  Inspired by the Solovay-Kitaev decomposition for approximating unitary
operations as a sequence of operations selected from a universal quantum
computing gate set, we introduce a method for approximating any single-qubit
channel using single-qubit gates and the controlled-NOT (CNOT). Our approach
uses the decomposition of the single-qubit channel into a convex combination of
"quasiextreme" channels. Previous techniques for simulating general
single-qubit channels would require as many as 20 CNOT gates, whereas ours only
needs one, bringing it within the range of current experiments.
