And welcome to part two of the quantum computer programming tutorials in this tutorial we're gonna be talking about is more on the Cuban itself as well as the gates.

And like what happens when we apply this gate to the cubit?

Really, my hope is at the end of this, you'll be able to sort of visualize what's going on when you see like an algorithm or a combination of gates.

A CZ Well, as if you wanted to make your own out rhythm.

What gate would you use to do certain things?

So sometimes you know you like, If you look up what a c not gate is, you'll see.

Oh, it's the equivalent of the X or gate.

Um, sort off.

It sort of is.

But it's also not so like the output is.

But if you start incorporating other bits, not anymore.

So anyway, that's by hope.

By the end of this is that you'll have a better understanding what the heck a cubit is and what a gait is doing to that Cuba, at least in terms of computer science.

Before we get into that, though, I want to address some of the more common kind of suggest not suggestions, but questions and points people made from video one.

There's only three, so it shouldn't take long.

So the 1st 1 was the circular table example with chairs Thea argument being, um, the number of combinations you have his end chairs, factorial.

People were pointing out that well, not really, because you could rotate the chairs and this one affect anybody's happiness.

So, um, I'm amending the story to be There's a stage in the front and, like, your happiness is also a function of what your orientation to the stage solved.

But good point.

That was absolutely true.

So so anyway, yeah, So that was the first thing.

The next thing is possible states versus like actually considered states logically.

So with bits you have, let's say you've got an eight bit a bit string.

Okay, each bit could be a zero or a one, right?

This is true for a cubit when measured, and this is true for a classical bit.

So the number of possible combinations is both for classical computers and quantum peters.

For a bit string the number of possible combinations of eight bits.

It's two to the power of eight.

This is true for both classical and quantum computers.

The difference is, what can a quantum circuit consider all in one pass?

And what can a classical circuit consider all in one pass?

A classical computer in a classical circuit can consider two times in bits states in, like one pass through the circuit.

So when you're when you're applying a logic gate to something, it can only consider the two states times and bits a quantum computer can consider logically in one pass through the quantum circuit, two to the power of n bits states.

And it could do this logically with a combination of bits and gates and all that.

And that is where we get this incredible ability this, this paradigm shifting, um, capability that we just don't have today with with classical computers but also can't have, like there are certain numbers.

Like, for example, I want to say the number I've seen is to 60.

So to put this in perspective, IBM and Google both have 50 plus cubit quantum computers already, and just like two years ago, they had, I think, 20 or so it was like 20 cubits so So it's increasing pretty quick and or was it five?

I can't remember, but it's a very small number and we're up to 50 now and probably Maur.

And who knows, like there's probably places I don't know.

Some Chinese company might have a bunch, too.

So So, anyway, we're already to that point, and I want to say it's two to the power of 60.

So a 60 Cuba quantum computer has Maur, um, can can can do calculations on more states at a time than if we were to combine all of the computers of the world.

I want to say it's 60.

It could be 70.

Whatever it's, it's an achievable number in the next say, 10 years even.

But probably in the next year or two, Max will be there, right?

That's crazy.

Also, number of particles in the entire universe two to the power of 300 again, that's conceivable.

That will hit that number in, like, a decade or less, who knows?

So, um, that's what's exciting about Quantum Peter's So, um so over that answers that question, but it also leads us into the next one, which is how is this useful What do I do with this?

Can I get a job with this?

Um, I think the answer to that is it's probably wrong attitude.

Like I wouldn't ask you.

Ask not what what quantum computing can do for you.

Ask what you can do for quantum computing or your job and quantum computing is literally to answer the question.

What do I do with this, right?

This is the same as is classical computers in the fifties sixties, arguably seventies, arguably eighties.

It's it's what do we do with this stuff?

How can we actually employ this?

And if you look at you know, the people that were into classical computers in the 50 60 seventies eighties, these were there's kind of two people.

There were people.

Most of the people, I would argue we're just there because it was interesting and cool, and they just were passionate on the subject.

But there were also pioneers, and there were people in businesses who made billions for themselves and generated trillions of dollars for the world.

I mean, we are almost certainly on a new age of technology and computing here.

I think that should be motivation enough, and then it's for free.

To me.

It's crazy.

You can't afford not to get into it.

But whatever I understand, if you want an employable skilled, I've got Web development, data analysis, machine learning tutorials.

If you want to follow those instead.

So anyway, I'm gonna get back to driving my Mars rover for free.

So So, back to our story of cubits.

Um, we're now going to visualize cubits on the block sphere.

So the block sphere is, um, is this this representation of the Hilbert space, which is a step above the Euclidean space, which is just basically it's just infinite number of dimensions.

Okay, but that doesn't matter.

You don't need to know that it's a sphere and it has a space inside it.

Okay.

And then at the tippy top Bibbidi bottom, tippy top and bottom of the sphere, You've got your actual cubit value.

Um, you know the top.

Well, let's say is zero.

The bottom is a one.

So the notation you see here it's like a bar, the actual zero or a one, and then you've got this kind of, like, arrow looking thing.

That's just the notation for the cubit value.

So them in this block sphere.

You know, shooting out from the middle is your vector.

This is your cubits.

Actual vector.

Um, And again, it could be pointing perfectly to a zero or one value.

And then when you measure it, it will always collapse to a zero world one, whichever one it was pointing to.

But it doesn't have to be.

It could be anywhere in this faith in the space.

Um, and then when you take your measurement, it's a It's a probability, right?

So this little green arrow here is our kind of our vector, and you just assume that's a straight line.

Um, when we go to take our measurement here, I don't know, let's say 20% of the time it will collapse to a one.

Maybe not 20.

I don't actually know what the number would be, but a non zero chance of collapsing toe one.

It'll mostly collapsed to zero, but it can collapse to a one.

But you take your measurement, it collapses, and I've got a little purple line here, pink line, whatever you wanna call it.

That's what happens when we actually go to measure it.

But before we measure that we can.

Actually, we apply our gates to it so the gate can take your vector and do all kinds of things.

Um, basically, all of them, I believe, are just a rotation.

It's some function of a rotation.

So as you can see here, we've got that green vector, and it's just rotating to the where I've got this yellow vector.

And then again, so So all of the gates that we're doing are actually applying this logic to the Cube it while it's in this this this Hilbert space here.

We're applying the gate to that.

So it's not a gate that's being applied to a 01 or both.

It's a gate is being applied to this thing that has a potential or a probability to collapse to zero or one.

But that probability is actually stored like it's there.

And when we perform that gate on it that stays, it goes forward, which is freaking nuts.

Um, okay, so cool.

So that is kind of that's That's how our thinking of what actually is a ah Cubitt.

And how do we represent this Cuban now?

Luckily kiss kit does this for us.

We can actually represent um uh, the cubits is at least at the output stage.

We can represent them on a national bloc sphere, which is pretty cool again.

The visualizations from kiss kit or just just nuts.

So now we're going to actually code some of this and play with some of the gates as well as, um, visualized the gates, get just get an idea of what's actually happening here and what really are these Gates doing?

Okay, so now we're gonna do is kind of run through some examples and kind of visualize that the cubits themselves on their block sphere as well as see the actual distribution of outputs from some of the circuits that we build.

I'm only gonna build like a handful and show you a handful of gates just to give you an idea of what's actually happening.

There's also in the text based version of the story.

I'm gonna have way more examples of just things that you can do and how that's changing things.

But honestly, I encourage you to just kind of do it on your own.

So once you see some of the things that I've shown you, I'm gonna show you also all of the possible gates.

In fact, I could just do that.

Now, this is basically all the gates.

There's tons of gates here.

Um, but you basically it's all a combination of, you know, you've got Hatem art, which is super position.

Then you've got see, not for the entanglement.

Right.

And then you've got, um, rotations.

That's it.

So, really, it's the concept of controlled for the entanglement, and then it's just a bunch of rotations that'll make more sense momentarily.

Um, so, yeah, I encourage you to kind of think about, you know, apply a gate.

And before you visualize it, think about what it will look like on the block sphere.

And then also think about what will the distribution output look like?

What should that be?

Um, so, yeah, I'm gonna show some examples, but I strongly encourage you t just play with it on your own and see how wrong you are.

Okay.

Keyboard kiss, kid as q from kiss kit dot tools dot visualization, visualization, import plots, block, sphere.

Uh, and then from kiss kit dot visualization.

Actually.

Don't know.

Something tells me one of these is the old way and one of these is the new way.

To be honest, wouldn't this be in the same visto hist o gram?

Wendy's being the same location tools because the block sphere is actually not a visualization of output, right?

It's just a visualization of the circuit.

So price, pre measurement?

I don't know.

Anyway, someone let me know if those could be imported from the same location.

Uh, I'm gonna do something because I'm on the dark theme I'm gonna say from Matt plot live in poor style And this style that use we're gonna use the dark background.

I'm doing this because I've got the dark theme and I want to see the labels.

I also made some edits to the kiss get files.

They're just hard coded changes.

I'll put them in the textbooks for another editorial, and then, hopefully, at some point in the future, maybe I could make a pull request to kiss kit to fix this.

Because actually, Matt plot live dynamically changes the colors of labels for you, given the style that you use.

So this could be dynamic.

I believe so.

Anyway, I could maybe make a contribution to kiss kiss because this would be the only one that I could possibly make.

Um, typical.

Ah, Matt, Plot lib in line.

Cool.

I think we're good.

So now we're gonna do is I'm going to find our two state state vector simulator on.

This will be cute.

I air not get underscore Back end on This is State vector simulator Sim, you late tour.

Uh, and then we'll say chasm Sim equals this would be the chasm simulator chasm HQ as m simulate tour.

Cool.

We're gonna have to simulators one to plant the block vector.

We need the state vector simulator and then to to get the distribution outputs.

We're going to use the chasm simulator.

And now I'm gonna just make a function that will do a bunch of lines of code that we're gonna find ourselves needing to write many times when we're just kind of playing around and trying to see what changes are made.

Um, and I know in a notebook you could, like, go up, change one thing and then run it again.

But I kind of at least this is what I did when I was kind of playing around.

I actually wanted to save the changes that I meant I made along the way just to kind of see how how things were actually impacting things.

So anyway, find duke job, Uh, and then this will take a circuit, and then we're just going to dio um, basically run the two jobs on the two Sims.

Rather.

So the first job will be cute dot Exe cute.

We will execute the circuit.