A simple quantum system is the two-level
spin- particle. Its basis states, spin-down
and spin-up , may
be relabelled to represent binary zero and one, i.e.,
and , respectively. The state of a single such
particle is described by the wavefunction
.
The squares of the complex coefficients and
represent the probabilities for finding the particle in the
corresponding states. Generalizing this to a set of **k**
spin- particles we find that there are now
basis states (quantum mechanical vectors that span a Hilbert space)
corresponding say to the possible bit-strings of length **k**.
For example, is one such state for
**k=5**.

The dimensionality of the Hilbert space grows exponentially with **k**.
In some very real sense quantum computations make use of this enormous
size latent in even the smallest systems.

Wed Aug 23 11:54:31 IDT 1995