Year: 2026
Type: preprint
Abstract: We study the number of independent stabilizer syndrome outcomes needed to resolve errors at known erased locations. For every matrix with paired columns, rank r, and maximum independent-pair cardinality ν, we prove the exact profile max |I|=δ rankGI = min{2δ,δ +ν,r}. One ordering of the pairs attains every entry of this profile. For an isotropic stabilizer space encoding at least one logical qudit, every inclusionwise maximal independent-pair set A satisfies d ≤|A|+1. Consequently, in the declared syndrome model, the worst-case measurement budget for δ < d erasures is exactly 2δ, including for degenerate codes. A CSS specialization gives matching and rank-partition certificates. For binary surface-code check matrices, we replace dense elimination with connected-component selection of an optimal native check set, in linear time in the sparse affected incidence input. Complete proofs, exact finite-field audits, and executable code accompany the manuscript.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224946384