  We give a heuristic argument for disorder rounding of a first order quantum
phase transition into a continuous phase transition. From both weak and strong
disorder analysis of the the N-color quantum Ashkin-Teller model in one spatial
dimension, we find that for $N \geq 3$, the first order transition is rounded
to a continuous transition and the physical picture is the same as the random
transverse field Ising model for a limited parameter regime. The results are
strikingly different from the corresponding classical problem in two dimensions
where the fate of the renormalization group flows is a fixed point
corresponding to N-decoupled pure Ising models.
