Quantum random walks on congested lattices

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walkers direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walkers as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices. Also, we observe that a quantum walker is extremely sensitive to our model of dephasing.