How does the thermal noise of components at different temperature stages affect qubit coherence?

Thermal noise from microwave components at different temperature stages of a dilution refrigerator directly affects qubit coherence by introducing photon noise that causes energy relaxation (T1 decay) and dephasing (T2 decay). Each component at temperature T contributes thermal photons at the qubit frequency f according to n_th = 1/(exp(hf/kT) - 1). At 5 GHz: 300K contributes 1249 photons, 4K contributes 16.6 photons, 100 mK contributes 0.42 photons, 20 mK contributes 0.083 photons. The effective noise photon number at the qubit is the weighted sum of contributions from all stages, attenuated by the intervening attenuation: n_eff = sum_i(n_th(T_i) × product_j(10^(-A_j/10))), where A_j is the attenuation between stage i and the qubit. With proper attenuation (60 dB total from 300K to qubit): 300K contribution at qubit = 1249 × 10^-6 = 0.00125 photons. 4K contribution after 40 dB from 4K to qubit = 16.6 × 10^-4 = 0.0017 photons. 100 mK contribution after 20 dB = 0.42 × 0.01 = 0.0042 photons. Total: ~0.007 photons, dominated by the closest (warmest inadequately attenuated) stage. Each residual thermal photon at the qubit frequency drives transitions between |0⟩ and |1⟩, limiting T1 to T1_thermal ≈ 1/(2*pi*kappa*n_residual), where kappa is the qubit-environment coupling rate. To achieve T1 > 100 μs at 5 GHz, the residual photon number must be below ~0.01.