# Quantum Topology

### Overview

The problems of interest in this CRG are (i) the so-called "many-body problem" in non-relativistic physics, particularly on lattices in low spatial dimension; and (ii) the problem of finding a universal quantum computer which evades decoherence. Phrased this way, these problems seem almost parochial. However we now know that they are in many ways equivalent, and that moreover they are closely related to important problems in theoretical computation, graph theory, in topology, in black hole physics and string theory, and in non-commutative geometry. There is also a strong relation to problems in number theory.

The main purpose of this CRG is to bring together a group of mathematicians and physicists whose interests are united by the 2 problems stated above. Our aim is to resolve some critical issues, which are issues in both mathematics and physics. The work we plan will focus around the following projects:

- 1-dimensional Problems
- Renormalisatoin Group
- Topological Methods
- Numerical Methods
- New Field Theories
- Quantum Environments and Decoherence
- Spin Nets of Qubits

### PIMS Distinguished Chair

In October, 2006, Prof Alexei Kitaev will be visiting PITP and PIMS; he is also holding a 'Distinguished PITP/PIMS visiting Professorship'. During his time here he will be giving a short lecture course, which should be of interest to those in theoretical physics (particularly condensed matter physics and quantum information), in mathematics (particularly topology and related areas), and in computer science. Details of the course, and also some biographical details about Kitaev appear below:

Kitaeve was originally trained as a theoretical physicist (he did his PhD in the Landau institute with V Pokrovsky). However he branched out after that into both mathematics and computer science. Upon arrival in the USA he worked as a postdoc both in Microsoft and in Caltech, and then in a very unusual move, he moved from a postdoc to a full Professorship at Caltech in 2002, with positions both in Theoretical Physics and Computer Science. He now also has a position at Santa Barbara, in the new centre for quantum information there.

Kitaev is well known for fundamental work both in physics and mathematics. Perhaps his best known recent work, published in 2003, was the invention of the topological quantum computer, in a paper which was already cited over 500 times before even being published.

Alexei Kitaev has an office in the PITP visitor centre.

**Faculty**

CRG Leaders:

- Philip Stamp (UBC)
- Boris L. Spivak (U. Washington)
- Joel Feldman (UBC)

UBC:

U. Alberta:

U. Calgary:

SFU:

U. Washington:

Others:

M. Freedman (Microsoft Research), A. Kitaev (Caltech), C. Bourbonnais (Sherbrooke), D. Senechal (Sherbrooke), A. M. Tremblay (Sherbrooke), R. Gill (Utrecht), R.B. Laughlin (Stanford), A.J. Leggett (Urbana), S. Popescu (Bristol, UC Berkeley), P.B. Wiegmann (U Chicago), S.C. Zhang (Stanford), C. Nayak (UCLA).

Postdoctoral Fellows