Strong convergence of quantum random walks via semigroup decomposition

We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.