We can get upper and lower bounds on the area and time to solve problems. However, there is no practical multiplier which can meet this bound. Another model of computaion, which models circuit elements which are just beginning to be feasible, is the quantum model. This model was first discussed, by Feynman, Deutsch, and others, about 1980. If two qubits q1 and q2 interact then they can change state due to the interaction.
Superposition implies that many computations can be carried out simultaneously.
Several practical problems in realizing such a computer exist. For example, 1. Currently efforts at MIT and other places are resulting in some progress in this area. For example, an AND gate is not time reversible since there is no way to recover the inputs by observing the outputs. This idea leads to some interesting computaional abilities.