 174/-! ## Qubit Decoherence Examples -/
 175
 176/-- Typical superconducting qubit parameters. -/
 177structure QubitParams where
 178  /-- T1 relaxation time (seconds). -/
 179  t1 : ℝ
 180  /-- T2 dephasing time (seconds). -/
 181  t2 : ℝ
 182  /-- Operating temperature (Kelvin). -/
 183  temperature : ℝ
 184  /-- Number of coupled modes. -/
 185  env_modes : ℕ
 186
 187/-- Typical superconducting qubit. -/
 188def typicalSCQubit : QubitParams := {
 189  t1 := 50e-6,        -- 50 μs
 190  t2 := 70e-6,        -- 70 μs
 191  temperature := 0.015,-- 15 mK
 192  env_modes := 10     -- Estimated
 193}
 194
 195/-- Predicted decoherence time for the typical qubit. -/
 196noncomputable def predictedQubitDecoherence : ℝ :=
 197  decoherenceTime ⟨typicalSCQubit.env_modes, 0.5, by norm_num, by norm_num⟩
 198
 199/-! ## The Gap-45 Threshold in Practice -/
 200
 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.

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