Prove2Me

HH18 Parameterized: error Word Weight sum

Proved
QEC.Distillation.HH18Parameterized.errorWordWeight_sum

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

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

The physical error-word law is normalized over the actual finite site type, without specializing or enumerating a concrete block.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/Preparation.lean#L84-L89

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.errorWordWeight_sum (m w : Nat)
    (epsilon : HH18NoisyInput.DiagonalErrorRate) :
    ∑ error : PhysicalErrorWord m w,
      HH18NoisyInput.errorWordWeight epsilon error = 1 := by sorry
Source
https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/Preparation.lean#L84-L89

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