  We present a new method to measure 1/f noise in Josephson quantum bits
(qubits) that yields low-frequency spectra below 1Hz. Comparison of noise taken
at positive and negative bias of a phase qubit shows the dominant noise source
to be flux noise and not junction critical-current noise, with a magnitude
similar to that measured previously in other systems. Theoretical calculations
show that the level of flux noise is not compatible with the standard model of
noise from two-level state defects in the surface oxides of the films.
