Tight binding Hamiltonians and quantum turing machines

This paper extends work done to date on quantum computation by association of potentials with different types of steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding Hamiltonians each with a different potential distribution. Which distribution applies is determined by the initial state. An example, which enumerates the integers in succession as binary strings, is analyzed. It is seen that for some initial states, the potential distributions have quasicrystalline properties and are similar to a substitution sequence.