Abstract: A serious challenge in making quantum computers and quantum computation is that most of quantum systems are highly fine-tuned and are very sensitive to any perturbation. In this talk I will first briefly discuss that exchange statistics in 2+1 D is fundamentally different than other dimensions and the quasi-particles are no longer classified as fermions and bosons. Indeed we can have an infinite tower of particles referred to as anyons. The reason is that the braid group instead of the permutation group describes the exchange in 2+1 D. Hence, the mathematical theory of the 2+1 D systems is the modular tensor category theory. Next, I will explain that a certain type of anyons, those with non-Abelian exchange statistics, can be employed to build upon topologically protected quantum bits immune to interaction, disorder, thermal fluctuations and other sources of quantum decoherence.
In the second half of my talk, I will discuss our recent proposal of realizing Fibonacci anyons, a non-Abelian anyon that can store and process quantum information and perform all the required logical gates through braiding operations. I start with the experimentally accessible bilayer 2/3 fractional quantum Hall state, and investigate the effect of strong interlayer tunneling on it. Using a variety of distinct approaches I show that the system will undergo a continuous phase transition to the non-Abelian Fibonacci phase. This raises the question whether the Fibonacci phase has already been realized in experiments on wide quantum wells of GaAs.
Reference: A. Vaezi, M. Barkeshli, arXiv:1403.3383
Time: Monday, June 9, 2014 at 15:00 in Larak Seminar Room