  We present geometric methods for uniformly discretizing the continuous
N-qubit Hilbert space. When considered as the vertices of a geometrical figure,
the resulting states form the equivalent of a Platonic solid. The
discretization technique inherently describes a class of pi/2 rotations that
connect neighboring states in the set, i.e. that leave the geometrical figures
invariant. These rotations are shown to generate the Clifford group, a general
group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert
space allows us to define its digital quantum information content, and we show
that this information content grows as N^2. While we believe the discrete sets
are interesting because they allow extra-classical behavior--such as quantum
entanglement and quantum parallelism--to be explored while circumventing the
continuity of Hilbert space, we also show how they may be a useful tool for
problems in traditional quantum computation. We describe in detail the discrete
sets for one and two qubits.
