NUI MAYNOOTH  DEPARTMENT OF MATHEMATICAL PHYSICS SEMINAR

Friday 2 December at 3:30 p.m.

Lecture hall CS1, Callan Building, NUIM North Campus


Dr. Jiri Vala
Department of Mathematical Physics, NUI Maynooth

Topological Quantum Computation

Classical physics underlies existing computational technologies and determines their limitations. A number of important problems, e.g. factorization of integers into their prime factors, the graph isomorphism problem, or evaluation of the Jones polynomial of knots, are intractable on a classical computer.

Quantum computation is able to make some of these problems tractable because its computational power derives from physical processes of a quantum nature. Its realization however poses nontrivial technical challenges from which the most significant one is protection of quantum computation process against errors. Fault-tolerant quantum computers can be engineered using concatenated quantum error correction techniques but this requires an extremely large overhead in physical resources. Topological quantum computation provides natural fault tolerance, thereby circumventing these difficulties.

After introducing quantum computation from a computational complexity perspective, I will focus on topological quantum computation, on its relevance to quantum algorithms and on its natural fault tolerance. Essential materials for topological quantum computation are certain topological phases of two-dimensional many-body quantum systems. I will review main properties of these phases, and will conclude with a discussion of their physical realization.