Alfred Harwood comments on Why are there no interesting (1D, 2-state) quantum cellular automata?

[Alfred Harwood]

When you are considering finite tape length, how do you deal with $x^{(k-1)}$ when $k=0$ or $x^{(k+1)}$ when $k=N$ ?

[Optimization Process]

I was imagining the tape wraps around! (And hoping that whatever results fell out would port straightforwardly to infinite tapes.)