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_I₀1∕2(10.3em0exHz), where Ω∕2π is the energy-level splitting frequency, S_I₀(10.3em0exHz) is the spectral density of the critical-current noise at 10.3em0exHz, 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(10.3em0exHz) scale to within a factor of 3 of [144(I₀∕μA)²∕(A∕μm²)](pA)²∕Hz at 4.20.3em0exK. We empirically extrapolate S_I₀1∕2(10.3em0exHz) to lower temperatures using a scaling T(K)∕4.2. Using this result, we find that the predicted values of τ_φ at 1000.3em0exmK range from 0.80.5em0exto0.5em0ex120.3em0exμs, and are usually substantially longer than values measured experimentally at lower temperatures.