Bubbles forms spheres because it is the shape with the lowest surface area to
volume ratio, you couldn't package that air in a more efficient way. Nature is
good at working out things like that quickly for example if I was to dip this
strange shape here into some soapy water nature would figure out how to span this
shape was a soap film whilst using the least amount of surface area.
Quantum computing hopes to piggyback off this computational power of nature and I
hope that we can explore this concept a little bit more today. For this video
I've teamed up with Brilliant to show you through part of a course on quantum
computing, it's a course made in collaboration with Microsoft and
Alphabet X, companies which are taking quantum computing very seriously. We will
work through the nature of computation quiz and if by the end of the video you
are still hungry to learn more about this topic you can sign up for an
account at the brilliant.org/tibees using that link you can get 20%
off a brilliant premium subscription. So welcome to quantum computing. Our focus
is learning how to exploit the laws of quantum mechanics in order to compute so
we need to see the big picture here and we're going to do that by answering two
questions. Number one, what is the nature of quantum computing? and number two, why
do scientists think it will lead to speed ups on a variety of important
problems? So it says here that in the dawn of the 20th century deterministic
predictions from classical mechanics we're failing to explain new experiments
I think I know one of the things they're talking about and they have a picture of
it here it's the double slit experiment and so a new theory was necessary to
describe the results of experiments performed with quantum objects that's
photons, electrons and other microscopic particles. Quantum mechanics forgoes
deterministic predictions and instead embraces the concept of probability so I
guess with the double slit experiment what's meaningful is the distribution of
all of these particles that you end up with in the end but actually the path of
any single one of them seems random and doesn't really give you
much information it's the distribution of all of them together that that leads
you to understand what's going on. All right so we've got
classical mechanics we've got quantum mechanics, and the course says here that
we're going to now go on to play a little bit of a game. The game that we're
going to play is one that I know as the Galton board although apparently has
other names. The game is a simple demonstration of how probabilities can
emerge from a mechanical object so each bin at the bottom is associated with a
different prize and the thrill is to watch as your fate is determined by the
random bounces of the ball off the pegs so you put a ball down here it
apparently randomly bounces off these pegs or seems to do so and lands in one
of these bins at the bottom. That's the way it would classically happen with a
ball and pegs but we're going to remake it with our quantum objects, our photons.
It asks us what is the most likely outcome of these
games? And well choosing from which bin the ball would land in I would say it
would most often land in bin number two that would be the middle, just because
there are two different paths that it could take to end up in number two
while there's only one path to get into bin one or bin three. With a single photon
the quantum game behaves much like the mechanical version with the bouncing
ball the more possible paths that lead to a given outcome the more likely
that it is, but if we shoot two photons into the top of the grid things get
more interesting. When two or more photons meet somewhere on the grid they can
interfere with one another. Interference can lead to anything from the
two photons adding constructively and appearing like two photons or cancelling
each other out entirely as if there were no photons at all. Yeah thanks to
this interference we don't have any better way to find where the
photons will most likely end up than to trace out all the paths each photon can
take and calculate the interference effects where they meet so we can't just add
up the paths like we would do classically so
what we're concerned with here is that to predict the end state of a quantum
object we need to account for all the paths it could have taken to get there.
And so how difficult is it to computationally predict the outcomes of this
quantum game? In just this most simple example where we're putting in two
photons and we have two rows of beam splitters then each photon can take one of
four paths leading to 16 different total combinations of paths and that's 16
different interference calculations that we would need to do. Obviously as the
game gets larger with more photons or just more rows of beam splitters it's going
to get a lot more complicated. It tells us here that calculating the interference
for each path combination it's not too hard it takes tc seconds and
it asks us, how much time does it take to calculate the photon distribution
for a three-layer quantum game with two photons? So we need to figure
out how many total path combinations there are and then times that
by tc to find out how long this calculation would take us. For two rows we
had 16 path combinations and for three rows we're going to have more than 16
because there's more possible paths that can be taken so I'm going to put in 64
tc as my answer to how long this is going to take. All right so instead of doing
all of those calculations the question is what if we just build this thing?
So if we had a beam splitter we can just shoot two photons into the top and
use photon counters to find the distribution at the bottom experimentally
instead of even trying to work out the distribution so for each measurement
the sampling time would be equal to the time the photons take to traverse
the gap L from the first beam splitter to the row of photon counters at
the speed of light. For a single beam splitter with two detectors like this one
here this photon sampling time a time tq so the question is how much time
does it take for a three-layer experimental solve of this quantum game?Alright
so if tq is how long it takes the photons to go from there to there this
looks like it's just three times as much so I would go for three times tq.
So how long will a photon counting measurement in an n-layer game take experimentally?
so if we had n layers that would just be n times tq I think the idea
here is that n times tq is increasing a lot less quickly than our computational
one, our two to the 2n, yeah so the time required in these two different
methods computational and experimental are increasing at different rates.
As the number of layers of n increases our classical computation is increasing
exponentially with in whereas our quantum experiment is increasing only
linearly with n. This is because the quantum objects in the experiment have no
obligation to compute every path according to the rules of quantum mechanics
like we're trying to do with our computer, they obey quantum mechanics as
a matter of course. It's just what nature does. If we assign a time to tq from
our quantum experiment and tc from our computational one, even though tc is lower
than tq we can see visually down here what is really gonna start to happen
so for a low number of rows in our experiment it is quicker to you know just
do it classically to just figure it out you know if there's less than about 10
rows we can just do the maths and work out the interference paths in a pretty
quick time but once you get up to about 11-12 layers deep it's really going
up exponentially and it's starting to take you ages each time to calculate all
these paths whereas the quantum experiment which is just going up linearly
although at the start it would take you a little bit longer to do it through
the experiment and the long run it will be much much quicker. With the language
we've been using it's been kind of obvious that
the classical approach is occurring on an actual computer whereas the quantum
approach we could believe it's happening in kind of a lab experiment setup
but actually because it says here both methods produce the same information
so if one is a computation so is the other. The basic truth of what's
happening in quantum computing is that we're directly employing quantum objects
to perform a specific computation to whatever extent we can map
and mold our computational problem on to quantum objects we'll be able to use
it to our advantage. If a problem has an inherent quantum aspect
to it like finding the interference pattern then we could expect
a quite big speed-up. This problem was really hard to compute on a classical
computer because the resources that it requires grow exponentially as n increases
but I like the way they said here it is quite easy to compute 'quantumly'
with an experiment and I think that's basically what our quantum computer
is doing it's it's not an experiment in a lab like we might think with
a Galton board and beam splitters and things like that but we're mapping our
problem on to quantum objects and kind of exploiting that way of nature to try
and do things quicker. To take things back to where we started off the video we
can take a little look at this green sculpture here which I think is really cool
and it is made of these big metal circles with a green fabric draped between
them so the shape we see here in the picture is apparently ideal in this way
it is impossible to find any other such smooth shape that contacts the metal
rings while using any less material. All right so this is an optimized
sculpture, to figure out things like this, so to find this surface, this green
surface, computationally is quite involved and requires algorithms built
on sophisticated mathematics. The quiz asks us here, is there an easier way to
work it out and which phenomenon might be able to compute this surface in real
time using the laws of physics? Well if we go back to the start of the video I
used a soap bubble. Soap bubbles always minimize the surface area so we can have
a little look on this page, yeah natural systems like soap bubbles have a tendency
to wiggle around until they minimize their energy. Minimization problems
make up so much of physics and you might have encountered them in problems
before things like the principle of least action, trying to I guess
minimize the action on a path that an object would take. For a soap film the energy
is equal to its total surface area times its surface tension so this is
basically the energy required to keep the layer of soap stretched out. Here's another
picture of dipping a spring into the soap and this soap goes all the way around
the fingers as well, there's your answer from nature and here's your answer
from an actual classical computer as well. I could try to use quite a complicated
shape one that is definitely very difficult to find the spanning surface
area computationally, nature however still gives me this answer
instantly and it's really fascinating. So you might consider the computational
power of soapy water to be essentially zero but if you have a very unique
problem to solve it can be far superior to a modern computer I guess quantum
computing is a bit about trying to make humans as clever as soapy water.
We would like to piggyback nature to perform our calculation for us so in a
real sense quantum computers do not compute at all but simply carry on according
to the laws of physics. The extent to which quantum computing can revolutionize
computation depends on us finding ways to restate computational problems
in equivalent quantum systems. I think this kind of makes me realize that quantum
computing is not really just a magical increase in all of the normal computing
that we do and all of the normal problems that we try to solve on computers
but it's rather coming at computing from a different angle and it's
going to be up to us to be able to map our problems into the quantum world so
that we can take advantage of quantum computing, but it's all very clever and it
also makes you realise how clever nature is itself that you know nature can
calculate these things so instantly on on such a grand scale and I don't know
if we really have any idea how it happens. I hope that you've learned a thing
or two in this video today and thank you for watching.