  Quantum fermionic computations on occupation numbers proposed in
quant-ph/0003137 are studied. It is shown that a control over external field
and tunneling would suffice to fulfill all quantum computations without
valuable slowdown in the framework of such model when an interaction of
diagonal type is fixed and permanent. Substantiation is given through a
reduction of some subset of this model to the conventional language of quantum
computing and application of the construction from quant-ph/0202030.
