  We study the renormalization group flow in general quantum field theories
with quenched disorder, focusing on random quantum critical points. We show
that in disorder-averaged correlation functions the flow mixes local and
non-local operators. This leads to a new crossover exponent related to the
disorder (as in classical disorder). We show that the time coordinate is
rescaled at each RG step, leading to Lifshitz scaling at critical points. We
write a universal formula for the dynamical scaling exponent z for weak
disorder.
