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Quantum Information and some of its underlying Mathematics
At the moment this is just a place to put useful links.
In particular here is
an
announcement of some positions that we have available.
Quantum computer: Feynman's idea is, broadly, to use the quantum nature of
physical systems to build a massively parallel computer.
There are several major technical obstructions to puting this into practice.
One is that this device breaks the discreteness of binary computation,
so problems have to be recoded to make computation
computational-fault-tolerant.
One kind of discreteness that can be set up (in principle) to survive
the quantum setting, is topological discreteness.
(Very roughly speaking, while the precise trajectories of a collection of particles in a plane from one time to another
are obscured from us by system noise, the braiding of particle time-lines
is a relatively robust datum.)
This leads us to study certain realisations/representations of the braid group, such as that provided by the Temperley-Lieb algebra.
The TL algebra and its family can be studied from a number of different
perspectives.
From the representation theory perspective, the fundamental invariants
of TL (and several other such algebras) over the complex field
have been worked out by members of the Leeds AGIS group and their collaborators.
(Our original motivation was applications in statistical mechanics.
But the algebraic framework seems well suited, in principle,
to mathematical studies of QI
as well. In actuality, of course, the contribution of our old representation
theory results to QI is epsilonic at best... but it does seem like a
good excuse to get involved.)
Leeds:
Jiannis Pachos,
Paul Martin,
Frank Nijhoff, Tim Spiller,...
EPSRC Project: Physical, algebraic and geometric underpinnings of topological quantum computation
EPSRC Physics Panel (Project Investigators are the 4 named above.)
Start: September 2012
Idea:
Try to build computers with quantum nature of physics used in software/hardware integration (rather than just ``accidentally'' as reason why some hardware components work).
Bleeding edge Physics (in the sense that quantum physics is functional as Engineering, but somewhat open as Physics).
and - serendipitously - ...
bleeding edge maths.
Proposals for addressing the quantum computation challenge use mathematics from several areas (including category theory, diagram algebras, quantum groups,
algebraic representation theory, K-theory, integrable systems, statistical mechanics, q-spin chains and so on).
Positions available on project (to commence after Sep 2012)
2 PhD studentships (enquiries to Paul, Jiannis, Frank or Tim)
2 PDRAs (3 years each) (enquiries to Paul, Jiannis, Frank or Tim)
Other relevant positions available now
lecturer in algebra (1 year)
lecturer in applied mathematics (continuing)
lecturer in pure mathematics (continuing)
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