The history of computer technology has involved a sequence of changes from one type of physical realisation to another --- from gears to relays to valves to transistors to integrated circuits and so on. Today's advanced lithographic techniques can squeeze fraction of micron wide logic gates and wires onto the surface of silicon chips. Soon they will yield even smaller parts and inevitably reach a point where logic gates are so small that they are made out of only a handful of atoms; i.e. the size of the logic gates become comparable to the size of atoms.
On the atomic scale matter obeys the rules of quantum mechanics, which are quite different from the classical rules that determine the properties of conventional logic gates. So if computers are to become smaller in the future, new, quantum technology must replace or supplement what we have now. The point is, however, that quantum technology can offer much more than cramming more and more bits to silicon and multiplying the clock-speed of microprocessors. It can support entirely new kind of computation with qualitatively new algorithms based on quantum principles!
The advantage of quantum computers arises from the way they encode a bit, the fundamental unit of information. One number, 0 or 1 specifies the state of a bit in a classical digital computer. An n bit binary word in a typical computer is accordingly described by a string of n zeros and ones. An atom might represent a quantum bit, called a qubit in one or two different states, which can also be denoted as 0 or 1. Two qubits like two classical bits can attain four different well-defined states (00, 01, 10 and 11).