stab_9_3_3

[[9,3,3]] engineering not started

[[9,3,3]] Quadric code

Family:: small_distance/small/9/stab_9_3_3

Citations:: 1

Est. LoC:: 400

Description

Nine-qubit \hyperref[topic:quantum-weight-enumerator]{pure} Hermitian qubit code constructed from the almost MDS [9,3,6]_4 Hermitian self-orthogonal code. It is the only \hyperref[topic:quantum-weight-enumerator]{pure} Hermitian code wi…

Introduced in: doi:10.1137/S0895480104441085, doi:10.2140/iig.2008.6.53

Rationale

Re-scored 2026-05-23: the new `local instance` `DecidableEq (NQubitPauliGroupElement n)` + `Decidable (Anticommute p q)` pattern from FiveQubit_5_1_3 (template; copy-paste-ready) closes weight-{1,2} anti-witness tables by `by decide` instead of ~7-10 LoC per case. Combined with `no_weight_two_mem_centralizer_of_anticommute_witness` (Core/CSSDistance.lean) and `negIdentity_not_mem_of_indep_phase_zero_commute` (BinarySymplectic/SymplecticSpan.lean), non-CSS d=3 codes are now ~100 LoC instead of ~1000 LoC. Previous rationale: [[9,3,3]] non-CSS code: small distance-3 example. Direct instance of existing stabilizer infra; distance by enumeration.

Scoring composite 7.95

Reuse

10/10 ×0.25

Canon

4/10 ×0.15

Hardware

3/10 ×0.15

Tract

10/10 ×0.15

Prereq

10/10 ×0.2

Effort

9/10 ×0.1