[Music]
The problem with the constituents of a quantum computer, so called qubits,
is that they are very small, very fragile, and
Its inevitable that they will be effected by outside noise.
My research mostly focusses on quantum fault tolerance
which is the study of how to make quantum computers robust against noise.
So we work on something called error correction codes
which is analogous to
classical codes which are used for data storage
and data transmission every day,
So if you use your cell phone or CDs,
they use classical codes.
Currently, people favour planar
architectures, meaning that
your constituents, your qubits are kinda on a plane
and they can only talk to their nearest neighbours,
and of course this makes a lot of sense in current setups in the lab
you only have a few qubits
currently the world record is I think 50 qubits, by the Google team, or there around 50 qubits
And everything is inside the one fridge and I don't know the control is very hard so you
certainly want things to be as easy as possible for the experimentalist.
So,  my current work,
together with Vivien Londe at Inria
and we considered some
more exotic geometries, these are
codes where the qubits, or where we pretend
as if we lived in some 4-D curved space
and the qubits still only interact with their nearest neighbours
but according to this curved dimensional geometry.
At first, it sounds insane for doing this because
obviously we don't live in 4-d space and also there is also no
hyperbolic curvature, at least on small scales.
The reason to do this is essentially this is like a
way of deriving
these quantum codes, which have very high performance
extremely nice properties for
error correction detection.
So this would be like one tile that we
use to tesselate this 4-D space. I mean
you kinda use a polygon to tesselate a space.
You can use like a square
to tesselate  space or like a hexagon to tesselate space
and this would be the 4-D analogen of this square or this hexagon.
So you take this which is a 4-dimensional polytope
and, you
at its boundary because its 4-dimensional the boundary is 3-dimensional
so you take a 3-dimensional boundary and you attach another copy of this
and they align, and you can use this to tile the full space.
Just as in 2-D you would take like a hexagon and you'd take an egde
and  you kind of put them together such that the edges meet.
Here, the edges are actually dodecahedra
and you make them align so that meet.
This is  essentially one of these tiles
called the 120-cell,
which is a highly geometric object.
The first who suggested to use 4-D hyperbolic geometry
were two mathematicians,  Larry Guth and Alex Lubotzky,
and they
essentially showed that
using 4-D hyperbolic geometry you can derive codes which
break certain conjectured bounds.
They were interested in disproving this conjecture,
but in their work
it wasn't really clear how to actually build this stuff.
And this was something Vivien and I provided.
The next step regarding this project would be to really make
a very detailed comparison
to currently favoured schemes
So most likely their will be
a regime where the current scheme will be favourable,
certainty, inside a fridge yo want things to be
locally connected
certainly has some advantages
but certainty for modular architectures
I think our scheme is very competitive
it has very appealing features,
such as simplified control,
better use of resources.
So doing this comparison and really showing
in detail
how it might beat the current schemes.
