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 I ₀/ΩΛS_I0^1/2 (1 Hz), where Ω/2π is the energy-level splitting frequency, S_I0(1 Hz) is the spectral density of the critical-current noise at 1 Hz, 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 (1 Hz) scale to within a factor of 3 of [144(I₀/μA) ²/(A/μm²)](pA)²/Hz at 4.2 K. We empirically extrapolate S_I0^1/2 (1 Hz) to lower temperatures using a scaling T(K)/4.2. Using this result, we find that the predicted values of τ_φ at 100 mK range from 0.8 to 12 μs, and are usually substantially longer than values measured experimentally at lower temperatures.