Ternary (and beyond) computation and quantum computing? Binary math is at the heart of most computing, in large part because of the ease with which two energy states can be achieved.  I have always thought that having more states could improve computing power (e.g. using a trit instead of a bit), but there is a seeming lack of attention being paid to the problem.

Some work has been done in the quantum computing area using qubits to achieve more than the normal two energy levels (see, for example, the recent effort at UCSB).

What advances have been made toward having ternary (or greater) computers, and what are the primary the implications of the extra states?
Actually the usual RAM model is just this approach taken into extreme: each "storage unit" has as many as $\textrm{poly}(n)$ possible states (instead of just 2 states). We assume that each memory word can store $O(\log n)$ bits and word-operations have unit cost.

Cf. this question.