  Errors in quantum logic gates are usually modeled by quantum process matrices
(CPTP maps). But process matrices can be opaque, and unwieldy. We show how to
transform a gate's process matrix into an error generator that represents the
same information more usefully. We construct a basis of simple and physically
intuitive elementary error generators, classify them, and show how to represent
any gate's error generator as a mixture of elementary error generators with
various rates. Finally, we show how to build a large variety of reduced models
for gate errors by combining elementary error generators and/or entire
subsectors of generator space. We conclude with a few examples of reduced
models, including one with just $9N^2$ parameters that describes almost all
commonly predicted errors on an N-qubit processor.
