 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
 235  | DecoherenceStrategy.reduceCoupling => 10
 236  | DecoherenceStrategy.reduceModes => 100
 237  | DecoherenceStrategy.errorCorrection => 1000
 238  | DecoherenceStrategy.dynamicalDecoupling => 100
 239  | DecoherenceStrategy.topologicalProtection => 1e6
 240
 241/-! ## Falsification Criteria -/
 242
 243/-- The decoherence formula would be falsified by:
 244    1. Systems with decoherence times not scaling as φ^(-N)
 245    2. Gap-45 crossover at a different mode count

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.