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