Prove2Me

HH18 Parameterized: decoded Instrument observe

Proved
QEC.Distillation.HH18Parameterized.decodedInstrument_observe

by marwahaha · Nov 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-qecert-4a64933quantum-computingquantum-error-correction

The visible observation is exactly the real postselection outcome of the retained syndrome branch.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/DecodedInstrument.lean#L98-L103

Preamble
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_PhysicalEndpoint
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Decoder
import Definitions.Def_QEC_Semantics_Channels_Instrument
import Definitions.Def_QEC_Semantics_Instruments_TensorPower_BornMass
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_DecodedInstrument
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
attribute [local instance] QEC.Distillation.HH18Parameterized.instDecodedInstrumentClassicalDecidable
Formal statement
theorem QEC.Distillation.HH18Parameterized.decodedInstrument_observe {w r m : Nat}
    (h : Admissible w r m) (hdegree : 3 * r < m)
    (index : decodedRawIndex h hdegree) :
    (decodedInstrument h hdegree).observe index =
      (postselectionInstrument h).observe index.1.2 := by sorry
Source
https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/DecodedInstrument.lean#L98-L103

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