### Minicourse Algebraic Aspects of Quantum Computing

From ** 30 October---3 November ** a DIAMANT minicourse on
quantum computing and its algebraic aspects is held at the CWI. Lecturer: Gábor Ivanyos.

Goal: Understanding the most
important results and tools in the non-commutative hidden subgroup
problem, including the algebraic
background.

Prerequisites:
The audience is assumed to be familiar with
quantum complexity theory, especially with
the quantum circuit model, with the underlying
linear algebra. Basic knowledge in group theory
(groups, subgroups, cosets, normal subgroups,
homomorphisms, structure of finite abelian groups).

## Coordinates and Schedule

All lectures take place in room M280 at the CWI (
address,
maps , and
directions).

The daily schedule is as follows:
10:00-11:00 | lecture 1 |

11:00-11:15 | break |

11:15-12:15 | lecture 2 |

12:15-13:30 | lunch break |

13:30-14:30 | lecture 3 |

14:30-14:45 | break |

14:45-15:45 | lecture 4 |

15:45-16:00 | break |

16:00-17:00 | exercise session |

Participation is free, but you'll have to pay for coffee and lunch yourself.

## Course outline:

Algebraic introduction:
Introduction to the structure of finite groups.
Introduction to representation theory of finite groups and Fourier
transforms.

Quantum HSP algorithms based on the
abelian Fourier transform: abelian HSP, dihedral HSP, HSP in
solvable groups of bounded exponent.

Single register methods: weak
and strong Fourier sampling, hidden normal subgroups, HSP in affine
groups.

Multiregister methods: missing
harmonic, pretty good measurements, HSP in dihedral groups again, in
Heisenberg groups, and in extraspecial groups.

Limitations of the approaches above.

Note: The first two days will be principally
devoted to the algebraic introduction. However, it will be mixed with
some quantum algorithms, therefore it might be useful for those with
strong background in algebra as well.

## Slides

These can be found here.
## Registration

To register for this event, please send an e-mail to j DOT draisma AT tue DOT nl

For information about the contents of the course, mail gabor DOT ivanyos AT sztaki DOT hu