  Dielectric loss from two-level states is shown to be a dominant decoherence
source in superconducting quantum bits. Depending on the qubit design,
dielectric loss from insulating materials or the tunnel junction can lead to
short coherence times. We show that a variety of microwave and qubit
measurements are well modeled by loss from resonant absorption of two-level
defects. Our results demonstrate that this loss can be significantly reduced by
using better dielectrics and fabricating junctions of small area $\lesssim 10
\mu \textrm{m}^2$. With a redesigned phase qubit employing low-loss
dielectrics, the energy relaxation rate has been improved by a factor of 20,
opening up the possibility of multi-qubit gates and algorithms.
