Does somebody knows how to project a discrete-time quantum walk with a Grover coin on the hypercube onto the line? I was trying to reproduce this paper (http://arxiv.org/abs/quant-ph/0210064)"A Quantum Random Walk Search Algorithm" by Neil Shenvi, Julia Kempe, K. Birgitta Whaley, and I cannot understand how does it manage to do that. I'm posting as an attachment to this post the part of the paper that I cannot solve (I hope it doesn't violate any rules of the forum, since it is available in quant-ph).

Thanks in advanced!!