  Fault-tolerant quantum computers compose elements of a discrete gate set in
order to approximate a target unitary. The problem of minimising the number of
gates is known as gate-synthesis. The approximation error is a form of coherent
noise, which can be significantly more damaging than comparable incoherent
noise. We show how mixing over different gate sequences can convert this
coherent noise into an incoherent form. As measured by diamond distance, the
post-mixing noise is quadratically smaller than before mixing, with no
additional resource cost. Equivalently, we can use a shorter gate sequence to
achieve the same precision as unitary gate-synthesis, with a factor 1/2
reduction for a broad class of problems.
