What I'd like to do today is talk a bit
about quantum computing which is my
own research area,  and tell you a bit about where we are now and where we might be in a few years time.
So what's a quantum
computer?  So it's a machine which is
designed to use quantum mechanics to do things that can't be done by any
standard classical computer based only
on the laws of classical physics.  There's
a quantum computer - it's the thing in the
middle not the people around the outside.
OK. So even though quantum computing is in the news a lot today,
the theory of quantum computing is been around for quite a long time.
It was really kick-started back in 1994 where Peter Shor
gave a quantum algorithm for
factorising large integers efficiently
which we don't know how to do
classically.  And this breaks the RSA
cryptosystem. 
And this created a huge amount of
interest in quantum computing. Since then there's been a lot of hard work that
many people have been doing, including on the theory side. We've been developing
new quantum algorithms, new quantum error correcting codes, but crucially also
on the experimental side, and people have
been working very hard to develop better
and better quantum computers using lots
of different technologies. And we're now
finally at the stage where a quantum
computer has, for the first time,
outperformed our best classical
algorithms running on the world's best
classical supercomputer, solving a
particular problem.  So this is a point
with a somewhat terrible name of quantum supremacy and this is a paper from end of 2019.
So what did they do to get this
result?  This is a team at Google who
built a device using
53 qubits which is quantum bits and they
ran a particular task on it and they
showed that this was better than the
best algorithms they could come up with
using a classical supercomputer.
And what did they actually do? They ran a
random quantum algorithm. So they ran a
so-called quantum circuit, which is
basically a sequence of small operations
called quantum gates, and they ran a
randomly generated quantum circuit, and
they showed that, as far as they know,
that the best algorithm that they have,
couldn't reproduce what that algorithm
did. And in fact there's some good
theoretical evidence why this should be
the case too,  because I can't resist
referring to one of my own papers, this
is one example, you can come up with some
theoretical evidence that it should be
hard for classical computers to
reproduce these results even though we
don't have a proof. But so far you know
this thing that we've run is not
necessarily interesting for practical
reasons.  So it's a random algorithm,
it's not necessarily useful.  So it's an
obvious point like what are we going to
do next?  We're going to try and do
something practically useful with these
sorts of devices, because we don't just
want to demonstrate outperforming these
classical machines. We want to do something
useful with quantum computers but in the
next few years the quantum computers
that we have will still be fairly
limited. And in particular they won't
have fault tolerance, they'll be affected
by errors.
They'll be fairly small.  So we don't yet
know how useful these devices are going
to be. And it's a really hard task to try
and make best use of them.  So what I'm
going to try and talk a bit now is what
we could actually do with such a device,
a so-called noisy intermediate
scale quantum machine, and talk about
one particular direction which might be
interesting to try to approach on these
machines. And this is a direction
which I guess a few people think is
interesting, which is simulating a
quantum physical system using a
quantum computer. And this is something  I've worked on recently with Chris Cade, Lana Mineh and Stasja Stanisic.
And this is interesting for practical reasons
because many systems we care about in
the real world are quantum physical
systems, and they are based around the rules of  quantum mechanics.  One very
exciting sample is this model called the
Fermi Hubbard model which is a famous
model in condensed matter physics that
models strongly correlated systems of
electrons. And here we've shown like a
5x5 lattice for this
system so this is a very small example
of a system in this model, but in fact
even a 5x5 array of atoms,
solving this completely is beyond the
reach of today's best classical
supercomputers.  But with a quantum
computer we might be able to approach
this.  So mathematically what does this problem mean?
Well, when I say solving here,
what I mean is basically finding the
lowest possible energy of this
particular physical system, which
mathematically just means finding the
lowest eigenvalue of a matrix. The only
problem is that this matrix is a huge
exponentially big matrix, which is why we
can't do it efficiently but with a
quantum computer. We can try to solve
this problem by producing a quantum
state which encodes this sort of low
energy vector, and we have a classical
optimisation algorithm,which optimises
over these quantum states using a
quantum computer, to try to find this
lowest possible energy. And interestingly
this approach basically works so,
building on a lot of previous work, we
were able to show that
as the depth of your quantum circuit
increases, then the fidelity with which
you achieve the low energy state for
relatively small examples increases
exponentially, which is what you want.  And we're also able to show that for small
amounts of noise in the
quantum computer, then the algorithm
still basically works okay.  I should say
these results are classical simulations
because we don't yet have quantum
computers that are big enough to to
really outperform our classical desktops
for problems of this practical sort.
But still this is interesting
evidence that in the future we will, and
in fact the results we show even though
they're promising, they're still slightly
beyond the reach of the quantum
technology we might have in the next few
years.  So there's still a fair amount of
work to be done here I think. This is
everything I wanted to say I think.  I'm
just about on time and if you'd like to
read more there's a paper on the archive
you can read.  Thanks very much.
