  The success probability of a quantum algorithm constructed from noisy quantum
gates cannot be accurately predicted from single parameter metrics that compare
noisy and ideal gates. We illustrate this concept by examining a system with
coherent errors and comparing algorithm success rates for different choices of
two-qubit gates that are constructed from composite pulse sequences, where the
residual gate errors are related by a unitary transformation. As a result, all
of the sequences have the same error relative to the ideal gate under any
distance measure that is invariant under unitary transformations. However, the
circuit success can vary dramatically by choosing error orientations that do
not affect the final outcome and error orientations that cancel between
conjugate controlled-nots, as demonstrated here with Clifford circuits,
compiled Toffoli gates, and quantum simulation algorithms. The results point to
the utility of both minimizing the error and optimizing the error direction and
also to the advantages of using multiple control sequences for the same gate
type within a single algorithm.
