  A representation of complex rational numbers in quantum mechanics is
described that is not based on logical or physical qubits. It stems from noting
that the zeros in a product qubit state do not contribute to the number. They
serve only as place holders. The representation is based on the distribution of
four types of systems on an integer lattice. The four types, labelled as
positive real, negative real, positive imaginary, and negative imaginary, are
represented by creation and annihilation operators acting on the system vacuum
state. Complex rational string number states correspond to strings of creation
operators acting on the vacuum. Various operators, including those for the
basic arithmetic operations, are described. The representation used here is
based on occupation number states and is given for bosons and fermions.
