`gap45CrossoverModes`

definition

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module: IndisputableMonolith.QFT.Decoherence
domain: QFT
line: 204 · github
papers citing: none yet

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IndisputableMonolith.QFT.Decoherence on GitHub at line 204.

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formal source

 201/-- Number of modes to cross from quantum to classical (Gap-45 crossover).
 202    For τ_target = 1 s (human scale), coupling = 1:
 203    N ≈ 45 × ln(10) / ln(φ) ≈ 45 × 2.3 / 0.48 ≈ 215 -/
 204noncomputable def gap45CrossoverModes : ℝ :=
 205  criticalModes tau_bio 1.0
 206
 207/-- Approximation of Gap-45 crossover modes as a rational.
 208    N ≈ ln(τ_bio/τ₀) / ln(φ) ≈ ln(1/(5.4e-44)) / 0.48
 209    ≈ 99.3 / 0.48 ≈ 207
 210
 211    Since τ₀ ≈ 5.4×10⁻⁴⁴ s, τ_bio = 1 s:
 212    ln(1/5.4e-44) ≈ 44 × ln(10) ≈ 44 × 2.3 ≈ 101
 213    ln(φ) ≈ 0.48
 214    N ≈ 101/0.48 ≈ 210 -/
 215def gap45CrossoverApprox : ℚ := 210
 216
 217/-- **THEOREM**: The Gap-45 crossover occurs at approximately 100-300 modes. -/
 218theorem gap45_crossover_range :
 219    (100 : ℚ) < gap45CrossoverApprox ∧ gap45CrossoverApprox < 300 := by
 220  unfold gap45CrossoverApprox
 221  constructor <;> norm_num
 222
 223/-! ## Decoherence Suppression Strategies -/
 224
 225/-- Strategies to extend decoherence time. -/
 226inductive DecoherenceStrategy where
 227  | reduceCoupling    -- Lower g
 228  | reduceModes       -- Lower N (isolation)
 229  | errorCorrection   -- Actively correct
 230  | dynamicalDecoupling -- Pulse sequences
 231  | topologicalProtection -- Use topological qubits
 232
 233/-- Expected improvement factor for each strategy. -/
 234noncomputable def strategyImprovement : DecoherenceStrategy → ℝ

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