HH18 Parameterized: syndrome Outcome accepted iff
ProvedQEC.Distillation.HH18Parameterized.syndromeOutcome_accepted_ifflean-qecert-4a64933quantum-computingquantum-error-correction
The coarse accepted outcome is exactly the all-positive syndrome.
Preamble
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Syndrome import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Postselection set_option autoImplicit false noncomputable section open QEC open QEC.Distillation open QEC.Distillation.HH18Parameterized open Coding Semantics open Coding.PauliSymplectic open Coding.ReedMuller Coding.PuncturedReedMuller open Semantics.Qubit open scoped BigOperators attribute [local instance 100] Fintype.ofFinite universe u
Formal statement
theorem QEC.Distillation.HH18Parameterized.syndromeOutcome_accepted_iff (w r m : Nat) (syndrome : Syndrome w r m) :
syndromeOutcome w r m syndrome = .accepted ↔
syndrome = HH18PuncturedReedMuller.allPositiveSyndrome w r m := by sorrySource