Topological Quantum Computing with Majorana Fermions Sergey Frolov, University of Pittsburgh
Majorana fermions are real solutions to the Dirac equation, meaning they are their own antiparticles. For 80 years they have been and continue to be searched for among elementary particles, with some people believing neutrinos to be Majorana fermions. In the context of this talk, Majorana particles are quasiparticles made of millions of electrons in a crystal in a quantum superpositon. We study these quasiparticles for their fundamental importance, which is directly linked to their potential for quantum computers. In a semiconductor crystal, Majorana particles are still their own antiparticles, but they are not fermions. Neither are they bosons. Their technical name is ‘non-abelian anyons’, which means that if two Majorana particles are swapped the Universe can tell – while it can’t with electrons or photons! Swapping, or braiding, Majorana particles in low-dimensional crystals such as pristine sandwiches of a superconductor and a semiconductor, thus becomes a way of storing (quantum) information. One just needs to keep track of how many braids were performed on a system of Majorana particles. One bit of quantum information , a qubit, is stored in a pair of Majorana particles which can be in remote locations – this makes information protected. So far we haven’t performed this braiding experiment, thus it represents the holy grail for the field of topological quantum computing.