Full transcript
0:00This is my homemade quantum computer.
0:03It's totally useless because of how small it is, but technically it is a quantum computer.
0:08I made this because despite doing my whole PhD on quantum computing, I'd never actually
0:12seen one in real life before.
0:14And all the pictures I'd see were of these crazy space age looking contraptions.
0:19Quantum computers aren't at their core actually that complicated.
0:24So I figured I'd try and explain them to you while I work out how to actually make one.
0:30I had some ideas going into this, as well as an unhealthly large collection of crystals
0:34and lasers.
0:35So I figured, how hard could this be?
0:38In theory, a quantum computer is pretty simple.
0:42In the first part, you have these things called qubits.
0:46And in this case, I'm going to be using light to be making my qubits.
0:50There's many other choices you can make, but light is by far the easiest thing that you
0:54can do at home.
0:55Usually, for a good quantum computer, you would have a whole bunch of qubits.
0:59Like, at least 20 to be respectable.
1:02For me, though I'm just going to have the one because it's going to make the whole thing
1:07just way way easier to do.
1:09But that's why this quantum computer is going to be, while technically a quantum computer,
1:15pretty useless.
1:16In this first step we want to guarantee that the light that's going to be exiting the step
1:21is in a particular state.
1:22So what I mean is there are lots of different states that light could be in when it comes
1:26out of this laser.
1:28But we're going to put in this little filter here that is going to filter out all of the
1:33different types except one.
1:35And so that guarantees that the light that is coming in here is of a particular state.
1:41And we know what that state is, but what's going to happen in the computation step is
1:46that that light state is going to change.
1:49And the way we're going to do it is by using this calcite.
1:52Depending on what computation I want to do, I can change the thickness of the calcite,
1:57I can also change the orientation.
2:01And I could even, you know, add in some other ones that are also at different orientations.
2:06In a quantum computer with more than one qubit, you would actually need some more fancy crystals
2:12than the ones that I can afford.
2:14For example, one called BBO.
2:16what would happen in that case is that the two qubits would enter and exit but the light
2:21that comes out afterwards is in a particular state called entangled.
2:25So these two qubits are now entangled with each other.
2:27But we're not going to have to worry about that because frankly I can't afford BBO crystals
2:32and also even if I could.
2:33They're super, super hard to work with, so we'll stick with calcite.
2:36All right, so our light starts off in a state that we know, then it goes through this computation
2:41step and gets changed in some way, and the final step is really simple.
2:45We're going to try and figure out something about how the light's changed.
2:48We won't be able to figure out exactly what it's doing now, but we will be able to figure
2:52out at least some, hopefully, useful information about the light.
2:55At a high level, that's all a quantum computer is.
2:58But you might be wondering, how is this like a computer at all?
3:02Well, computers also just take inputs in the form of 0s and 1s, and then they transform
3:08them in some way.
3:09For example, imagine a computer program that helps you add.
3:12You put in two numbers, which it'll interpret as 0s and 1s, and then it'll start processing
3:17those in, like, the standard algorithm for adding.
3:19Like, first step, add the rightmost numbers.
3:22Second step, add the next two numbers, and if there's an overflow, put that into the
3:26next column, etc.
3:28Then the new set of processed bits is the answer.
3:32In a similar way, quantum computers take some qubits of light in some state and then process
3:36them to give you some new state.
3:38A quantum algorithm might look like, first put this crystal at this angle, then put in
3:43another fancy crystal, and then whatever you get out at the end is the answer you were
3:47looking for.
3:48But going back to our standard computer, you can do a lot more than just add numbers.
3:53You could, for example, multiply numbers, or you know, render an image of an oscillating
3:58electron, or really whatever you want.
4:00And in the same way, a quantum computer is something where you can do a bunch of different
4:04processing of light, depending on exactly what it is you want to compute.
4:09We'll get back to the question of what quantum computers are actually computing in the next
4:13video, but for now, our aim is just to show that this setup can transform light in lots
4:19of different ways.
4:20Because yeah, that's what a quantum computer is.
4:23So, that's what's going on here at a high level, but let's get into the details, starting
4:28with what is a qubit exactly?
4:33Here's everything that you need to know about light to be able to make a qubit from it.
4:37Light's whole thing is to harass charged particles like this electron.
4:42So this is what I mean.
4:44Imagine we've got some light coming along.
4:46I've represented it like this because as the light passes by this electron, These little
4:53things are supposed to represent the force that the electron will feel because of this
4:57light.
4:58So you can see that this light is first pushing this electron up and then down, and then up
5:05and down.
5:06So as the light goes past, the electron will jiggle perpendicular to the direction of the
5:12light.
5:13But we live in 3D space and so that leaves the light with lots of different options in
5:17terms of harassing this poor electron.
5:19So one option is that the light is oriented like this, which means that the electron will
5:24jiggle up and down as the light goes past.
5:27But we can orient the light anyway so it could be like this, which means that the electron
5:32will be jiggling forwards and backwards.
5:34But it can be any other direction as well.
5:36So, if I put the electron here, and the light is coming towards, that's directed like this,
5:41we'll call that horizontally polarized light, whereas light that is oriented like this is
5:47called vertically polarized light, and you can have every option in between.
5:53So if the light was like this, we could write the state of the light like that.
6:00All right, so if I have some light and it is in a particular state, so say this state,
6:06then this is a qubit.
6:08Now you might be wondering, what has this got to do with a bit?
6:12A bit has, like, just two possible states that it can be in.
6:15It can either be in the zero state or it can be in the one state.
6:18Whereas this thing has an infinite number of states.
6:21So where's the, like, two ness in this?
6:23Well there actually is a two ness in this state.
6:25And that is that if I take two of these, and let's say this one is oriented horizontally
6:30and this one is oriented vertically, and I combine them, I can actually make any other
6:36type of light that I want.
6:38Here are two laser pointers and this one only gives out horizontally polarized light, this
6:43one only gives out vertically polarized light.
6:46And my claim is that by combining these two lasers, you can actually get any other qubit
6:52that you want.
6:54But it just depends on how you combine them.
6:55So for example, which one is stronger, but also how in sync or out of sync these two
7:00lasers are.
7:01If you think of the horizontal state as the zero state of light and vertical as the one
7:06state, then you can see what people mean when they say that a qubit is both zero and one
7:11at the same time.
7:13No matter what type of light you have, you can always think of it being made of some
7:17zero part and a one part, but the light might be more horizontal or more vertical, in which
7:24case it's more zero or more one.
7:27But the important thing to remember is that any light state can be made by adding zero
7:31and one.
7:33Now that's really not obvious, so I'll try and prove it.
7:35Say that the light that you really want is this kind of 45 degree light.
7:39So that's light that originally pushes in this direction, and then eventually will push
7:44in that direction.
7:45How can I get that by just combining the two bits of light that I do have, which are oriented
7:50like this and this?
7:51Well, here's what would happen if I just shone some horizontally polarized light at the same
7:56time as some vertically polarized light.
7:58At first, this one is pushing in this direction, and this one is pushing upwards.
8:04So in total, it's like this electron's getting pushed up and to the right, which is exactly
8:10what we wanted this light to do.
8:11So you can see that shining these two things at the same time just gives you light in the
8:1745 degree polarisation.
8:20That's not going to be quite right because if you just shun these two bits of light then
8:22you're going to get something that's a bit too strong, even if it is in the right direction.
8:26So you kind of need to tone both of them down.
8:28And these two factors just represent how much you're going to tone down both of them.
8:32You've got to do a little bit of trigonometry to figure out that those are the right numbers,
8:36but it's not a really big deal.
8:38The point is just combining horizontal and vertical light got you the light at 45 degrees,
8:43which is what you wanted.
8:44But say instead you want your qubit to be in another state.
8:47So, for example, More like this, and you can see that this is mostly upwards, but a little
8:55bit to the right.
8:57So to actually do this, all you've got to do is combine these two lights as before but
9:02make the horizontal bit of light way less strong.
9:05So in other words, like literally turn down how strong the light is that's coming in the
9:09horizontal direction.
9:11And so now the electron will be pushed very weakly to the right, but much more strongly
9:16upwards.
9:17And so in total it's going to be pushed in this direction, which is exactly what we wanted.
9:21So, in other words, this has to be a small number, and this has got to be a bigger number.
9:26Okay, so that works, but here's a way more tricky one.
9:29What if the qubit that I want is light going in this direction?
9:33Now what I want is light that is going still in the right direction at first, but instead
9:41of pushing up, it actually pushes downwards.
9:44Is that possible?
9:45Well, it is, because if these are my two light beams, so far I've been considering the case
9:50where both of them start off at their sort of maximum strength.
9:54But what about if I start off the horizontal component at its maximum strength as before,
9:59instead of starting this one off so that it is pushing upwards with its maximum strength,
10:04what if I start it so that it's pushing downwards?
10:07Now I got exactly what I wanted.
10:09This light is going to be pushing to the right.
10:11This one is going to be pushing downwards, so the total effect is like you're pushing
10:16in that direction.
10:17Because we have to flip this light sort of upside down, um, the way that we're going
10:22to represent it in the equation is to represent this as a negative.
10:27There's another way to think about this same state of light that's going to be really useful
10:30later on in the video.
10:32So let's start with this horizontal and vertical light as before.
10:37But, now we're going to start with them being perfectly in sync with each other.
10:42So now when this is pushing upwards, that is pushing to the right.
10:47Which isn't what we wanted.
10:48So how do we get the type of light that we want, which is the one that pushes to the
10:53right at the same time that it pushes downwards?
10:56Why don't we just move these two bits of light out of sync with each other, until they're
11:03here.
11:04So now they're kind of perfectly out of sync with each other, and you can see that this
11:09light is pushing down when this one pushes to the right, which is exactly what we wanted.
11:16So another way of thinking about light is it's not just about how much horizontal and
11:21vertical there is.
11:22It's also about how in in-sync or out of sync they are.
11:25Okay, so I hope that gave you the gist of why you can get any polarisation of light
11:30you want, so any qubit that you want, by just combining light that is in this state and
11:36this state, and by adjusting A and B, which is both the relative strength of these two
11:41lasers, but also how in sync or out of sync these two lasers are.
11:45So, this is your qubit.
11:47The horizontal state is kind of like the zero state, and the vertical state Is like the
11:54one, but you might be wondering, like, how is this actually like a bit because bits contain
11:59information?
12:00Where's the information in this?
12:02Well, there is information because if I have a bit of light that's in a particular state
12:08and I don't tell you what that state is, then you don't know what A and B are.
12:12But if you find out later what that state is, then you do know A and B and you've learned
12:16something.
12:17And so that's the kind of way that information is encoded in a qubit.
12:21But you can see that it's like a lot more information than what would be inside of a
12:25bit.
12:26Because to find out what a bit is, you just need to know, is it zero or is it one?
12:30Whereas there are so many more options for what a and b can be.
12:34And so in a way, a qubit really contains a lot more information than a bit.
12:40It's another question whether you can get that information out, but for sure there is
12:44more information encoded in there.
12:46The first step in any quantum computation is to start your qubits off in the state you
12:51want them to be in.
12:52So far, I've been saying that the way to do that is by combining this horizontal light
12:57and this vertical light in exactly the right way.
13:00But that's actually a really, really difficult way to do it, um, and it's not going to be
13:04the way that we're going to do it at all, because it's really hard to determine how
13:08in sync or out of sync these lasers are.
13:10Like, I'd have to start them at exactly the right time for them to be in sync, and that
13:15just Basically impossible.
13:17So the way that we're going to do it is instead using this piece of plastic.
13:25These bits of plastic are called polarizing film and they don't look like much but look
13:30what happens when I do this.
13:32If I put it like this and then I slowly rotate it you can see it gets darker and darker until
13:40it gets to its maximum darkness and then gets lighter and lighter again.
13:44You may have seen these things in science class, um, I certainly had, but it was only
13:48when I was researching this video that I understood how it works, and it's super clever.
13:53So essentially, this is made out of long, plastic polymer molecules.
13:59that are all aligned with each other.
14:00There's a whole bunch of them in here and they're all facing in the same direction.
14:05This has a really interesting effect on light because it acts as a filter for certain polarizations.
14:10I'll show you how.
14:12Let's represent one of the polymers in the material like this.
14:15And it's going to have a bunch of electrons in it.
14:17By the way, the reason why we're always talking about electrons is that electrons are generally
14:20a lot more free than protons are.
14:23Um, protons are heavier and they're bound up in the nucleus and so they just aren't
14:27that likely to move around.
14:29Whereas electrons, especially like these outer shell electrons, can be quite mobile.
14:33And so that's why when we're talking about what happens when an electric field passes
14:37through a material, it's more useful to talk about what happens to the electrons.
14:42Let's say I have this electron and indeed a bit of light comes and hits the electron.
14:49Now if the light is oriented in this direction, then what happens is the electron feels a
14:55force up and down.
14:58And because it's pretty mobile, it [00:15:00] has a long bit of molecule that it can move
15:02up and down in.
15:04But that means that as this light comes and hits this material, It makes all the electrons
15:12in here jiggle quite a bit and all of that long distance movement means that, uh, the
15:18light's energy gets wasted.
15:20And so the energy of this light just gets used up before it goes through.
15:26And that's why you don't get light that is of this polarisation go through that material.
15:32On the other hand, what would happen if the light is perpendicular to the direction of
15:36the molecules?
15:37Well, in this case, the electron wants to be able to move in this direction.
15:43But it can't really, it's sort of stuck, like the molecule isn't that big on that direction.
15:48And so it doesn't really move at all.
15:51And that means that this energy from the light coming in on this direction doesn't really
15:56go to the electrons, they don't really do anything with it.
16:00And so it's able to pass right through.
16:02And so that's why this simple bit of plastic is able to filter light that's coming in in
16:08this direction and pass through light that's coming in in this direction.
16:13But what about light that's oriented in some other direction?
16:15Well, for light coming in like this, remember, it's the same as if we had a bit of horizontal
16:21light plus a little bit of vertical light.
16:25And so we know exactly what's going to happen.
16:27The vertical part, which is this part, is going to get used up.
16:31The electron is going to use that to jiggle up and down and so that bit will just get
16:36wiped away.
16:37The bit remaining will be the horizontal part of the original light because the electron
16:42can't use that and so it just stays.
16:45But you can see this A demonstrates that the light has gotten weaker.
16:49So if you originally had light that was very, very close to vertical, then most of it will
16:55be cut out.
16:56Whereas if you have light that's pretty close to horizontal, then most of it will go through.
17:01So no matter what type of light we had coming in, we know that afterwards, as it goes through,
17:07it's all going to be horizontally polarized, in this case.
17:11Or, if I turn the filter around, now it filters all of the horizontal light, and so we can
17:17guarantee that the light's going to be vertical.
17:19Alright, so that's how you make your state.
17:21You get a laser, you put a filter on it.
17:24And now you can guarantee that the light is in the state you wanted it to be in, because
17:28only one type of light can go through the filter.
17:31The next bit that we use the filter for is the measurement, and that's because as you
17:35put this filter in front of the light, it will cut out some of the light.
17:40Remember that all the light that gets through to the measurement stage is going to be a
17:44combination of horizontal and vertical light and This filter is going to cut out all of
17:50that horizontal component and just leave behind the vertical component.
17:55So if we look at the percentage drop in the brightness, we know how much of the [00:18:00]
18:00light that got through the computation step was in the vertical direction.
18:04What we're not going to be able to know from this measurement though is how the vertical
18:08and horizontal components were aligned with each other.
18:11Were they very in sync?
18:12Were they very out of sync?
18:14We don't know.
18:15This measurement will tell us absolutely nothing about that, but it will tell us just at least
18:20how strong those two components were.
18:24It's finally time to understand the computation section and what exactly this calcite is doing.
18:30So check this out.
18:36You can see that this calcite splits this line into two lines, one to the left and one
18:41to the right.
18:42But what's really interesting about how the calcite does it is that it splits the light
18:46according to its polarization.
18:49So if I go like this, It filters out just the one on the left, and if I instead change
18:58it to filter the other polarization, you can see that it just filters out the one that's
19:05on the right.
19:06So that means that these two lines are light with different polarizations.
19:10Here what I've done is start the light with the filter at 45 degrees.
19:15But remember, light that's oscillating at this angle is just an equal combination of
19:20horizontal and vertical light that are in sync.
19:23That's exactly why it's a good idea to start the quantum computer in this state, because
19:27both the zero and the one are there at the same time, and that's usually when something
19:32interesting starts to happen.
19:33If I put this calcite into the laser beam, it splits it into two different polarizations,
19:39and you can see that by putting this filter in.
19:42If I put this to the right angle What the hell?
19:50I hate doing experiments.
19:53Oh wait, nah, it worked.
19:58Okay.
19:59This is the [00:20:00] right angle that cuts out one of them, so that means the other one
20:03should be 90 degrees from that.
20:07Yeah, that worked.
20:08Okay, sorry, I take back what I said.
20:11This calcite will split any incoming light into two different polarizations and exactly
20:17what those two polarizations are will depend on how you orient the calcite.
20:20So if I orient the calcite just right, then that means that the light that's coming in
20:26will be split into horizontal and vertical light.
20:30I went online and I looked up ways that you could make a quantum computer using birefringent
20:35crystals like calcite and it was really clever how they worked.
20:40I would definitely not have come up with it and so I'm going to try and explain that by
20:44first understanding exactly what it is that calcite does.
20:48Calcite is a birefringent material.
20:51That means that it treats the two different types of light very differently.
20:54For example, if the calcite is oriented a particular way, it might let horizontal light
21:00pass through fairly quickly, but slow down vertical light a lot more.
21:04Which is strange.
21:05I mean, why does light even slow down in a medium in the first place?
21:09If you want to know why, well that was a whole other video I did, and the answer basically
21:14boils down to, I have no idea, stop asking me.
21:18Anyway, remember that if we want this thing that we're making to be a quantum computer,
21:23it needs to be able to transform the input light.
21:26There are two things that you can transform about the light that's coming in.
21:30One is how much horizontal versus vertical light there is.
21:34But the other is just how in sync or out of sync those two components are.
21:39Our calcite computer is actually just going to change how in sync or out of sync these
21:44two are.
21:45And it's actually kind of perfect for doing that, right?
21:48Because it slows down the vertical component.
21:51more than the horizontal component.
21:52And so once these two bits have gone through the calcite, there is naturally a lag between
21:58the two.
21:59That's actually why the light splits up when it hits the calcite in the first place.
22:02Because as you might remember, the slower that light goes in a medium, the like more
22:06it bends.
22:08And so the one that gets bent more is the one that is going slower through that material.
22:14And so then these two things split away from each other.
22:17But that has actually gone from a feature to a bug now.
22:21We want this lag between the two bits of light, but we don't want it to be that the horizontal
22:27and vertical split away from each other too much.
22:30Instead we want them to still be pretty much overlapping with each other.
22:34Because that's when the two bits of light can interfere with each other.
22:37We're going to try and get around it by having an incredibly thin slice of calcite.
22:43So something like this will not do at all because the light can split very appreciably
22:47in that distance.
22:49What we need is a slice of calcite that is just thin enough to introduce a little bit
22:56of lag between these two, but not too thick that the beams really split from each other
23:03very much.
23:04Is that possible?
23:05Is it possible to cut something like this so thin but so precisely?
23:10Apparently, uh, I saw it online for a lot of money.
23:16Much, much, much more than I was willing to spend.
23:19Um, but there is a cheaper alternative than doing it with calcite.
23:27This sort of stuff makes me so nervous because it's all like so precise and I don't want
23:31to mess it up.
23:34All right, here we go.
23:37Look at this marvel of engineering.
23:41It doesn't look like much, but this is precisely the right kind of material with the exact
23:48right thickness, such that if I place it in the beam, then what is going to happen is
23:55these two bits of light have gotten slightly out of sync with each other, but the thickness
24:02is still small enough that the two beams haven't diverged very much.
24:07And you can see that that's true because there's only one dot there.
24:11And so This, here, is it.
24:14This is the quantum computer.
24:15This is really cool for me because I literally just opened this and so this is the first
24:20time I've actually seen this quantum computer work.
24:22Alright, let me just play around with this a little bit.
24:24Oh, it's so exciting!
24:27That is so cool.
24:30See, if I put it at this angle, it exactly cuts out.
24:38I have no idea how it's this good.
24:40This half wave plate is made for a specific wavelength of laser, which this is not.
24:45Um, but even so, it's pretty much giving me the right result.
24:50That is really surprising.
24:52I didn't expect it to be this good, to be honest.
24:54I guess that actually means that I can use this quantum computer to really do a calculation.
25:00I kind of didn't think I would be able to, like, I thought that, um, you know, technically
25:04it would do a computation.
25:06But.
25:07Noisily and badly enough that it wouldn't really be useful for anything.
25:11But now I think I can actually do a real computation and show you it and like get the right result
25:19even.
25:21That's cool.
25:22All right.
25:23Well, I guess that's going to be the next video then.
25:25Bye.