Wolfram Quantum Framework

Hello, everyone. My name is Mads Parami. I'm the manager of Academic Innovation Team. Our team is highly involved with offering.

Many workshops like, you know, on many different topics. Two topics that we have been involved.

You know, in detail, are LLM and Quantum. So today, you know, I'll be talking about like, you know, our quantum framework, which is a packlet. Packlet is basically a connection of, you know, interconnected functions that like, you know, running these two code, like, you know, we can install it and then, you know, just start using that. Very similar to the rest of functionalities that we have.

You.

It has a detailed documentation and, and everything it's is basically good. Very well. Like, you know, our initial plan was to have a joint session together with Nick.

Nick is here.

But it seem like, you know, Nick, you know, can you hear me? Or like, you know, there's any issue with your audio. Okay, I'll, I'll, I'll, I'll handle that once, you know, Nick, your audio is okay, just, just let me know. So, you know, many of like, you know, functionalities that we have, like, you.

Know, you would see like, you know, they have the name like, you know, quantum. And that's basically like, you know, a list of them.

Some of them are like, you know, are, let's call them like, you know, our important objects such as like, you know, quantum basis, quantum channel, quantum, you know, circuit operator, quantum operator, quantum state. So these are like, you know, the functionalities that you are gonna, you know, create the quantum objects. Some of them are for like, you know, some calculations such as like, you know, quantum evolved, take care of slot, you know, take, takes care of like, you know, time evolution, quantum distance, distance between, you know, different quantum states. But let, let's, I'm going to focus on like, you know, the fundamental abstraction that, that, you know, that we have in our framework. Let us start with, I don't know.

A simple case of like, you know, a quantum state. I'm going to start with state, and let's go with the random pure state of like, you know, one qubit.

So as you see, like, you know, what I did is just like, you know, it's a traditional form of like.

You know, the same object. Okay.

So it's like originally what you would see is this, you know, object and the summary box. But like, you know, if you want to look at the traditional form, that's.

A traditional form, like, you know, you.

May ask like, oh, why you are not showing me, like, you know, this traditional form? Because for any serious, like, you know, Quantum computation, you are not dealing with.

Like, you know, only one qubit.

You are usually dealing with a large number of qubits. And for a large number of qubits, looking at, like, you know, those traditional.

Forms that you have seen in the.

Textbook example, like, you know, it's just, like, you know, pointless.

Look at here.

Like, nobody's gonna, like, you know, look into that. Okay, so what you would do, you would like, you know, look into the corresponding, like, you know, the tensor or, like, you know, the object that is, like, you know, there. So that's the main reason, like, you know, this. This whole concept of, like, you know, representing things with an object, like, you.

Know, looks much nicer.

So what is like, you know, this, this, this animal for us, this animal is basically like, you know, at behind the scene is a tensor. On the top of that tensor, we have, like, you know, metadata helping us, like, you know, to do the computation in a quantum way. Okay. From this point on, like, you know, I'm gonna use, like, you know, our.

Quantum object quantum circuit operator. Let me just show you one example.

And then I'm gonna tell you, like.

You know, why I'm focusing on, you know, quantum circuit operator.

So quantum circuit operator is like, you know, usual quantum circuits. Like, you know, each wire represents different quantum states. And then, like, you know, you have different boxes representing, like, you know, transformations. Okay? And then you can have like, you know, any other operation like, you know, on each wire or the connection between the wires, such as, like, you know.

This cnot that we have, you know.

Acting like, you know, on the, you know, second wire as, like, you know, control and the first wire as target. So why I'm focusing on quantum circuit operator because, you know, let's put vstate.

That I created there into this circuit. And let's just, like, you know, call it for the sake of, like, you know, for our cosmetic touch. Let's call it.

I don't know. Sorry.

Okay. And when I feed it into this state, looks how it looks like.

So what you would see here is a box, like, you know, the usual box that you had there. But here there is no input wire, and there's only one wire coming out of that. So this is basically the way that you would understand this quantum process. This is like, you know, the underlying semantic that we have for us. Like, you know, it's a quantum process with no input and only output. Let me just like, you know, let's go through, like, you know, the usual, like, you know, textbook example that we have, like, you know, in the world of quantum. What if I, you know, look at.

Like, you know, the complex conjugate of this estate. Like you know, so this representation is.

Your basically like you know, cat and what about bra? So everything is going to be reversed. So this time it has an input, okay. And it has no output. You see here like, you know, a wire goes to that box and then like, you know, there's no output. This is basically like, you know, a representation of that. Like you know, that underlying animal, which is basically your, your tensor. And then you know, on the top of that you can do any other operation.

So let me just, you know, I know it's a very, you know, trivial statement, but let's do it like this. Look at here. Like you know, I'm starting with the.

State and then the next is like, you know, the action of like you know, dagger. So it's like, you know, a broad kit. And we know that, you know, this is inner product. So the result of like, you know, this operation that I'm doing here is practically like, you know, no input, no output. This is basically a scalar, like you know, animal.

And if you want to show, see it, you know, look at here, that's basically the state that we had.

Of course this state is normalized. That's why like, you know, the value.

That you see is one. If you want, let's do like you know, symbolic one. I'm gonna call it, you know, A and B. And then you would see like, you know, as some of you already guess, this result is gonna be like, you know, the norm of that estate.

Which is exactly what we expected, right? Like you know, but like, you know, now you see it in this particular picture, okay? Like you know, input, output, this is echo. Like you know, I don't know why like you know, this is the, basically the whole like you know, the concept that, you know, whenever you are working our framework, think about it like you know, okay, these are a bunch of like, you know, transformation behind the scene. Everything is tensor. So I should like, you know, use all those functionalities. Otherwise like, you know, unless you do a very simple computation, everything else is just like, you know, non efficient. Let me show you like another example.

Like you know, let's, you know, let's do it like this.

I'm gonna say let us start with.

The quantum state, which is a.

Fellow state. And then you would say like, you.

Know, look, you know, I would like.

I don't know what kind of transformation. Let's go with the rotation along, you know, y axis. And then Go with the generic angle theta. Okay, so look at here like you know, what's, what's happening.

Just again, like, you know, let's do a cosmetic touch. I'm gonna call the label. And by the way, all the details.

That you see, like, you know, they are in our documentation.

So we can, we can look into documentation everything that I'm showing you here.

Look at, look, look at like, you know, this representation, we have a quantum state. This quantum state is basically two qubits, okay?

So like, you know, it has like.

You know, two input, sorry, two outputs. Look at the dimension, two output. The dimension is two by two. By the way, in our framework you can go to higher dimension, you can have qu dates, but for the time being, let me just focus on qubits. And then no input. You see, like, you know, it's empty for the input. And that's exactly the picture that we have. Look at like, you know, the box representing your Bell estate. There are only two wires coming out of that. And then on the first wire you're applying like, you know, your operators. And now look at the operator. For your operator, you have input. A wire goes into that and a wire comes out of that. So this is how we would understand. So like, you know, what we usually call as like an operator, it has input and also output. And that's how like, you know, you could understand the transformation. Of course, like, you know, the quantum operator. And by the way, literally behind the scene, the design that we have for this quantum operator is literally like, you.

Know what I just told you? Let me show it to you. Look at the input form.

So in the input form you have your quantum state, okay, with all these like, you know, fanciness. And then the only extra information that you are adding is your input output. Okay? This is what we usually refer to as like, you know, your metadata. The extra information that you're adding. The rest is just like, you know, your quantum state. So basically you have an animal, which is quantum state. And now you're adding more information. And that information here, which is the, like, you know, the order. The first one represents like, you know, the output. The, you know, the second one represents your input. This is the extra information, the metadata that you're adding on the top of your previous quantum one object. Okay, you may think like, you know, it's non trivial, it's not the textbook example. Yes, I totally get it. You know, it's not that, but like, you know, welcome to the world of quantum computing. If you want to do any good, you know, Algorithm developments, forget about like, you know, that conventional things that you learn in mostly physics textbooks, which is what I learned. Like, you know, that's how we learn quantum here. Like, you know, you need a different, like, you know, semantic, a different approach, a different abstraction to do your calculation. Okay? And of course, like, you know, look at here, you have two wires as the output. So this operator, I don't know, let's call it qc. If you, you know, evaluate that, the.

Result is basically a quantum state. And like, you know, you see a symbolic quantum state.

Okay? So that's basically like, you know, at the very fundamental level that that's what's happening like, you know, behind the scene, the way that we do the computation.

Now let's see, like, you know, I would like to do it like, you know, like this. And then let me add. Measuring the first one and the second one. Let's look at like, you know, this circuit. And then, I don't know, like, you know, some of you may say, like, you know, what about the noise? So I'm gonna add like, you know, a bit.

Flip with the probability of.

Like, you know, 0.3. So it's acting on the first qubit. Let's, you know, act it on the second qubit. So that's. That's the case that we have.

And then what's happening here is actually, let's now, let's go for the first.

Qubit for the time being. And I'm gonna explain like now what's my plan?

So look at here. So we have a Bell estate, which is your preparation. Then, like, you know, you have a rotation and like, you know, that's the effect of logging on noise. And then you would measure that. Okay. This is like, you know, the normal way, like, you know, that you would understand it. But the way that we understand, for us, like, you know, involved from quantum framework. This is basically our abstraction.

That's how we would basically, you know, me. Now, I cannot type edge labels. Let me just show, set it automatic. And in the meantime, I'm gonna set.

Vertex.

Labels also automatic.

Now you would see like, you know, what's happening here.

And let's do one more thing because, you know, this gr. Let's go with our graph layout. Now, which one maybe like, you know, layered embedding looks nicer. Okay.

So this is basically like, you know, what is happening, you know, for us. Look at like, you know, let me.

Also show you this.

So this is like, you know, the. The circuit that you see on the top. This is what we usually refer to as like, you know, conventional understanding of like, you know, quantum circuit. This is how we would understand it for us. It's a tensor network. And like, you know, this tensor network, like, you know, it represents like, you know, everything that is happening here. Each of these edges, like, you know, they represent a specific. The gate. Each of those edges, they have the information of the contraction that we do. And then like, you know, basically for us, quantum computation is a fancy tensor contraction. And you know, we do it in a way using that metadata that I told you to fulfill all the requirements that we need to get quantum results. So behind the scene, really, like, you know, we do a tensor contraction, for example, if we evaluate that circuit qc.

And this time, like, you know, you're going to get a new object, like, you know, your measurement object, you know.

And then for that measurement object, we.

Can ask, you know, it's going to look ugly and I'm going to explain why. If we ask for probabilities, these are.

The probabilities that you would see. You see, they are all function of theta.

And then we can say, okay, full simplify that. And for the assumptions, I can say, for example, I don't know that theta. Let's say that it's positive.

And voila. That's the basically symbolic quantum computation that we did. Okay. So this calculation that, that, that, that is here is not done in a normal way that we usually do, like, you know, quantum computation. Literally, like, you know, we focus. We basically started with this quantum tensor and then we did the corresponding contraction for that particular tensor. That's the basically like, not the semantic that we have in our framework. And of course, like, you know, you can extend it. I don't know. Let me just like, you know, a very.

Let's. I was hoping that like, you know, we would be able to show you.

Some fancy examples together with Nick.

But it seems Nick had some technical issues. But for now, let me focus on simple ones.

So this is a balance. You're here. Okay, then like, you know, you didn't want to interrupt it. Yeah, yeah, I'm gonna stop sharing so. Because, like, you know, it's easier. Like, you know, Nick is a master of live coding, as you notice. Like, you know, I was kind of struggling with the live coding, so it's not easy for me to talk and code. But Nick, you know, he's, he's very good. So Nick, please go ahead, share your screen. And then we are gonna show them.

Like, you know, some other examples.

So this is our documentation page that I was telling you Maybe set the.

Level as 125 so they can see everything.

Okay.

So.

What you wanted to show this kind of example, right?

Yeah.

Let's have with the magic and then tensor network for the magic foreign, let's show like, you know, the actual circuit too. Let lets our users see that. Like, you know.

Yeah, look at here.

Like, you know, you have two wires and like, you know what? What? Before evaluating that, Nick, let me just explain what we have here. So those initial zeros that you see, okay, those are basically your register states. Wire number one, wire number two. Now it goes through the pink box, which is S, which is the next, like, you know, edge, the vertex. Look at the next vertex, like, you know, two S's, and then on the second one you have the Hamiltonian. You see, like, you know, one of them follows by the Hamiltonian, the next vertex is Hamiltonian. And then C naught is acting on both of them. That's why, like, you know, you see, like, you know, both of them, they go like, you know, to C naught. So this is basically like, you know, the tensor. And for the tensor network, each edge represents a contraction, a specific contraction that we are doing. And like, you know, like, it's basically an annotated graph. And then you can extract whatever information that you want from this graph. By default, we always set our initial state as 0, 0, the register state. If you don't like it, you can remove that. So the next example, the tensor network, it is without the initial state, which was a register state. Okay? So just like, you know, we just, you know, remove that. And then you may say that, you know, Nanik is doing like, you know, like, you know, like the other functionalities that we have in, like, remember this quantum framework is built on the top of Wolfram language. So everything that you have in like, you know, Wolfram language is applicable here. So that tensor network was literally a graph. And as you saw, like, you know, the two labels that we had initially was like, you know, zero and negative one. So Nick is saying that, okay, delete those vertexes and you would get the next one, which is without the initial state. So it's a tensor network. So you can do whatever you want with this tensor network. For example, you can say that, you know, what are the three indices that we have in this tensor network? Okay, so like, you know, these are the free indices that we have within this tensor network. And you may say that, you know, look, you know, now I would like to add a new tensor on the top of, like, you know, that that tensor graph using those three indices. Remember, like, you know, that's the only one that is available. So what we would do is just, you know, we start with tensor network at, which is, you know, the function that we have in our framework. You would give your tensor. Nick is giving it in the most generic way, which is basically like, you.

Know.

A, B, C and D. Like, you know, those are like, you know, basically like, you know, your metrics. Read it as a matrix if you want, and voila, like, you know, we added like, you know, a new tensor, a new transformation in the middle of our tensor network. If it's not like. Now I want to tell, show you, like, you know, how different is this, like, you know, semantic, like, you know, this abstraction. Now you may say that, okay, like, you know, look, I'm coming from, like, you know, the background that I understand only the usual circuit diagram. Show me the circuit diagram. Now let's look at the circuit diagram. And you will see, like, you know, the circuit diagram is like, maybe a bit conventional for some of you because.

You may not have seen like, you.

Know, these kind of loops, but that's literally like, you know, what's happening there. It's like as if, you know, after applying that particular transformation, which is the simplest case, it's a simple, like, you know, applying like, you know, a linear transformation represented by that matrix abcd, we are tracing out the first qubit you see. Like, you know, that. That look that you see. Like, you know, it's literally like, you know, tracing out. If you want, like, you know, to see it like Nick, without that new tensor, literally show them the partial, like, you know, tracing.

And like, you know, they would see.

Like, that's literally the same case. That's your, you know, circuit. And then you would say, like, you know, look, you know, I would like to do the partial tracing. I would like to trace out the first one you see. Like, you know, that's how. That, that's literally like, you know, in the tensor network language, that's the literal meaning of, like, you know, doing partial trace. And I guess, like, you know, with this simple example, you already noticed, like, you know, how different is this abstraction and how flexible it is compared to the textbook example because, like, you know, it gives you all these possibilities of like, you know, playing around with your tensor and do all, like, you know, fancy manipulation. Now, for those of you, like, you know, what you see there is simply like, you know, a cap and cup, like, you know, on the left side. Like, you know, we have a cup on the Right side. Like, you know, we have a cap. Remember our diagram? Like, you know, it has tooltip. Like, you know, as Nick is, you know, hovering his mouse over, you know, different location. Like, you know, you see the labels. I don't know, hover it on C. Not like, you know, they would see.

The C. Not too.

So, like, you know, that's the C. Not like, you know, see how the mark. And if you want to know, like, you know, what are they? Literally, you remember that Bella state that I showed you? And it has like, you know, two outputs. No. Input cup is literally your Bella state. Cap is the dagger of your bell state. That's literally like, you know, the meaning of, like, you know, those fancy things that you see. Like, you know, look at here. Like, you know, that's that operation, the cup on the left. And then, like, you know, look at the Bell estate. Yes, normalization.

Like, you know, but, you know, we can. We can ignore it for the timing.

But that's literally the same thing, I guess. Like, you know, this very simple representation for cop that. That you saw, like, you know, Nick, show the summary box for copy. Like, you know, because in the normal quantum whatever, like, most of the time, you guys see is an operation which has like, you know, the usual quantum operator. In quantum, it has always input, output, the same number of input, the same number of output. Okay? Look at the order that we have. And like, you know, the way that is acting, it's different. This is much more generic because again, like, you know, as I told you, if you want to do like, you know, serious, like, you know, computation quantum, you need like, you know, different approach, you need different abstraction and why it is useful. Like, you know, very simple. Like, you know, if you go to the next level of abstraction, you can literally include anything you can. Like, for example, let us start like, you know, let's do something fancy. Like, you know, I don't know, like, you know, let us start with the magic state. And then like, you know, let's, you know, I don't know, like, you know, Nick, like, you know, what's the. Like, shall we merge two output wires together? Like, you know, just. Just showing like, you know, what. What we can do.

And it's literally like, you know, the.

Usual functionalities that we have. So look at here. Like, you know, Nick is adding an initial bell state. Like, literally, that's what I showed you. I showed you as a quant. Now you would see it as a wire. Okay, so it's like on the very left side, we start with the bell State composition is exactly the same as like you know, the usual composition that we have in WM language. Then you have the rest of like you know, your circuit operator. And now like, you know, let's do, I don't know, like you know, let's merge those two wires. Let's like, you know, and make it one like you know, wire with higher dimension. Yeah. And look at here like you know what we are doing here we are managing like you know, those two wires and each of these operations, they have a corresponding like you know, tensor manipulation implementations. And look at the very last wire. Because you merge two of them, the very last wire, it has higher dimension. Okay. Like you know, and like, you know, if you want to say like you know, what is on car is like really like you know, you have. It's Ankari and Curry that we have like you know, in. In I guess like you know, the conventional functions apply Curry. Right. Like, you know, that's the building functionalities.

That we have in Wolfram language.

And look at the dimension. It takes two and two, basically two input and then as an output you have higher dimension. And then like you know, that higher dimension. Like you know, in some like, you know, literature this is what usually refer to as like actual quantum wire because.

Like you know, it has, it has.

More information and you can do like you know, a family, a zoo of like, you know, different operation in our framework if you follow this approach. So not only you can have like, you know, do all the, you know, conventional ones, but because of locking on this very like sophisticated like no abstraction that implemented by Nick in our framework. So you have lots of freedom to play around like you know, whatever tensor manipulation you would like to do. As the last example, for example, let's say that like you know, you have a, I don't know it qubits. But let's have it like I don't know, A and B as like you know, as a state vector. Let's just start with that state. So it's a symbolic, you know, example. And let's have it like you know, in a circuit like you know, let's say that like you know, this is the very first wire of a circuit.

You know, quantum circuit operator.

Okay, some up to here, I guess everybody understands what's happening. And let's say that you know, you would say look, you know, I don't like to go with the state vector. I would like to have like, you know, the density matrix encoded in the wire of my circuit. It okay, you would say like, you know, look, you know, it's, I want to go to higher dimension and have like, you know, your, your density metrics. And that's the way that we would do it. Like, you know, maybe like, let's show them like you know, what is the matrix state. Like, you know, let's show the actual form. So you see, like, you know, that's the usual textbook example of you know, density metrics. And this time I wonder if you notice like, you know, when Nick did like, you know, that you know, metric states, like, you know, the box, you know, borderline is now thicker. It means like, you know, it is in higher dimension now like you know, what is happening there is like you are encoding your density matrix into like, you know, the computation for your tensor. And in this time, like you know, you are in higher dimension to do that. There are other tricks like, I don't know, like you know, that you can go with like, you know, dabbling that, bending that like, you know, it's like, you know, a collection of like, you know, different tricks that you can, you can do. But at the fundamental level, like, you know, think about it like, you know, you have a fancy tensor manipulation and on the top of that tensor manipulation, you can basically do anything that is okay by you know, laws of your, you know, tensor contraction. That's a very specific abstraction that we have in our framework. Like, you know, this approach of like, you know, tensor network in a sense is a state of art for, for to do, you know, quantum computation. It started with like, you know, condensed matter physics and like, you know, simulating, you know, many body systems. But very soon people they found like, you know, very fancy, you know, usage for quantum computing. And we can safely claim that any operation that you can think about like you know, in a finite dimensional space using like, you know, all of these tensors is doable in a framework, even the non conventional one that are like, I don't know, like you know, we are almost, you know, yes, one minute over. But as a last example, let us also show them like you know, a copy, a spider that basically you can copy a state the, the basically your estate.

And then let's show like, you know.

And let's just start, I don't know, let's give the same instead A and B and let's look at the, you know, show them like you know, how.

It works and copy.

Let's evaluate that and look at the amplitude. You see here we started A and B and now it is copied on the other qubits too. It's not cloning you're just copying the amplitude and it's again a tensor manipulation. This is ES spider, which can be easily implemented in Wolfram framework. I think the most important thing about quantum computation is we need to develop relevant algorithm important algorithms to tackle real world problems. And this is you know, one thing that you know, we would like to interact and collaborate more with our users out there. So if any question please feel free to contact us, you know, quantumoform.com and, and let us explore the uncharted territory of like you know, quantum computing. So I guess like you know, that that's it. Nick, is there anything else that you would like to add? Like you know, last word for you? Well, yeah, go ahead and explore our framework. Yeah, do it and, and let us know like you know, it's one thing like you know, I forgot to to add is I showed you like you know, how to install our packlet from our like you know, landing page. There is another link which is our developer page.

I don't know like if Nick, you have it, you can quickly show them what these are.

So the developer page, like you know, the main difference is that non stop days are nice. Like you know, me and Nick, like you know, we are adding new functionalities.

Like you know, updating that you know.

Cleanup and like you know, debugging if any bug. So you can also like you know, if somebody is interested to see like you know the, the latest that the last version of like you know, our packlet, like you know that that's the link that you can install it and that's the most updated the landing page like you know, once like you know, we are like you know every month or so when we do all the updates and everything works fine like you.

Know, we usually update.

So that's how you can get you know, the latest version of our framework. And right now the version is 1.2.11. Okay, any question? I don't know like you know, if I miss any question, was there any question or anything? Okay, so again like you know, thanks everyone, you know, feel free to reach out to us, you know, quantumorpham.com and like you know, explore our framework and let us know like you know, how you like it. Thank you. Thank you Nick. Thanks Matt. Thank you guys. Have a good one.