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(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.