Topological phases and quantum computation

The basic building block of quantum computation is the qubit, a system with two (nearly) degenerate states that can be used to encode quantum information. Real systems typically have a full spectrum of excitations that are considered illegal from the point of view of a computation, and lead to decoherence if they couple too strongly into the qubit states during some process (see Fig. 4.1). The essential problem, then, is to preserve the quantum state of the qubit as long as possible to allow time for computations to take place.