  The generalized counting quantum Turing machine (GCQTM) is a machine which,
for any N, enumerates the first $2^{N}$ integers in succession as binary
strings. The generalization consists of associating a potential with read-1
steps only. The Landauer Resistance (LR) and band spectra were determined for
the tight binding Hamiltonians associated with the GCQTM for energies both
above and below the potential height. For parameters and potentials in the
electron region, the LR fluctuates rapidly between very high and very low
values as a function of momentum. The rapidity and extent of the fluctuations
increases rapidly with increasing N. For N=18, the largest value considered,
the LR shows good transmission probability as a function of momentum with
numerous holes of very high LR values present. This is true for energies above
and below the potential height. It is suggested that the main features of the
LR can be explained by coherent superposition of the component waves reflected
from or transmitted through the $2^{N-1}$ potentials in the distribution. If
this explanation is correct, it provides a dramatic illustration of the effects
of quantum nonlocality.
