Temperature square dependence of the low frequency 1/f charge noise in the Josephson junction qubits

To verify the hypothesis about the common origin of the low frequency 1/f noise and the quantum f noise recently measured in the Josephson charge qubits, we study temperature dependence of the 1/f noise and decay of coherent oscillations. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge qubits off the electrostatic energy degeneracy point is consistently explained by the same low frequency 1/f noise that is observed in the transport measurements.