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In this talk I will describe recent work (in collaboration with M. Mukhopadhyay, O. Pujolas and T. Vachaspati) about the quantum formation of kinks and antikinks during a quantum phase transition in 1+1 dimensions. I will evaluate the number density of kinks as a function of time and show that it scales as t^{-1/2} in the late time limit (and independently of the details of the phase transition). This decay can be interpreted in terms of ballistic annihilation of kink-antikink pairs. Finally I will discuss the extension of the model to the case of asymmetric initial conditions.