Exponential speedup in progress
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Babej, Tomas
This talks overviews the available quantum computing paradigms and outlines the pratical possiblities of leveraging and exploring the promised power of quantum computing processors that developers have today.
 I guess it's time to start. So welcome to the first ever quantum computing bedroom at Fosden. My name is Tomas Kovey and I'll kind of try to introduce you to this world of quantum computing and also organize in this room so I'm responsible for anything that goes wrong. You can maybe notice that the title of the talk changed from what was announced. That's just because my and Mark's talk kind of when we were looking out the slides we figured that actually the titles match reversed more than the way they were announced previously. Okay so introducing the team behind this room it's mostly me, Mark and Will. Me and Mark are co-founders of a quantum computing company called Rotank here and Will is a person who started the so-called Unifold Fund, an organization that supports quantum computing by promoting it and issuing grants for people that are interested in building some independent quantum computing projects. So you can talk to Will when you are thinking about doing some non-prolucentry role and you can also look up some information about the fund at Unitary Good Fund. Okay so I just told that I would like to answer three questions and those three questions are basically, What is quantum computing? Why should we invest in learning quantum computing and why should we do quantum computing with open source? And I'm going to answer them in a reversed way so I'm going to start from the perspective of why quantum computing and open source makes sense. So the idea behind even having this room originally started back in the summer of 2018. I was in London and I met one of the organizers of POSDOM and I was going to get quantum computing talk at the local WITDA group there. And basically the question came up whether it would be a good time now to start a developer room at Quantum Computing. And back at that point, me and Margot were working on a review paper about quantum computing and open source, like all the different open source projects in the quantum computing space, evaluating them and comparing them and trying to identify what are the gaps and what are the strengths of these projects. And eventually we figured out that this is a new technology which is going to potentially revolutionize many industries. And similar to AI, we kind of felt that there shouldn't be some kind of mobilization by just one hardware vendor and them owning the whole software stack which would make it hard for other companies to develop their own hardware and capture some of the market. And also for that reason we actually just thought that there would be a useful contribution from our side. If we could start a formal body that would try to govern the space and try to like, steward people to publish their open source and make sure that companies govern themselves and they can be more like, opening governance models. The whole thing is like, a lot of the more community based smart. So that's what the Quantum Open Source Foundation is about. And to testify, the description of this room is posted on our site. So, please check it out. Oh, shit, I never thought about it. Okay, that's good. Can you stay between the two lines on your left here? Okay. Here. Between these two? Here's one line. Oh, between these two lines? Oh, okay. Okay, I haven't been notified about that. Okay, so that's good to know. All right. And do we have like a clicker or not? I can give you one. Okay. Never mind. So that's Quantum Open Source Foundation. So for those of you that are just joining us through the video streams and video recording, I was just describing the team behind the room and that's mostly the team behind the Quantum Open Source Foundation. What's right? Thank you. All right. So what awaits us here for the next two days is going to be two days full packed full of talks. Today is Saturday and basically we're going to have... You can just... I'm going to try it. You're wet for about 10 minutes. Huh? I have to turn it on? Beautiful. Okay. It's working now. So today, Quantum Computing Dev Room, we're going to have talks by basically every major so-called full stack Quantum platform out there. And some major open source projects. These are mostly often... Yeah, often companies supported projects, but they open to contributions and they are released under open source licenses. So these are projects like QuizKit, Forest, Strawberry Fields, and Multitude of other libraries and projects. And I'm not going to develop on them too long because there's going to be dedicated talk to each of these. And tomorrow, at least for me, the more exciting part is because we're going to have a portfolio of a total 11 open source projects that are less prominent because they are developed by let's say single main authors or contributors. And they're going to present their projects and we will try as a community to figure out ways how we can help. So we're going to hold a hackathon sprint in the afternoon where we will divide into different groups. And each group will try to hack on that particular project, maybe just learn how it works, provide feedback in terms of your documentation, works or not, what could be improved, stuff like that. And each group is going to be coached by the particular developer that is representing the project here. So if you want to make sure you have a spot and you don't wait in the line like people out there sign up, there's only like 20 people signed up and the capacity of Durham is like 90 people. So there is still some spots available. So why invest in learning quantum computing right now? Well, it's a good time because quantum chips are already here. This is I think the D-Waves chip but Google, Rigeti, IBM, they all have their own quantum computing hardware and they are not the only ones. But a couple of them also provide access. So you are able to play with these devices even as an independent researcher or just random person out there who's interested. You can get access to these things and you can try them out, try what you can do with them. So it's no longer a thing which is a purely academic thing. It's a domain which is being explored also for commercial purposes which creates interest, creates jobs, creates opportunities. And there is like a fight going on. Every country wants to be labeled as being the progressive one and the one which invests in these technologies. So we can see that China, European Union, USA, they are all passing these big bills saying that we are going to support quantum computing. And there is also a bunch of private funding going on and totaling 700 million dollars into multiple companies. The most funded ones or the ones raised the most money I've listed here. But there is a bunch of other ones including my company that isn't on the list. And if you have ideas that you want to explore, there is also support for early entrepreneurs. ProtonQ was founded as part of the CDL which is the most prominent incubator or slash accelerator thing in Canada basically. And probably the only specific to quantum computing or they call it quantum machine learning domain in the world. So applications that are open now, I encourage you to Google out to see what this is about. It's a really good experience to go through this. Alright, so in the interest of time, I still have I think 16 minutes. So we'll do a very quick overview over the paradigms of quantum computing. Each of these will be covered in depth today. So don't worry if you don't understand something. I'm going to provide just like a very high level intuition behind these things. Okay, so the three paddlers are going to describe our quantum annealing, then discrete gate based computation and the continued gate based computation. Alright, so in the quantum annealing, basically what you're doing, you are crafting energy landscapes that you want to explore. On the left, there is a particular example of what we're doing. It's an optimization problem for trying to find confirmations of a protein. This is so-called protein folding problem. And you know, going through some hoops, you can express that as a so-called binary optimization problem. And what the quantum computer does is that it explores this landscape using some elements of or properties of quantum mechanics such as quantum annealing depicted on the right. And one of the biggest players in that space is D-Wave. There have been a round for many, many years, I think, making quantum chips since 2000, early 2003. I'm not sure they started developing hardware at that point, but the company is around for 15 years. I'll be corrected on that number probably, but it's the longest company that is around. And this is a little bit of math, but basically what it describes is just, oh, I have a pointer. Cool. So what it describes is just like you have two variables, binary variables that are coupled by a constant. So you have quadratic terms and you have scalar terms. And you are basically able to specify this polynomial and that polynomial describes the energy landscape. And the device tries to find the assignment of these variables such that the energy of this term or this expression is minimal. And the way this is done is basically it happens on this chip and your goal is to embed your problem on the variables such that the connections between the variables are realized on the chip. So this is the problem of the so-called graph embedding and I'm not going to elaborate on it, but it basically creates additional overhead in putting the problem on the hardware. So we can imagine that this is very low-level approach. You can have problems here like missing qubits because they were disabled, they had some manufacturing problems or missing couplings. And you have to account for these things when you are embedding. Okay, so just a quick code demonstration how it looks like such that you have just a cursory glance. This is a very simple problem where you have four qubits here and they're all anti-correlated, which basically means that we have couplings of one here. And what this system is supposed to be, what the lowest energy system of this, or lowest energy state of the system is, is basically like, alternations of ones and minus ones. So these variables, they can be either one or minus one. And to achieve basically the lowest expression value, you have to alternate them here. Anyway, this is how we do it. They have a pretty nice API. You just specify these couplings in a dictionary and then you embed it using this class and then you can directly sample using this interface. And you can use either classical samplers or you can sample out of the machine if you have access. It's basically transparent. So from a high level, this is what is going on, you have problem. You formulate it in terms of this quadratic binary optimization problem or Isling model is another name for it. Then you embed the problem, the problem's graph into the chip, and then you sample out of it your solutions. And there's the WaveLeap, which is basically a platform which gives you access. I'm not sure it's available in Europe, but it definitely is available in North America. And you can get one minute free of time to explore these things. Some more resources for people that are watching this on the video later. So the other paradigm is so-called universal gate-based quantum computing. And there you are designing these quantum circuits. An example of quantum circuit is on the right. So these are the gates. This is a gate, but this is also a gate. So this gate interacts with two qubits. That's why it stretches two lines. Each line is one qubit. I should probably explain that. And these boxes are basically measurements. So to read out the result of a competition, you have to measure and collapse the quantum state. And that's depicted by this symbol. And big players here are basically IBM, Google, Rigeti. The reason majority of these big companies are investigated, this kind of platform is because this is actually where the majority of the theoretical results were proven at. Like all these Shor's algorithm, all these frets that we hear about quantum computing come from theoretical results on these kind of architectures. So this is the qubit. No reason to get too scared about it. I'm not going to delve too much. I just want you to see these equations first. These are two basic states. These are two complex numbers that together comprise the quantum state. And usually we depict the qubit as living on this sphere called the block sphere. All right, so here basically we don't have binary variables anymore, like during the competition, but the variables themselves are quantum variables. And there are basically a combination of those two basis states, and you apply these operations and you read out at the end your result. So again, it's very, very low level. You're designing a circuit. It's almost like doing some board. You're not soldering it, but you are basically operating on a very low level. All right, so I'm just going to rush through this. This is an example of how you apply to gates. The first gate, which basically does to state zero does this and to state one does this. Yeah, but really important for the demonstration here, just for illustration. This is a different gate, so-called controlled not gate. And if you combine these two gates together, you can create what we call maximally entangled state. So if you measure this, you can get one of the two outcomes, it's either zero, zero on both of these qubits or one, one on both of these qubits. And why is that? It's going to be explained later today. I mostly wanted to share with this so that you have actual idea how it looks at the software layer. Basically, you are writing Python code, which generates this quantum assembler, you might think, or this is so-called quill code. So it's really low level instructions, apply this gate at this qubit, apply this gate for those two qubits, then measure these two qubits, and here's your result. And you have to be clever about what you're doing, such that you, at the end, measure something which is going to be useful for you. All right, so the gate model, workflow from the high-up, basically, you have the problem, you encode your problem, I mean, you have to figure out the quantum algorithm for your problem, and then you basically implement that algorithm as a quantum circuit. Then that quantum circuit has to be compiled, because the actual hardware platform doesn't support all the gates that you might think that you need. They actually support only subset of the gates, so-called fundamental subset. And that basically means that some of the gates here will be expanded into multiple gates in the series of different gates, which again, like, a little bit boosts or blows up the circuit of the computation. Which is basically the problem we're facing right now with the devices, because each operation is noisy to a certain degree, so the more of these gates you apply, the less certain you can be about the result that you're going to get at the very end. Okay, so some further resources about this for people that are interested, but mostly for people that are just going to look at this over the internet or later just look at the slides. And very briefly about the continuous variable quantum computing. So here you switch the concept of the qubit with the concept of a Q-mode, which you can see it's continuous. See this nice integral sign here, as opposed to, you know, having two discrete states, basic states here. And the big player in this field is Xanadu, and we're going to have two talks from people from Xanadu today. So they're going to delve much deeper into this topic than I could. So, yeah, I wanted to also give some further resources about this. They have nice API layer. I would almost say one of the best out there is like the API of the strawberry fields. And that's that. Thank you for your attention. And if you have any questions, please shoot me up. We have some time. applause I know very little about quantum customers, you can assume nothing. you said something that picked my interest. You mentioned that as you work with more gates, you have an increased uncertainty on the result. But I'm very curious, what do you mean by increasing uncertainty? Well, okay, so the question was I mentioned during the talk that the more gates you apply, the less certain you can be about the result you're going to get at the end. So when people are developing these quantum algorithms, they are operating in a fairytale world, basically, where everything works nicely and physics of the system don't interfere with the computation, which is a big problem because reality isn't like that. In reality, we have noise. The operations you're trying to do aren't perfect. So these gates that I described are basically all, in some sense, rotations of the states on that block sphere. And you can imagine that the rotation itself can be imprecise. Now, what happens if I do one imprecise rotation and then I end up a little bit somewhere else than I thought and I'm going to apply another little bit imprecise rotation? And after multiplying these imprecisions, they're going to blow up and they're going to basically make my state be somewhere completely elsewhere than I was planning it to be for it to perform the computation I wanted to perform. So there's remedies for this. There's so-called quantum error correction, and that's what the industry is aiming for, to find the good quantum error correction algorithms that will basically use multiple qubits, multiple hyperqubits as one logical qubit, but which is error-free, which basically is able to carry on the computation almost indefinitely long. And then you can basically perform the algorithms that you wanted to perform in a theory sense of the word. So let me elaborate on that little bit. The big question right now is how do we use these devices even though they are not noiseless, even though we don't have enough qubits such that we can realize this so-called quantum error correction? And that's basically the purpose of the research, or one of the main areas of the research right now, so-called noisy intermediate-scale quantum computing. Thank you very much. Yes? Sorry? Yes, so the question was if all the qubits have like the same error in phase. I would say that's the question for an expert in quantum error correction, which I'm not, but definitely I didn't get the sense that this is one of the problems that maybe you can elaborate on. So, as long as your error rates per gate are below a certain threshold, you can correct them arbitrarily. There are different error models that people have tested. And when we build the devices, we're going to see how much our theoretical studies of the error models match to the real error models on the basis of the question. So, what is the channel, the error channel that's, those matches the physics, you know, by this metric, yeah, we can take this, but I'm sure it can come out of physics. Yeah? That's a thing I wanted to talk about. With the current number of qubits, is there any problem that you already have the key up that you cannot do with classical computers or the problem that's called less on quantum computer than classical computers? So, I want to drive this point home. Okay, so the question is whether with the current number of qubits, we can do anything on a quantum computer like faster or less expensive than we can do on a classical computer. And predominantly, answer that question is no, we can't. And that's, we can't solve any useful problems on a quantum computer right now like faster or better than a classical computer can. Although, that's something that we are basically trying to explore right now. Like, what is the point at which we will be able to? But yes, one of the concerns of mine, a long term concern is that, is the hype in the industry, which is going to, which can, you know, completely destroy the whole space. We had things like AI winter, basically, when people hyped up artificial intelligence too much and then funding for artificial intelligence went down. And that's the thing that I'm afraid of in quantum computing as well. So, yeah, not right now. But the question is, maybe in a near term, we'll be able to find some problems where quantum computing helps. That's the concept of having quantum advantage, strong or weak. So, to finish on a conclusive point, yeah, the answer to your question is no. Yeah, okay, so that's it. We're out of time. Thank you. Thank you.
 I guess it's time to start.  So welcome to the first ever quantum computing bedroom at Fosden.  My name is Tomas Kovey and I'll kind of try to introduce you to this world of quantum  computing and also organize in this room so I'm responsible for anything that goes wrong.  You can maybe notice that the title of the talk changed from what was announced.  That's just because my and Mark's talk kind of when we were looking out the slides we figured that actually the titles match reversed more than the way they were announced previously.  Okay so introducing the team behind this room it's mostly me, Mark and Will.  Me and Mark are co-founders of a quantum computing company called Rotank here and Will is a person who started the so-called Unifold Fund, an organization that supports quantum computing by promoting it and issuing grants for people that are interested in building some independent quantum computing projects.  So you can talk to Will when you are thinking about doing some non-prolucentry role and you can also look up some information about the fund at Unitary Good Fund.  Okay so I just told that I would like to answer three questions and those three questions are basically,  What is quantum computing? Why should we invest in learning quantum computing and why should we do quantum computing with open source?  And I'm going to answer them in a reversed way so I'm going to start from the perspective of why quantum computing and open source makes sense.  So the idea behind even having this room originally started back in the summer of 2018.  I was in London and I met one of the organizers of POSDOM and I was going to get quantum computing talk at the local WITDA group there.  And basically the question came up whether it would be a good time now to start a developer room at Quantum Computing.  And back at that point, me and Margot were working on a review paper about quantum computing and open source,  like all the different open source projects in the quantum computing space, evaluating them and comparing them and trying to identify what are the gaps and what are the strengths of these projects.  And eventually we figured out that this is a new technology which is going to potentially revolutionize many industries.  And similar to AI, we kind of felt that there shouldn't be some kind of mobilization by just one hardware vendor and them owning the whole software stack  which would make it hard for other companies to develop their own hardware and capture some of the market.  And also for that reason we actually just thought that there would be a useful contribution from our side.  If we could start a formal body that would try to govern the space and try to like, steward people to publish their open source and make sure that companies govern themselves  and they can be more like, opening governance models.  The whole thing is like, a lot of the more community based smart. So that's what the Quantum Open Source Foundation is about.  And to testify, the description of this room is posted on our site.  So, please check it out.  Oh, shit, I never thought about it.  Okay, that's good.  Can you stay between the two lines on your left here?  Okay.  Here.  Between these two?  Here's one line.  Oh, between these two lines?  Oh, okay.  Okay, I haven't been notified about that.  Okay, so that's good to know.  All right.  And do we have like a clicker or not?  I can give you one.  Okay.  Never mind.  So that's Quantum Open Source Foundation.  So for those of you that are just joining us through the video streams and video recording,  I was just describing the team behind the room and that's mostly the team behind the Quantum Open Source Foundation.  What's right?  Thank you.  All right.  So what awaits us here for the next two days is going to be two days full packed full of talks.  Today is Saturday and basically we're going to have...  You can just...  I'm going to try it.  You're wet for about 10 minutes.  Huh?  I have to turn it on?  Beautiful.  Okay.  It's working now.  So today, Quantum Computing Dev Room, we're going to have talks by basically every major so-called full stack Quantum platform out there.  And some major open source projects.  These are mostly often...  Yeah, often companies supported projects, but they open to contributions and they are released under open source licenses.  So these are projects like QuizKit, Forest, Strawberry Fields, and Multitude of other libraries and projects.  And I'm not going to develop on them too long because there's going to be dedicated talk to each of these.  And tomorrow, at least for me, the more exciting part is because we're going to have a portfolio of a total 11 open source projects that are less prominent  because they are developed by let's say single main authors or contributors.  And they're going to present their projects and we will try as a community to figure out ways how we can help.  So we're going to hold a hackathon sprint in the afternoon where we will divide into different groups.  And each group will try to hack on that particular project, maybe just learn how it works,  provide feedback in terms of your documentation, works or not, what could be improved, stuff like that.  And each group is going to be coached by the particular developer that is representing the project here.  So if you want to make sure you have a spot and you don't wait in the line like people out there sign up,  there's only like 20 people signed up and the capacity of Durham is like 90 people.  So there is still some spots available.  So why invest in learning quantum computing right now?  Well, it's a good time because quantum chips are already here.  This is I think the D-Waves chip but Google, Rigeti, IBM, they all have their own quantum computing hardware  and they are not the only ones.  But a couple of them also provide access.  So you are able to play with these devices even as an independent researcher or just random person out there who's interested.  You can get access to these things and you can try them out, try what you can do with them.  So it's no longer a thing which is a purely academic thing.  It's a domain which is being explored also for commercial purposes which creates interest, creates jobs, creates opportunities.  And there is like a fight going on.  Every country wants to be labeled as being the progressive one and the one which invests in these technologies.  So we can see that China, European Union, USA, they are all passing these big bills saying that we are going to support quantum computing.  And there is also a bunch of private funding going on and totaling 700 million dollars into multiple companies.  The most funded ones or the ones raised the most money I've listed here.  But there is a bunch of other ones including my company that isn't on the list.  And if you have ideas that you want to explore, there is also support for early entrepreneurs.  ProtonQ was founded as part of the CDL which is the most prominent incubator or slash accelerator thing in Canada basically.  And probably the only specific to quantum computing or they call it quantum machine learning domain in the world.  So applications that are open now, I encourage you to Google out to see what this is about.  It's a really good experience to go through this.  Alright, so in the interest of time, I still have I think 16 minutes.  So we'll do a very quick overview over the paradigms of quantum computing.  Each of these will be covered in depth today.  So don't worry if you don't understand something.  I'm going to provide just like a very high level intuition behind these things.  Okay, so the three paddlers are going to describe our quantum annealing, then discrete gate based computation and the continued gate based computation.  Alright, so in the quantum annealing, basically what you're doing, you are crafting energy landscapes that you want to explore.  On the left, there is a particular example of what we're doing.  It's an optimization problem for trying to find confirmations of a protein.  This is so-called protein folding problem.  And you know, going through some hoops, you can express that as a so-called binary optimization problem.  And what the quantum computer does is that it explores this landscape using some elements of or properties of quantum mechanics such as quantum annealing depicted on the right.  And one of the biggest players in that space is D-Wave.  There have been a round for many, many years, I think, making quantum chips since 2000, early 2003.  I'm not sure they started developing hardware at that point, but the company is around for 15 years.  I'll be corrected on that number probably, but it's the longest company that is around.  And this is a little bit of math, but basically what it describes is just, oh, I have a pointer.  Cool.  So what it describes is just like you have two variables, binary variables that are coupled by a constant.  So you have quadratic terms and you have scalar terms.  And you are basically able to specify this polynomial and that polynomial describes the energy landscape.  And the device tries to find the assignment of these variables such that the energy of this term or this expression is minimal.  And the way this is done is basically it happens on this chip and your goal is to embed your problem on the variables such that the connections between the variables are realized on the chip.  So this is the problem of the so-called graph embedding and I'm not going to elaborate on it, but it basically creates additional overhead in putting the problem on the hardware.  So we can imagine that this is very low-level approach.  You can have problems here like missing qubits because they were disabled, they had some manufacturing problems or missing couplings.  And you have to account for these things when you are embedding.  Okay, so just a quick code demonstration how it looks like such that you have just a cursory glance.  This is a very simple problem where you have four qubits here and they're all anti-correlated, which basically means that we have couplings of one here.  And what this system is supposed to be, what the lowest energy system of this, or lowest energy state of the system is, is basically like, alternations of ones and minus ones.  So these variables, they can be either one or minus one.  And to achieve basically the lowest expression value, you have to alternate them here.  Anyway, this is how we do it.  They have a pretty nice API.  You just specify these couplings in a dictionary and then you embed it using this class and then you can directly sample using this interface.  And you can use either classical samplers or you can sample out of the machine if you have access.  It's basically transparent.  So from a high level, this is what is going on, you have problem.  You formulate it in terms of this quadratic binary optimization problem or Isling model is another name for it.  Then you embed the problem, the problem's graph into the chip, and then you sample out of it your solutions.  And there's the WaveLeap, which is basically a platform which gives you access.  I'm not sure it's available in Europe, but it definitely is available in North America.  And you can get one minute free of time to explore these things.  Some more resources for people that are watching this on the video later.  So the other paradigm is so-called universal gate-based quantum computing.  And there you are designing these quantum circuits.  An example of quantum circuit is on the right.  So these are the gates.  This is a gate, but this is also a gate.  So this gate interacts with two qubits.  That's why it stretches two lines.  Each line is one qubit.  I should probably explain that.  And these boxes are basically measurements.  So to read out the result of a competition, you have to measure and collapse the quantum state.  And that's depicted by this symbol.  And big players here are basically IBM, Google, Rigeti.  The reason majority of these big companies are investigated, this kind of platform is because this is actually where the majority of the theoretical results were proven at.  Like all these Shor's algorithm, all these frets that we hear about quantum computing come from theoretical results on these kind of architectures.  So this is the qubit.  No reason to get too scared about it.  I'm not going to delve too much.  I just want you to see these equations first.  These are two basic states.  These are two complex numbers that together comprise the quantum state.  And usually we depict the qubit as living on this sphere called the block sphere.  All right, so here basically we don't have binary variables anymore, like during the competition, but the variables themselves are quantum variables.  And there are basically a combination of those two basis states, and you apply these operations and you read out at the end your result.  So again, it's very, very low level.  You're designing a circuit.  It's almost like doing some board.  You're not soldering it, but you are basically operating on a very low level.  All right, so I'm just going to rush through this.  This is an example of how you apply to gates.  The first gate, which basically does to state zero does this and to state one does this.  Yeah, but really important for the demonstration here, just for illustration.  This is a different gate, so-called controlled not gate.  And if you combine these two gates together, you can create what we call maximally entangled state.  So if you measure this, you can get one of the two outcomes, it's either zero, zero on both of these qubits or one, one on both of these qubits.  And why is that?  It's going to be explained later today.  I mostly wanted to share with this so that you have actual idea how it looks at the software layer.  Basically, you are writing Python code, which generates this quantum assembler, you might think, or this is so-called quill code.  So it's really low level instructions, apply this gate at this qubit, apply this gate for those two qubits, then measure these two qubits, and here's your result.  And you have to be clever about what you're doing, such that you, at the end, measure something which is going to be useful for you.  All right, so the gate model, workflow from the high-up, basically, you have the problem, you encode your problem,  I mean, you have to figure out the quantum algorithm for your problem, and then you basically implement that algorithm as a quantum circuit.  Then that quantum circuit has to be compiled, because the actual hardware platform doesn't support all the gates that you might think that you need.  They actually support only subset of the gates, so-called fundamental subset.  And that basically means that some of the gates here will be expanded into multiple gates in the series of different gates,  which again, like, a little bit boosts or blows up the circuit of the computation.  Which is basically the problem we're facing right now with the devices, because each operation is noisy to a certain degree,  so the more of these gates you apply, the less certain you can be about the result that you're going to get at the very end.  Okay, so some further resources about this for people that are interested,  but mostly for people that are just going to look at this over the internet or later just look at the slides.  And very briefly about the continuous variable quantum computing.  So here you switch the concept of the qubit with the concept of a Q-mode, which you can see it's continuous.  See this nice integral sign here, as opposed to, you know, having two discrete states, basic states here.  And the big player in this field is Xanadu, and we're going to have two talks from people from Xanadu today.  So they're going to delve much deeper into this topic than I could.  So, yeah, I wanted to also give some further resources about this.  They have nice API layer.  I would almost say one of the best out there is like the API of the strawberry fields.  And that's that. Thank you for your attention.  And if you have any questions, please shoot me up. We have some time.  applause  I know very little about quantum customers, you can assume nothing.  you said something that picked my interest. You mentioned that as you work with more gates,  you have an increased uncertainty on the result. But I'm very curious, what do you mean by  increasing uncertainty?  Well, okay, so the question was I mentioned during the talk that the more gates you apply,  the less certain you can be about the result you're going to get at the end. So when people  are developing these quantum algorithms, they are operating in a fairytale world, basically,  where everything works nicely and physics of the system don't interfere with the computation,  which is a big problem because reality isn't like that. In reality, we have noise. The operations  you're trying to do aren't perfect. So these gates that I described are basically all, in  some sense, rotations of the states on that block sphere. And you can imagine that the  rotation itself can be imprecise. Now, what happens if I do one imprecise rotation and  then I end up a little bit somewhere else than I thought and I'm going to apply another  little bit imprecise rotation? And after multiplying these imprecisions, they're going to blow  up and they're going to basically make my state be somewhere completely elsewhere than  I was planning it to be for it to perform the computation I wanted to perform. So there's  remedies for this. There's so-called quantum error correction, and that's what the industry  is aiming for, to find the good quantum error correction algorithms that will basically use  multiple qubits, multiple hyperqubits as one logical qubit, but which is error-free, which  basically is able to carry on the computation almost indefinitely long. And then you can  basically perform the algorithms that you wanted to perform in a theory sense of the word.  So let me elaborate on that little bit. The big question right now is how do we use these  devices even though they are not noiseless, even though we don't have enough qubits such  that we can realize this so-called quantum error correction? And that's basically the  purpose of the research, or one of the main areas of the research right now, so-called  noisy intermediate-scale quantum computing.  Thank you very much.  Yes?  Sorry?  Yes, so the question was if all the qubits have like the same error in phase.  I would say that's the question for an expert in quantum error correction, which I'm not,  but definitely I didn't get the sense that this is one of the problems that maybe you  can elaborate on.  So, as long as your error rates per gate are below a certain threshold, you can correct  them arbitrarily. There are different error models that people have tested. And when we  build the devices, we're going to see how much our theoretical studies of the error models  match to the real error models on the basis of the question.  So, what is the channel, the error channel that's, those matches the physics, you know,  by this metric, yeah, we can take this, but I'm sure it can come out of physics.  Yeah?  That's a thing I wanted to talk about.  With the current number of qubits, is there any problem that you already have the key  up that you cannot do with classical computers or the problem that's called less on quantum  computer than classical computers?  So, I want to drive this point home. Okay, so the question is whether with the current  number of qubits, we can do anything on a quantum computer like faster or less expensive than  we can do on a classical computer. And predominantly, answer that question is no, we can't. And  that's, we can't solve any useful problems on a quantum computer right now like faster  or better than a classical computer can.  Although, that's something that we are basically trying to explore right now. Like, what is  the point at which we will be able to?  But yes, one of the concerns of mine, a long term concern is that, is the hype in the  industry, which is going to, which can, you know, completely destroy the whole space.  We had things like AI winter, basically, when people hyped up artificial intelligence  too much and then funding for artificial intelligence went down. And that's the thing that I'm  afraid of in quantum computing as well. So, yeah, not right now. But the question is,  maybe in a near term, we'll be able to find some problems where quantum computing helps.  That's the concept of having quantum advantage, strong or weak. So, to finish on a conclusive  point, yeah, the answer to your question is no.  Yeah, okay, so that's it. We're out of time. Thank you.  Thank you.
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