Quantum Computing or: "Quantum Chat Room"
Topological Electronic Phases and Quantum Computation
Gil Refael, California Institute of Technology, Pasadena, USA
A main obstacle to the realization of a quantum computer is the tendency of quantum system, no matter how small, to interact with the environment and entangle with it. If the quantum system is used as a memory device, that will mean that the information in it is lost. Alexei Kitaev, trying to find a general platform which will overcome this difficulty, proposed that if the quantum system is in a topological phase, it will be protected from much of the decoherence . In a topological quantum Qubit, Kitaev argued, the information will be stored in the long range structure of an electronic state, rather than in a local degree of freedom of a particular electron. In my talk, I will begin by explaining what a topological phase is, and continue by discussing how correlated electronic systems may realize such phases. A particularly revealing example is that of a Majorana Fermion, which is, in some sense, half an electron. I will explain this mysterious statement, and explain how to use Majorana fermions for the purpose of quantum memory.
Fault-tolerant quantum computation by anyons, A. Yu. Kitaev, Annals Phys. 303 (2003).