I'm gonna explain what a quantum computer is on how it works.

Using a relatively simple example on, I'm gonna try to explain it as clearly as possible.

So you be able to on the sadness video, even with no prior knowledge of either quantum mechanics or computer science.

So let's get started.

Uh, okay, First of all, let me give you a one cent this summary off what a corner computer is.

A quantum computer is a type of computer that makes use of quantum mechanics so that it can perform certain types of competitions more efficiently than a regular computer camp.

Okay, so right now that sent this might seem a little bit vague, but my goal in this video is to make that sentence make a little bit more sense on a little bit more concrete.

By the end of this video, to get study with that, we need to get started with a non quantum computer or a classical computer, as it's known, just like my laptop right here.

A classical computer stores, information and what's called bits.

As you might already know, bits are expressed as a bunch of ones and zeros on different kinds of the information can be represented as bits, whether it's numbers, text photos or videos.

Now a quantum computer is radically different from that because it does not use.

You know, these classical bits to store information, instead uses what's called cubits.

Each cubit is just like a bit, but the difference is it's possible for a cubit to be not just one or there, but it's also possible for it to be one answer at the same time on that's achieved by making use of the properties of quantum mechanics on.

The reason why it's possible for a Q B two B one and there at the same time is because on an extremely tiny scale or in the quantum realm, it's possible for particle to have two different states at the same time.

So it's possible, for example, for a party go to point up and down at the same time.

It's a really strange concept, but once you accept that, you be able to assign one of those states, let's say up to me one and then the other states.

Now let's sit down to means there.

Once you do that, if that particular particle happens to be pointing up and down at the same time, then that would mean that the cubit that it's supposed to represent is one and zero at the same time on, by the way, in theory, you could use a number of different types of particles to represent a cubit, whether it's a foot on another strong on iron or regular Adam.

So here you might think that it's kind of strange for particle to be able to point up on down at the same time.

On I find it pretty strange to, you know, some people try to explain it with some kind of an ology from the classical world, which were used to, but there's actually no good analogy for it because this phenomenon of a particle having two states at the same time is really unique to the quantum realm.

Maybe all you need to know for now for this video is that it's possible for a cubit to be one and zero at the same time.

Okay, And once you have a bunch of two bits like that, not just one cubit, then it's possible to put them together so that they'll interact with each other in a certain weight s O, for example, you might design a system with two cubits.

Where, when the first Cuban is one The second cube, It always becomes zero on when the first cubit is zero.

The second cube it always becomes.

What on?

If you have those two conditions, then when the first cubit is one in there at the same time, the second cube, it becomes zero and one at the same time on.

In order for us to have those two conditions be true for those two cubits will need to first design a fiscal system where the equivalent to conditions are true for the two particles representing those two cubits on once we have a way of doing that, you know, a way off having two cubits interact with each other in the way that we want them to.

We can expand the same thing to a number of different cubits, not just two.

We're talking hundreds to thousands of cubits right now on.

That's basically what a quantum computer consists of s so in summary, a quantum computer is essentially a group of cubits designed to interrupt me each other in a certain way that we want them to so that we can perform some competition on them because of the way cubits work, as opposed to how regular bits work, a quantum computer can be faster at solving certain kinds of problems than a regular computer can.

Okay, now, to give you a better idea about how a quantum computer works, exactly, I'm gonna dive into the relatively simple example I mentioned at the beginning of this video.

Now this particular example might not be a particularly realistic or maybe practical, but I think it's too good for understanding how quantum computing works.

Okay, so for this example, suppose that you're running a travel agency of some kind on that you need to move a group of people from one location to another on to keep this simple.

Let's say that for now you only need to move a group of three people for now, Ali's Vicky and Chris on for this purpose.

Let's say that you have booked two taxis.

You want to figure out who gets into which taxi.

You also give us some information about who's friends with who and whose enemies with who and here.

Let's say that Alison Vicky of friends, always on Chris, our enemies on Becky increase our enemies as well.

On the goal of this problem is to divide this group of three people into the two taxes that we have to achieve the falling two objectives.

The 1st 1 is to maximize the number of friend Paris sharing the same car on the second objective is to minimize the number of enemy Paris sharing the same car.

Okay, so this is the basic premise of the problem.

Let's first think about how we would solve this problem using a non quantum classical computer first.

And then we'll come back to solving this problem, using a quantum computer later.

Now, to solve this problem, using a classical computer, you need to first figure out how to store all the relevant information with bits.

To do that, let's first label the two taxis Taxi zero on Taxi one, and then you might decide to represent who gets into which car with three bits.

These three boxes representing those three bits on the first bit is gonna show which car Alice gets into on the second bit is going to be for Becky on the third bit is going to be for Chris.

So, for example, you might set these three bits to 001 to show that Alice gets into Taxi zero.

Becky gets into taxis there as well, and Chris is gonna be in taxi one on just like that, you can represent all the possible ways off dividing this group of three people into the two taxis with just three bits.

And if you want, you can put all of those possible ways into a single table just like this one.

So just like we saw earlier, one possible combination off these three values is 00 on one.

Another possible combination of thes values is if they all get into toxic zero, they would all be zero.

And just like that, we can keep populating this table.

As you can see right here, there are eight possible configurations here, and that makes us because there are three people here on for each person.

There are two possibilities, and that's why we have two to the power three or eight waves dividing the three people into the two taxis.

Now using a classical computer, how can we determine which of these configurations is the best solution.

Well, you know the force to do that, I will first need a concrete way off measuring how well each of these configurations achieves the two following objectives that we saw earlier.

And they were first maximizing number friend Paris, sharing the same car and then also minimizing the number of enemy pairs sharing the same car.

Remember that we were given some information about the relationships between these three people.

So again, the question is how can we measure how well each of these configurations achieves the two objectives?

One way of doing this is by defining a single score that we can compute for each of these configurations on the score should be made so that the better each of these configurations achieves the two objectives, the higher the score becomes.

Now there's a number of different ways of defining such a score.

But here is one simple way of doing it.

The score of a given configuration is defined as the number of friend Paris sharing the same core in that con figuration minus the number of enemy pairs sharing the same car.

So this way we're basically incorporating both of these two objectives into a single score.

So if we have a lot of friend pairs sharing the same car in that particular configuration, we're doing well on the first objective, so the score will be higher.

But if we have a lot of enemy Paris sharing the same car at the same time, we'd be doing poorly on the second objective, so the score will be lower.

So in order forced to maximize this score, ideally, we need to achieve these two objectives at the same time.

Okay, so, for example, if Ali's Vicky and Chris all get into toxic zero, uh, that can't be expressed as 000 in these three bits on what's the score of this one?

Well, there's only one friend pair that's sharing the same car.

That's Alice and Vicky.

So the first part of this equation will be one on their two enemy pairs sharing the same car.

That's Becky and Chris as well as always, and Chris sharing car number zero.

So the second part of this equation will be too.

So the total score of this particular configuration.

Now let's call it s will be one minus two, which is equal to minus one.

Now, given this set up, all we need to do now is we just need to find the configuration with the highest score on.

That's gonna be our answer.

And to do that with a classical computer, we'll need Thio.

Compute the score for each configuration one by one sequence.

Really?

So first, set the three bits we have 2000 and then compute the score for that, which, as we said earlier, is minus one and then set the same three bits to 001 this time and then compute the score for that.

And that's gonna be one.

And just like that, we'll need to go through all of these configurations one by one.

Sequence.

We after computing all of that, you see that there are actually two best solutions here with the highest score that stairs there, one with the score one on 110 with the score of one.

And here you might notice that there's actually one simple optimization step that you can make here on.

That is you actually don't have to look at all the configurations to find the best solution.

You only need to look at exactly half of them.

But just to keep this whole argument a simple as possible, we're gonna continue our discussion with this brute force solution off looking at all the possible configurations for now and may even without the optimization step.

This problem is pretty simple.

Dissolve because there are only eight values to compute here.

But as we increase the number of people in this problem on, this problem quickly becomes too difficult to solve with a classical computer.

So let's quickly see why that's the case here.

When we have three people in this problem like we saw earlier, we needed to compute two to the power three or eight Barry's for eight possible configurations.

What if there are four people in this problem, then the number of configurations that we need to consider becomes two to the power four or 16 s O.

If we keep going like that, if there are any people in this problem, we would need to consider, too, to the party and values without that optimization step.

So now just consider increasing this problem sized to 100 people.

So it's sort of like trying to divide 100 people into two buses on.

Once you have that, you will need to consider, too to the party 100 configurations to solve this problem exactly on.

That's about equal to 10 to the power 30 or 1,000,002,000,000 million configurations on dhe.

That's simply impossible to solve with a non quantum classical computer, because it would just take too long.

Now, how can we solve this problem using a quantum computer to think about that?

Let's go back to the case of trying to divide three people into two taxis like we saw earlier.

There were eight possible solutions to this problem on with a classical computer.

Using three bits were only able to represent one of these configurations at a time, for example, it 00 and one.

But what if we had a quantum computer weighs three cubits represented by these three boxes?

Then what we can do is we can set each of these cubits to be one of their At the same time on, I'm gonna use this symbol to denote that it's set to one on there at the same time, so we can do that with all of these three cubits on.

Once we do that, these three cubits together are actually representing all of these eight possible solutions all at the same time.

Personally, I think it's a pretty strange notion that these three cubits are able to represent all of these eight possible configurations all at the same time.

On there are debates as to what it means exactly, but here's the way I think about it.

First, let's examine the first cubit out of these three cubits.

Let's say that that Cubit is set to one on there at the same time right now.

Then what's funny about this Cubit is that if we try to measure what the value of this cubit is, it turns out to be 0 50% of the time on it turns out to be one the other 50% of the time.

These percentages might be a little bit different, depending on your particular environment.

But let's just say that in our current environment, this is 50%.

Anyway, As soon as we measure the value of this cube, it it turns out to be either there or one, but on two, we measure it.

It's in both of those states at the same time, they're on one now.

What if we have two cubits on that are both set to They're on one at the same time.

Then when we try to measure the values off thes two cubits, these turn out to be one of these four outcomes 000110 or 11 on each of these outcomes would appear, with the equal probability off 25%.

And here, just like the previous case of having just one cubit A soon as we measure the bodies of these two cubits, they turn out to be one of these four states.

But until we measure them there in all of these four states, all at the same time on what if we have three cubits just like that, each of which is in the States off one and there at the same time, then those three cubits together would be in all of these eight states at the same time onto we measure them.

And so that's why three cubits together is able to actually represent all of these age possible configurations all at the same time.

Again, I think it's kind of strange that it's possible for us to even have something like that, but it is possible.

And that's how a real content computer works, too.

Now, when he applies some sort of competition on these three cubits and a quantum computer, the results from all of these AIDS possible configurations are computed all at the same time.

So with a corner computer, you don't need thio compute the score for each of these states, one by one sequentially, you can just apply the function that turns each of these states into a single score that we define earlier on these three cubits.

And then the Colonel computer will be able to find one of the best solutions in a matter off milliseconds.

Now, if you actually wanted to solve this problem using a quantum computer, you will need two things.

Now.