The field of research is known as Quantum Computing. Whereas DNA computers operate with molecules quantum-mechanical computers operate with fundamental atomic particles such as atoms, electrons and photons. Quantum mechanics describes the interactions between such particles and these interactions are very strange. The act of measuring the state of a particle is an interaction that fixes its state - until the measurement is taken it could be in any one of the possible states. Scientists have developed a new type of probability theory to describe the probability that a particle is in a particular state.
Conventional computers work with logic gates.
For example, the AND gate takes two inputs and the output is 1 if both inputs are 1, otherwise the output is 0. Any arithmetic task can be achieved using a combination of these logic gates. It turns out that quantum particles can be manipulated in ways that achieve the same logic and this is how scientists are building the first quantum-mechanical computers. The task of making a useful device is going to be very difficult but some simple demonstration devices have already been made. It is the second property of quantum particles that is so alluring.