Lectures on TQC: Miguel Aguado 9-13/5/2011
An introduction to topological order and topological quantum computation
Miguel Aguado,
Max-Planck Institute for Quantum Optics, Garching, Germany
In this course we will cover the basics of topological order, the collective organisation of matter in extreme circumstances that lies at the heart of phenomena such as the fractional quantum Hall effect. We will focus on topological order in quantum lattice systems, with emphasis on Kitaev's proposal to use such systems as quantum computers taking advantage of the emergence of anyonic excitations.
Lugar: Sala de conferencias, Serrano 121, CSIC
Día y hora: 9-13 de mayo, 16:00 - 19:00
The preliminary plan for the course is as follows:
Day 1: Basics of topological order. The toric code.
Day 2: The mathematics behind topological order.
Day 3: Examples on the lattice. Quantum doubles. Colour codes. The honeycomb model.
Day 4: Fragility and stability of topological order. Implementations.
Day 5: A bit of condensed matter. The quantum Hall effect, topological insulators.
Some bibliography:
- A. Yu. Kitaev, Fault-tolerant quantum computation by anyons, Annals Phys. 303, 2--30 (2003), arXiv:quant-ph/9707021.
- E. Dennis et al., Topological quantum memory, J. Math. Phys. 43, 4452--4505 (2002), arXiv:quant-ph/0110143.
- M. A. Levin and X.-G. Wen, String-net condensation. A physical mechanism for topological phases, Phys.Rev. B71, 045110 (2005), arXiv:cond-mat/0404617.
- A. Kitaev, Anyons in an exactly solved model and beyond, Annals Phys. 321, 2--111 (2006), arXiv:cond-mat/0506438.
- H. Bombín and M. Á. Martín-Delgado, Topological quantum distillation, Phys. Rev. Lett. 97, 180501 (2006), arXiv:cond-mat/0605138.
- C. Nayak et al., Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083--1159 (2008), arXiv:0707.1889.
- M. Z. Hassan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82, 3045--3067 (2010), arXiv:1002.3895.
