC, cs.IT, math.IT · Submitted 2026-09-19 · Read on arXiv

quant-ph, cs.CC, cs.IT, math.IT

Submitted: 2026-09-19

Updated: 2026-09-19

Terminology

• Adjacency Matrix — 7× in this paper · explained in 1 episode
• Generalization — 5× in this paper · explained in 13 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Hamming Distance — 2× in this paper · explained in 2 episodes
• CSS Codes — 1× in this paper · explained in 2 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes

Sources

• A Simple Deterministic Reduction for the Gap Minimum Distance of Code Problem
• Shortest self-orthogonal embeddings of binary linear codes
• Inapproximability of Finding Sparse Vectors in Codes, Subspaces, and Lattices
• Good Quantum Error-Correcting Codes Exist
• On the hardness of approximating minimum distances of quantum codes

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