  The representation of numbers by tensor product states of composite quantum
systems is examined. Consideration is limited to k-ary representations of
length L and arithmetic modulo k^{L}. An abstract representation on an L fold
tensor product Hilbert space H^{arith} of number states and operators for the
basic arithmetic operations is described. Unitary maps onto a physical
parameter based tensor product space H^{phy} are defined and the relations
between these two spaces and the dependence of algorithm dynamics on the
unitary maps is discussed. The important condition of efficient implementation
by physically realizable Hamiltonians of the basic arithmetic operations is
also discussed.
