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 _ scales as I₀∕S₈₀^1∕2 (10. 3em{0ex}Hz), where ∕2 is the energy-level splitting frequency, S₈₀ (10. 3em{0ex}Hz) is the spectral density of the critical-current noise at 10. 3em{0ex}Hz, and I₀d∕I₀ 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 (-t^2∕2_^2) 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 S₈₀ (10. 3em{0ex}Hz) scale to within a factor of 3 of 144 ({I₀∕) }^2∕ (A∕m^2) (pA) ^2∕Hz at 4. 20. 3em{0ex}K. We empirically extrapolate S₈₀^1∕2 (10. 3em{0ex}Hz) to lower temperatures using a scaling T (K) ∕4. 2. Using this result, we find that the predicted values of _ at 1000. 3em{0ex}mK range from 0. 80. 5em{0ex}to0. 5em{0ex}120. 3em{0ex}, and are usually substantially longer than values measured experimentally at lower temperatures.