Prove2Me

HH18 Parameterized: noisy Input eq independent Noisy TRegister

Proved
QEC.Distillation.HH18Parameterized.noisyInput_eq_independentNoisyTRegister

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

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

The parameterized physical input is the generic independent finite register construction on its actual physical-site type.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/Preparation.lean#L75-L80

Preamble
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Types
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Preparation
set_option autoImplicit false
noncomputable section
open QEC
open QEC.Distillation
open QEC.Distillation.HH18Parameterized
open Coding Semantics
open Semantics.Qubit
open scoped BigOperators
attribute [local instance 100] Fintype.ofFinite
Formal statement
theorem QEC.Distillation.HH18Parameterized.noisyInput_eq_independentNoisyTRegister
    (epsilon : HH18NoisyInput.DiagonalErrorRate) (m w : Nat) :
    noisyInput epsilon m w =
      HH18NoisyInput.independentNoisyTRegister
        (ι := PhysicalSite m w) epsilon := by sorry
Source
https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/Preparation.lean#L75-L80

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