Decoherence in Josephson-junction qubits due to critical-current fluctuations

We compute the decoherence caused by 1/f fluctuations at low frequency f in the critical current I₀ of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time τ_ϕ scales as I₀/ΩΛS_I0^1/2(1Hz) , where Ω/2π is the energy-level splitting frequency, S_I0(1Hz) is the spectral density of the critical-current noise at 1Hz , and Λ≡∣I₀dΩ/ΩdI₀∣ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time t scales as exp(-t²/2τ_ϕ²) when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in I₀ and area A , and show that their values of S_I0(1Hz) scale to within a factor of 3 of [144(I₀/μA)²/(A/μm²)](pA)²/Hz at 4.2K . We empirically extrapolate S_I0^1/2(1Hz) to lower temperatures using a scaling T(K)/4.2 . Using this result, we find that the predicted values of τ_ϕ at 100mK range from 0.8to12μs , and are usually substantially longer than values measured experimentally at lower temperatures.