Okay, welcome everyone. It is great to have everybody here. We are very excited to have this opportunity to introduce Pasqal and talk a bit about all the work that we have been doing. Before we get started, I want to make some introductions. I want to start with an acknowledgment. We have our partners from Bleichroeder here, and I would like to acknowledge Marcello. Oh, there we are. Marcello, sorry. Marcello, and then we have other members of the Bleichroeder team here as well. These are our partners. With that, before I do a personal introduction, before we go into introduction to Pasqal, I would like to ask my colleagues to provide a brief introduction to themselves. Starting with Loïc, our CTO.
Hello, everyone. I am very happy to meet you. I am Loïc Henriet. I am an Engineer and a Physicist by training. I have been spending the last 12 years working on quantum computing, first in the academia, and then at Pasqal for the last seven years as a founding member, and I am the CTO of the company. Happy to meet you.
Good morning, everyone. I am Stéphane Rougeot. I am the CFO of the company. You may have seen the announcement that came out yesterday, so it is pretty recent. I have been CFO of listed companies for the last 25 or more years. Always at the crossroads of corporate finance, business, and how to scale and transform company and grow the business, and then technology. I was CFO of listed company out of Europe. I did the IPO of Thomson back in the days, not Thomson Reuters, but Thomson Multimedia in Paris and New York at the end of the '90s. Long career and very excited to join Pasqal and scale the company, and exploit all the leadership that you are going to hear about today. Great to be with you today.
Thank you. I would like to also introduce Mark Armstrong, our Chief Commercial Officer, who brings a long, distinguished career from HPE.
Yeah. Good morning, everyone. As Wasiq says, it's like day two for me, so the announcement's got to get here, but very excited to join Pasqal. I had a long career at Hewlett Packard Enterprise. For the last five years, I ran their AI and HPC business across Europe, Middle East, Africa, which I think has got some interesting similarities to this industry. I am looking forward to having success and working with the team. Nice meeting you. Thank you.
Thank you very much. This slide shows that's a photograph of our quantum processor. We have multiple of these commercially deployed across the world. This beautiful machine is 10 ft by 7 ft by 6 ft, and it requires less than 4 kW of power, and it goes into standard data centers. For us, quantum computing is a reality today. It is not something in the future. I am going to start with the three most important things that we are going to talk about in this presentation. These are the key takeaways. I am going to tell you what we are about to tell you in the whole presentation, and then we will go into more details. The first thing, we are focused exclusively on quantum computing.
We believe this is the most important sector, the most demanding sector, the sector with the greatest opportunities out of all the possibilities of quantum technologies. We believe it requires relentless focus on this to build the right systems that result in world-class computing systems. That's the first message I want to get across. Now, building on that, we are a global leader in industrialized and operational high-complexity quantum computers. I have a couple of words in there that I just want to talk about: industrialized, high-complexity, operational quantum computers. Let's start with high complexity. We can make quantum computers which have 1 qubit, 2 qubits, 10 qubits. These are not high-complexity quantum computers because we can simulate them on existing classical computers. They are interesting from maybe some R&D or educational point of view, but they cannot do useful workloads.
Only when you start to get beyond 100 qubits, and our commercial systems are 100- 200+ qubits, only then can you do work that you cannot do on any other form of compute. That's the high complexity part. Industrialized, that's another very important vector. Many universities with brilliant people will create labs. Industrialization means that you have to think about the key attributes of compute at scale. These attributes are reliability, scalability, the supply chain, unit economics, redundancy. You have to think from an engineering systems principle. That is a very hard road to take. We took this decision years ago in the infancy of our history that we will not ship lab equipment. It was a deliberate decision.
We said we will engineer our systems properly, even if it means that we go a little bit slower, but if this results in us delivering actual compute systems that can stand alongside traditional HPC and now GPU-based compute, then we have achieved our mission. That is exactly what we did. We are one of the very few companies in quantum computing world who have actually crossed this threshold of properly engineered systems. That is the second item in that headline. The third one is operational, which is a very important point. If you build well-engineered systems, and these are high complexity quantum computers, they have to be able to be deployed in standard data centers and work reliably, and we have a track record of that. With that clarification, here is where we are.
We believe off IBM, we have the second highest number of high complexity quantum computers deployed in the world. We are a much younger, much smaller company, and we are very proud of this fact. We have seven of such units, all between 100- 200+ qubits operating across three continents, and we have an established track record in terms of their operational capabilities. All of our QPUs operate without deep cryogenic systems, which is a really big advantage. They can go into standard data centers. The room that they stay in is identical to the rooms that the standard CPU and GPU racks are installed in. This is a major advantage that we have. That is the point number one that I want to talk about. Point number two, we deliver useful quantum computing today.
There is an inherent advantage in the way we build quantum computers based on neutral atoms, and the advantage is this: it gives us the best of both worlds. What do I mean by that? It means we can deliver full analog quantum computing today with which we are solving business problems today, and the same hardware, literally the same hardware platform, gives you cutting-edge, industry leading, fault-tolerant quantum computing with the same specs and the same timelines as any other company in the world. Only we have this advantage. I will talk about this as well, but this is a very powerful advantage that we have. Here are some specifics on this. We are one of the few companies that have actually delivered more than 1,000 physical qubits. These are the highest quality, fully connected quantum qubits. We are one of the very few.
There is no roadblock for us to deliver, and we expect to deliver at least 10,000 physical qubits per single machine by 2029. On the same machines, the same hardware platform, we will deliver at least 200 logical qubits with six nines of fidelity. The same hardware approach gives you the best of both worlds. Really important point. I talked about analog and I talked about FTQC, and I will talk a little bit more about that. One of the big things that we have shown recently is that we showed rigorous quantum advantage in the simulation of real-world materials. This is a really important result that just came out a couple of months ago, and we can share the archive paper on this. That is the second point I want to share. We deliver the best of both worlds today and tomorrow on the same hardware platform.
Number three, as a business, we do not boil the ocean when it comes to solving problems. We are not just a tool looking for a problem. We made a deliberate analysis multiple years ago, and we identified specific mathematical problems that we have an unfair advantage in solving over any other form of compute. We map those problems to important industry problems in specific verticals, and that is what we focus on. In the end, we all agree quantum computing is computing. It has to solve a problem.
Customers do not care whether it is a quantum computer or a GPU or what kind of quantum computer. They just want the problem solved. So our focus has been laser-focused on finding the problems where we can solve it today, deliver business value proposition, and this allows us to go deep and solve those problems today. So our approach is very different.
Instead of boiling the ocean, we hyperfocus and we have picked three sectors. First sector is energy or oil and gas. Our reference customer there is Saudi Aramco, and I will talk about the use cases there. Second is financial services, and our reference customer there is Crédit Agricole. You might have seen the beautiful press release that came out today just prior to our meeting here today. The third is specialty materials, which is in line with what we demonstrated for quantum advantage. This focus, this readiness, and this inherent advantage of our technology approach allows us to build a business and a backlog today. These are the three key messages I wanted to share with you before the start of the presentation. If you just focus on the left-hand side of this presentation, I just want to highlight a couple of things.
We are one of the very, very few companies in the whole world, in any sector, that have been founded by a Nobel laureate, and it is just not any Nobel laureate. It is Professor Alain Aspect. He is the Nobel laureate in quantum physics. He is the person who experimentally proved quantum entanglement and therefore started the whole field of quantum information sciences. We are a deeply technical team with 70 +, actually much more, PhDs throughout the company. On the right-hand side, we are headquartered in France, but we are a global company. We have operations in Canada, in U.S., in Saudi Arabia, in South Korea, because we have deep customer engagements in those areas. Of course, we are backed by high-quality clients, partners, and investors. So I talked about this. Let me just summarize differentiators. Number one, commercially ready today. Really important point.
Number two, the same approach, same hardware platform solves problems today and gives future to our customers. Now, why is that important? Two reasons. Number one, customers. We need to earn trust with customers to show them that we deliver value, and that is a process we are able to start right now based on the maturity of our systems and our focus on areas where we can deliver value. Second, this reduces risks for our customers because once they commit to our hardware platform, our software platform, they know that they will not risk obsolescence because the same system will meet and deliver the best FTQC requirements as well. Loïc will talk about this slide in much more detail, but what I wanted to share with you here is something which we are very proud of.
We published this roadmap more than two years ago, I think almost three years ago now. We have delivered each and every element either on time or ahead of time. When we make a promise, we deliver, we execute, and we do not make idle promises. We believe this is a unique strength of our culture and our approach. When we talk about what we will deliver by the end of the decade, we bring the same level of earnestness and seriousness to those promises. We will talk more about in terms of what the technology roadmap looks like. Professor Alain Aspect, Nobel laureate, Professor Antoine Browaeys, the co-inventor of the neutral atom space itself, and Georges-Olivier Reymond, the first person to trap a neutral atom. What I am trying to say is that the history of neutral atom space is the history of Pasqal and its co-founders.
The modality that is now considered to be perhaps the most promising modality to create quantum computers is the history of Pasqal. The most important thing, if you look about it, trapping of neutral atoms, the basic principle of creating quantum entanglement in neutral atom systems is the Rydberg blockade discovered by Professor Antoine Browaeys. Quantum simulation, his work. You go to the right. After our founding, we deployed our first commercial quantum computer in 2022, 4 years ago. So we have a lot of operating history. Recently, we announced this result in Quantum Advantage on TmMgGaO4, and we also did a formal inauguration of our QPU at Aramco, which is installed in their Tier 1 data center in Dhahran, operating autonomously, reliably. Let me talk about quantum advantage for a second.
People talk about this term a lot, and I will just make some high-level remarks, and then we will talk in more detail about this. Last year, we wrote what we believe was the first paper with IBM on a scientifically rigorous definition of quantum advantage for material simulations, and that was intentional because we wanted to set a scientifically rigorous bar and a standard that everybody would adhere to. When we look at all the results and news that comes out around how quantum computers outperform non-quantum computers, we look at those problems in 3 different buckets. The first one is math for the sake of doing math. It is basically a problem which is, in some sense, an artificial problem. It may be interesting academically, but it is not something that you would actually use in the real world.
For that, you can run different tests and benchmarks and can show that, yes, quantum computers will do it really well, but they have no practical use. We are very pragmatic people. We want to create a new form of compute. The second class of problems is what I call toy simulation problems. So you take a real material, and you hyper simplify it, come up with a toy model for that, and then you run it, and you see whether you can outperform the classical compute. You can see various results there, but none of them have crossed the threshold of getting into the quantum realm. Starting this year, there are two important results that came out. The first one was by IBM, and this paper was about potassium copper fluoride. In the paper, they acknowledge that this result can be replicated using classical computing.
It is actually not demonstrative of quantum advantage. Our paper, which we co-wrote with Los Alamos National Laboratory, clearly demonstrates that we are in the realm of quantum advantage, and we will talk more about this. That really signifies our approach always is practical, usable, demonstrable quantum computing and its benefits. Everybody in this room knows this, which is quantum computers are not going to replace existing computers. They are going to work seamlessly with CPUs and GPU-based compute. At the heart of it, Loïc says it really well, which is what distinguishes quantum computers versus other forms of compute, is that for quantum computers, you give them problems where the problem complexity is high, but the data IO is relatively low. So where you have many, many different kinds of solutions, and you have to find the right solution, that is high problem complexity.
Where you have to really simulate material from a quantum mechanical point of view, and you cannot use approximations, that is high problem complexity. But the amount of data going back and forth is not very high, which makes them perfect complements to other forms of compute. In our case, we can clearly demonstrate which part is being done by the QPU and which part is being done by the CPU or the GPU. That is precisely how we work. So our systems have a native capability of working with other forms of compute. We build the hardware and all the low-level software. So that is your OS, electronics, everything related to the QPU runtime. That is part of our core that we built. On top of that, we have built this resource coordination layer that allows for that seamless working between CPU and GPU clusters.
On top of that, you have the application layer with the SDKs, with the mathematical libraries, the application libraries, and so on. So basically, we provide the whole stack, which makes it turnkey for our customers to start to use this in a useful way, whether we deploy it on-prem or whether they access this through the cloud. Again, this is part of a deliberate thinking of how do you enable compute, not just make quantum computers. Also, if you look at the other side of it, I talked a lot about our hardware, but if you look at our overall patent portfolio, it is almost at parity in terms of the software patents and the hardware patents. So we continue to focus on both areas.
Everybody in the room is also aware of this, which is from the current phase, from utility to advantage, to the fault-tolerant era. I want to talk about two things here before I get into some details. There are two ways in which you can do quantum computing. One is called analog, and the other is fault-tolerant. Analog is not a primitive form of fault-tolerant. It is a completely different way of doing computing. Here is the analogy. The brain is an analog computer. CPU-based digital computers are the equivalent of fault-tolerant quantum computers. They both solve problems. In fact, the brain solves some problems really, really well, really efficiently compared to other computers that we use. So analog and FTQC are completely different ways of computing, and they have their strengths and their challenges, but they are completely complementary. Quantum annealing is a small subset of analog quantum computing.
Here's the analogy. If I look at a landscape and imagine this landscape is your energy landscape, you have flat, or you have hills, or you have valleys and stuff. Quantum annealing is like a train that runs on a track. It is a fixed route. It goes from point A to point B, doesn't go anywhere else. Full analog quantum computing means you have a 4x4 all-terrain vehicle that can just go wherever you want to go, which means you can explore the entire domain of the problem, and you can explore it in a dynamical fashion. This is a really important thing. Just like the brain just doesn't do one thing linearly, analog quantum computing solves problems in a general dynamical way. It is a different paradigm of doing computing.
The beauty for us is the same hardware approach, the same machines give you the best of both. You get this today, and you get that tomorrow at the same spec, same timelines. That's what's unique about Pasqal. Why can we do that? Because we spent a lot of time industrializing and making our systems commercially ready, so they are actually usable as quantum computers. Then it is a switch between analog to digital mode or analog to FTQC mode. There's a very important implication of that. Everybody has this conception that if you're not doing FTQC, you can only solve certain kinds of optimization problems. But when you do full analog quantum computing, you can solve a much broader class of problems, which means you can do all kinds of material simulations, which currently we think we cannot do.
We can solve really complex optimization problems on top of it. That is why we are able to go and monetize these applications for these really important customers today. The market opportunity is very big. Everybody in the room knows these figures. These figures are looking at 2040 time screen. If you look at, again, the mapping of this to the industries that we look at, very large opportunities for us. Financial services, energy, specialty materials, very large end markets, very large opportunities for us. For us as a business, it's all about getting focus, getting traction, showing commercial value, earning customer trust, and building that flywheel. With that, I'm going to stop, and I'm going to hand it over to Loïc to go into more details about our technology.
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Now I will take you under the hood of our quantum computing platform and talk about the technology itself. Our qubits are single atoms of rubidium, and this translates into five key advantages when it comes to compute. The first one is about scalability. We see no fundamental roadblock to reach 10,000 physical qubits and even more because we're working with optics and lasers rather than fabricated chips. We don't have to manufacture our qubits. Nature does that for us. It keeps costs and manufacturing complexity down. Second, Wasiq talked about that already, is the key strength that we can have dual analog and digital modes on our same hardware platform. We can run in analog mode to deliver value today while we build for fault-tolerant quantum computers later down the road. Customers aren't asked to wait for our roadmap to be delivered.
They can get something useful right now. Third one, coherence, uniformity, quality. There is no fabrication spread, no defective qubit in the corner of the chip. Fourth is hybrid classical quantum. We are using QPUs alongside CPUs and GPUs. Fifth one is room temperature, low power. We don't need a specific infrastructure to make our quantum computing infrastructure work. No deep cryogenics, only 4 kW of electricity. If you read across to the right, you'll see that each of these translate in practice to, well, lower cost, clean upgrade path to FTQC, best performance, modularity, and very light infrastructure footprint. Back to our technology and product roadmap. This is really the single most important chart if we want to understand how we translate our scientific groundings into products and commercial activities. I will walk you from the left to the right.
As Wasiq said, what we said we would achieve, we did deliver on time. The top band is about the hardware engine. Physical qubits per machine. We went from 200 - 1,000 today, and we're on the path to between 10,000 and 50,000 qubits before the end of the decade. But I want to be precise here. Raw physical qubits is not the only thing that matters. What will matter in the long run is the number of logical qubits, error-corrected qubits. On that line, we go from 20 in the relatively short term to 200 by 2029. And very importantly, this number, it needs to come with the number on fidelity. You have to understand that logical qubits always comes with a fidelity associated with it, otherwise it doesn't mean anything.
What we are targeting is to reach the MegaQuOp regime, so 10 to the - 6 error rate with 200 logical qubits by 2029. In terms of what our customers actually buy, this is the middle band. So those products, they map directly onto the hardware engine. Orion is shipping today up to 200 qubits, very good analog performances. We will have Vela, which bring the first quantum advantage use cases to our clients, and then Centaurus with early FTQC and Lyra in 2029 with impactful FTQC. The bottom band is about the software and the upper layers, the libraries that make all of this usable in a computing environment. So hybrid classical quantum programming, SLURM integration that we developed alongside IBM and NVIDIA, and open source application libraries for simulation, optimization, graph machine learning.
We need to have an entire stack to support our users and to have the minimal amount of effort from users so that we integrate into the existing classical stack from standard HPC and AI. The message I want to leave you with is that this is a roadmap with products that are attached at every stage and with a release cadence that we are following. Now, if you ask, what is the best platform position for FTQC at scale? What I would say that there are, broadly speaking, two main categories, two metrics that you want to have a look at. The first one is scale, so the circuits on the left and how scalable the system is. Neutral atoms can reach up to 50,000, as I said, qubits in a single machine, a single vacuum chamber.
This is quite powerful compared to some other technologies and leading technologies around there. So here we do not need interconnects to reach those numbers. It is really within a single core that we are able to reach that. We think that we will be able to reach that bit by 2029. That is not a marginal lead. It is really an order of magnitude that in the end translates into computing power. The second metrics that you want to have a look at is fidelity. Look at the green curve. Neutral atom error rates are falling fast and have already converged right onto the others. Historically speaking, when you look back, it is a technology that is relatively younger.
When you compare it to ions and superconducting qubits, of course, it took a bit more time to develop and to reach the levels of fidelities that are necessary for quantum error correction to work. But right now, we have caught up, and we are at the level that is required for FTQC. So we combine the scale advantage with quality, and this combination that puts neutral atoms in the category of players that are the most likely to win at scale. If you want a direct comparison, this is a table that lays us against all the serious alternatives. We can start with scalability. Of course, number of qubits today that have been demonstrated. It is not a roadmap. It is not a plan. It is results that we have demonstrated and published. Connectivity, I think it is one of the most underappreciated metrics on this page.
We have native all-to-all connectivity, meaning that any qubit can communicate with any other one within our vacuum chamber. This is made possible by qubit movements. You can move a qubit around during the computation while preserving coherence. Actually, this feature was also developed by Antoine Browaeys in his lab at Institut d'Optique in Paris. Now it is used by most neutral atom labs around the world. Keep going down. Operating temperature, room temperature versus deep cryogenics. It is simpler. The fact that we can move the qubit around, it leads us to a relatively interesting logical overhead, 100 - 1, compared to some other typical architectures, which are more like 1,000 - 1. The bottom two rows are ours alone. Dual analog mode of operation and demonstrated quantum advantage on material simulation.
I will talk to you about that in a moment. One message that I want to emphasize is that when you read that table across, no single row tells you the story. It is the way each row combines and combined with the other ones that really matter in the end. How do we build physically a machine with 1,000 qubits? Everything happens in the greenish cylinder that you can see on the bottom. This is a vacuum chamber, and we have a very strong vacuum, so it is 10 to the minus 11 millibar. It is the pressure that you would find at the surface of the moon. We trap single atoms inside that ultra-high vacuum chamber. To do that, we proceed with three steps. First, we load atoms in an array of traps that are generated by lasers. The loading is probabilistic.
You begin with a partially filled array, as you can see on the top left picture. Then we move individually the atoms around to end up with an array with perfect filling after rearrangement. Making it work rests on several key ingredients. First is the optical architecture, high-power lasers, high-aperture optics, and you want also to have a strategy to rearrange the atoms that works well. These are deep engineering capabilities that we have developed and that are quite hard to replicate, and the next slide is a result of all of three coming together. This is a proof that this works. Those are real images from our machine, not simulations. Each bright dot that you see here is a single rubidium atom, and you can count them, and there are more than 1,024 qubits on the right image. No defects.
Now that we have built large qubit registers, what do we do with them? There are a variety of use cases and applications in several verticals. We talked about oil and gas, we talked about finance, but I want to deep dive on one very important result, which is related to material science field. This is the slide that I would like you to remember. It is quite technical, but I really love it, so I need to talk about it. It is our single most important scientific result. It is the first quantum advantage that Pasqal has delivered on a problem that actually matters, and I want to talk about that because it has been 12 years that I have been working towards this result, so I am quite excited about it.
Let me define quantum advantage carefully. It means producing a result that a classical computer cannot practically reproduce, and these problems need to be something of interest, something that existed before actually the quantum computer was designed. The famous early demonstrations, for example, random circuit sampling from Google, they cleared the bar on performance but not on usefulness, as Wasiq discussed. What is different here is that we have done it on a material with real interest. You have a picture of this TmMgGaO4 magnet on the top left. This is a real material, and this is a frustrated magnet.
What does that mean? It means that you have tiny magnets on a triangular lattice, and it is frustrated, meaning that all the constraints cannot be satisfied at once. This makes it hard for classical computers to describe how this magnet behaves.
The behavior of this whole class of material is actually very difficult, even on the most powerful CPUs and GPU clusters, to understand. That is what happened with this particular magnet. The team at Los Alamos National Laboratory was not clear on understanding why this magnet would behave the way it behaved. That was when put in a very complex scientific instrumentation with low temperature, strong magnetic fields. What we did is a one-to-one quantum simulation of that material. That is a strip on the right. We take the real material at the angstrom scale, we write down its microscopic magnetic model, and then we map this model onto our quantum processor, our quantum simulator. We are not approximating the physics in a simplified model.
What we are doing is that we are reproducing the actual material on the quantum computer and describing really the real model of this magnet. Now, the two charts at the center of the slide. The top one overlays our quantum simulation results, the green dots against the solid line, which are independent measurements that were taken at MagLab, and they match quantitatively, as you can see. You can even see that the system passes through this well-known one-third plateau for the magnetization, and our machine is able to capture it. The bottom chart to me is quite amazing. We have five separate machines, Fresnel Machine one, Fresnel Machine two, Fresnel Canada one, Ruby, and Jade. Those are five Pasqal machines, three in France, one in Germany, one in Canada, all able to solve that problem. What you have is that they all give the same answer.
Reproducibility across independent QPUs is a very hard thing to achieve. It is the difference between a true computing equipment and the lab apparatus and the lab experiment that you do once. For our users, it makes no difference to know if they have run their workload on FE1 or FM1 . They just launch on their cloud portal, it runs independently somewhere in the world, and they can trust the results. Finally, if we were to run the same procedure on classical GPUs, it would take several weeks to get to the same results that we were able to reach in a few hours on our quantum processing units. Even after waiting several weeks on GPUs, there would be no guarantee that the result that you would find would be a converged result.
So you would not be able to trust the result that would come out after several weeks, compared to something which takes a few hours for us and matches reality. So when we say that Pasqal has delivered quantum advantage, this is something that is with verifiable evidence behind that claim, and it is directly relevant to the field of advanced materials on which we are working. So this is one of the examples of the things that we can do with our analog qubit machines. We can do it right now. And the beauty of neutral atom is that actually using the exact same hardware platform, we can also implement logical qubits. Let me turn to that. When you scale the system, because physical qubits, however many you have, still make errors, you want to be able to correct for the errors.
To run the longest, most valuable computations at scale, you need logical qubits. You need error-corrected qubits. You need FTQC. How do you do that? Well, you put several physical qubits at work together, to protect one robust unit of information. So that is the graph on the left. Out of several physical qubits with redundancy, you build one logical qubit. In order to be able to do that, you need a few ingredients that are listed on the right. Robust physical qubits, of course. Reliable atomic operations with very low infidelities, high fidelities. All-to-all connectivity is best. You can manage if you do not have that, but the overhead to pay is quite large in that case. You need fast qubit readouts to be able to measure errors and feedback on the system to correct for the errors in real time.
Then you need a code, so a procedure to read out and correct the errors. So this is what is called the code, the quantum error correcting code or error detecting code. And there is a lot of work ongoing as to how you build your code with your hardware in mind, with the strength of your hardware in mind. So this is our collection working on our hardware today. So it is not a theory, not a roadmap. It is really something that we did implement. It is what we call the [[4,2,2]] code. So 4 physical qubits plus one flag qubit equals one logical qubit. So you get this ratio. Equal 2 logical qubits, sorry. So you get this ratio of 1: 2. You do not need to follow the circuit at the top.
What you want to look at is the story that is displayed by the histograms at the bottom of the slide. So on the left, you do not have any procedure, you do not have the error detection implemented, and so you see that we land on the correct state about 40% of the time. So what you would like to have, ideally, is to have the green histogram bars as high as 0.5 on the two left and right sides of this plot, but you see that you get only 40% probability of achieving that.
So you have noise, which is spread everywhere. You have wrong outcomes that pop up. On the right, we have implemented this error detection procedure, and you can see that we have enhanced the results because using the parity checks in the [[4,2,2]] code enabled us to actually detect the errors and correct for them.
The probability to reach the correct results is enhanced to 90% in that case. Real results on the hardware. The nice thing is that we did that particular demonstration on the hardware that was used primarily before as an analog machine. The exact same machine, which was used to run use cases for our clients, was turned into an R&D device for us to develop logical qubits, and we were able to turn that demonstration relatively quickly. After that demonstration, we said, "Okay, why does it matter commercially?" We did apply it to a real computational task. We did that to solving differential equations. Differential equations, as you know, they end up in an enormous part of engineering, finance, physics. We decided to benchmark our logical processor on this particular task, solving differential equation.
The top chart shows the error distribution, the frequency at which you get a given error, either on the physical qubit implementation of solving this differential equation or using the logical qubit implementation. As you can see with the green bars, the logical qubits are clearly shifted towards lower errors, so it gets beneficial to solve the differential equation using this logical encoding compared to physical encoding alone. The bottom chart, it shows both approaches, tracking the true solution because we are not in a regime of quantum advantage. You can do that using a standard classical computer. The logical run is far closer to the actual solution compared to physical qubits.
To our knowledge, this is the first time anywhere in the world that differential equations can be solved using a logical quantum algorithm, and we did that with performances that are better than with physical qubits alone. Let me close this technology session on the system engineering side of things. What I showed you earlier is the versatility of our platform. We can actually do analog and digital quantum advantage in material science, logical qubit demonstrations. This is very versatile, but what we are doing is that we are actually transferring this technology advantage into a commercial and engineering advance by defining a modular architecture. The QPU sits at the center, and the capabilities that are related to this QPU are shown on the side, and you can see that they can be upgraded independently. That is the thing that counts.
Why do we want to do that? Because on the R&D side, it enables us to decouple the various modules and to accelerate R&D by keeping a fixed set of interfaces. We can accelerate on the technology side. On the commercial side, a customer can increase qubit counts, reduce noise, add addressability, layer digital gates. That is something that is quite interesting because it does not have to replace the entire system. Our existing customers can inherit upgrades as well, as our system is very modular. Now, we will turn to the demonstration of our product.
Hello, my name is Jaap Kautz, and in this video, I will demonstrate how you can use Pasqal's QPU for real-life use cases. The two use cases we will discuss in this video are portfolio optimization and material simulation. Let's start with portfolio optimization. This is a problem which often occurs in finance, where people want to optimize their portfolio of stocks or bonds to either maximize return or to minimize risk, or a combination of both. To show how this problem can be tackled with a quantum computer, we developed a quantum portfolio optimizer, which in the background uses a QPU to solve this problem. When we use this application, we first have to choose which stocks we're interested in.
We can select a number of stocks, we can remove some, we can add some, we can manually add more, and then we can choose to either minimize the risk or to find a portfolio which maximizes the return. We'll go somewhere midway. We can run this experiment on a real quantum computer or on an emulator. For the demo, we will first show how the emulator works and then continue with the quantum computer. There's all kinds of advanced settings if you're interested, but if you're not, you can just choose optimize portfolio. The first thing the application needs to do is to translate this finance problem into a problem which can be handled by the QPU. The first step is to analyze the stock results of the past two years.
From this data, it will calculate an expected return and a standard deviation, so the volatility of the stock. In addition, it will analyze whether these stocks all move simultaneously or independently, and that is depicted in this covariance matrix. Finally, this covariance matrix is used to build a QUBO matrix, and this QUBO matrix is the formulation that our quantum computer understands. In the background, this job was already submitted to the QPU. If you are a finance person and not interested in how a QPU works, you can just wait, and then after a while you get an advice on which stocks to buy. However, for this demo, we will show what happens behind the scenes. We'll go to our cloud dashboard. Here you can see that indeed a job was submitted to an emulator, and we can see what that job looks like.
In a neutral atom quantum computer, the qubits consists of atoms. The QUBO formulation, which we submitted, needs to be translated into some atomic configuration. What you see here is the positions of the atoms in the QPU. They are arranged in a plane like this. Then we manipulate these atoms with lasers, and what you can see here at the bottom is the intensity of this laser over time. At the end of this laser pulse, we do a measurement, and that's the measurement which is then sent back to the portfolio optimization application. Good. While we wait for this result to complete, we will create a new job and submit it to the QPU. We create a new job. This time we will select more stocks.
As the number of stocks increases and we want to add some weights to the stocks, the number of possible configurations of our portfolio increases dramatically. With this number of stocks and 3 bits per stock, we end up with a number of configurations in the order of 10 to the 18th. That's a billion times a billion different configurations. This is very difficult to analyze classically already. We'll run it on the QPU because our emulator has a hard time running this as well. We again can choose what the return is we favored. This time will be a bit more risk-averse. We choose to run it on the QPU. We can choose our settings. We want to run it rather fast, so we reduce the number of shots, and then we submit it to the QPU.
We can look in our dashboard again, and there it is. In the meantime, our previous job has finished. This is our earlier job with only a few stocks, and this is what the results look like. To understand these results, I'll explain what this graph means. Each item in this graph is a potential configuration of our portfolio. A set of stocks you could buy. The height of each bar indicates how optimal this configuration is according to our QPU. Here we see that according to the QPU, this is the code for the most optimal configuration. If we now go back to our portfolio optimization application and we look at our earlier results, then we can see that the stocks we should buy out of these four stocks are Apple and NVIDIA.
This will give a return of roughly 18%, with a risk of 30%. This is better than what you would have gotten if you would have just randomly selected these stocks. This is a great example of how you can use a quantum computer for portfolio optimization. We can see what's happening to the QPU job. We see that it's still running, but secretly I ran this job also before. Here you can see if we have a job with many stocks. It also gives an advice of which stocks you should buy, and it gives you a distribution for your portfolio, which optimizes for either profit or minimized risk. This shows you how a finance problem is turned into a QUBO formulation, which is then executed on a QPU.
This is already very interesting for finance, but the good thing is that this QUBO formulation is not only used in finance, but is a very generic way to define optimization problems. It's used in telecommunications, in oil and gas, in logistics. Anywhere where you have discrete optimization problems, this QUBO formulation can be used. The second use case we will discuss today is material simulation. Material simulation is a method to discover the properties of a material without doing measurements in an actual physical lab. This is interesting because this way you can learn the properties of a material which you would like to use for new electronics or for other applications without actually having to measure them in the lab or without even having the material at all. It may not even exist yet.
Material simulation is already actively done on classical computers, but it is computationally very expensive, so it needs a lot of compute power to be able to do this. What makes it difficult is that the electrons in the material behave according to the laws of quantum mechanics, and this is difficult to simulate classically. However, our quantum computer already has these quantum mechanical laws built-in inherently, and it is therefore a natural fit to do these simulations on a quantum computer. This year, we have shown that we did the first simulations of a real material, which were later confirmed in laboratory experiments. The material we investigated is called TmMgGaO4, and what we were interested in is the magnetic properties of this material. So how strongly magnetic is this material, and what happens if you apply an external magnetic field to this material? What happens then to the magnetization?
Material internally consists of atoms, and these atoms are arranged in a lattice. On the left here, you see the lattice structure of TmMgGaO4. You see that these atoms are arranged in a hexagonal pattern. When we do quantum simulation on a neutral atom QPU, we position the atoms in our QPU in such a way that the behavior of the electrons around the atoms in the QPU simulates the behavior of the electrons in the material. Then if we do measurements on the atoms in our QPU, we can predict properties of the real material. In this case, we are interested in the magnetic properties of this material. We will look at the excitations of the atoms in our QPU, which will give us information about the magnetization of the real material.
The tool we use for this is Pulser Studio, and in this tool we can position atoms in our QPU as we want. We can increase the number of atoms, we can change the configuration of the lattice from square to triangular. Also here we can play with the number of atoms, we can change the distances, and then we say that we want to create this pattern in our QPU. We can even manually still move atoms to a different place if we want that. Now we have the atoms in our QPU, which represent the real-world material. Now, we were interested in the magnetic properties of our real-world material. However, in our QPU we will not apply a real magnetic field, but instead we will apply a laser pulse, and this laser pulse acts as our magnetic field.
It is a fake magnetic field, but the atoms will behave the same way under this laser pulse as the real material would behave under a magnetic field. We can change the shape of this pulse, so we can make it a ramp. What we do in this experiment is that we see what happens if we increase the magnetic field of a material over time. In reality, we are increasing the laser amplitude over time. We can emulate this, and the emulation is running. What it will show here is the magnetization of each of the atoms. All of the atoms are in the zero state at the beginning of the experiment. Then we run the experiment, and then you will see that the magnetization changes, and at the end of the experiment, there is various states the material could be in.
So there could be, in this state, there are several atoms excited as you see on the left. And in this state, there is a pair of other atoms excited as you can see on the left. From these results, we can calculate what the magnetization of the original material would be under this magnetic field. We do this repeatedly for various magnetic fields, and then we can really analyze the complex behavior of this material in a magnetic field. We did that, and you see the results here. You can see the result here is if we suddenly turn the magnetic field off, how the material behaves, and you can see all kinds of oscillations in the material. The great thing is that this simulation only took one day, while if you would run it on a classical QPU, this simulation would take weeks.
We ran this simulation on several of our deployed QPUs, one in Canada, three in France, one in Germany, and they all show the same results.
We will take a Q&A session now. Let me just open up the floor for any questions for Loïc and myself based on what we have shared. Yeah. Okay.
Thanks. Thanks for letting me be first.
Sure.
Gary Mobley with StoneX. You mentioned a number of partnerships and your full stack and the idea of heterogeneous compute. I think you had NVIDIA's logo up there. Maybe you can expand as to where you think the puck is going next from hardware perspective for partnerships and related. IBM is listed as a partner, but how do you manage that coopetition relationship?
You want to start with the-
I can take the first part on the technical side. As we said, we really believe that you want to have an entire compute workflow that uses CPUs, GPUs, and QPUs in the best way possible, so that you get the best result in the end. What we do want to do as an industry and as an ecosystem is to have a unified way of doing that. That is why I think most of the actors, the big actors in the field want to work together on that. We can think of the QRMI representation, the QSLAM plugin that we developed with IBM.
This is a joint open source effort that has been done by people from Pasqal, people from IBM, from NVIDIA, from people in the academia, because we do believe that there is actually an added benefit for everyone to simplify the life of the user. It will benefit everyone to be able to do that. At the technical level, it is really on how we think things going.
In general, in this field, we feel that the most important thing to focus on is the customer. If you deliver value to the customer, then you build a business. What we find in the field is that all the leading companies are quite aware of this, and we have a very healthy, cooperative way of working together. There are many more points of intersection for us to cooperate than not, and that is the spirit we bring to this field. That's why we are able to work with all the leading companies.
I noticed on your chart for 2040, optimization was the largest opportunity, and I was just wondering if you plan on still delivering analog computers in 2040 or if you're going to be only focusing on fault-tolerant computers.
That's a good point. It's a good point. It's very hard to predict the state of the field in 2040. Pasqal is only seven years old. You're asking for a rather bold prediction here. But our current understanding is that those machines are very good for doing specific things. Like you have several kinds of classical processors as well, CPUs, GPUs, TPUs, you name it. You might have several forms of quantum computers also coexisting, several modalities, but also within the same modalities, several types. In digital FTQC, analog, solving each particular problem most efficiently. Yeah, that's our current understanding of the value that analog has and will continue to have in the future alongside FTQC.
Okay. 2040, I don't know if I'm going to be still around. John McPeake from Rosenblatt Securities. You used stocks in the demo on the optimizer for the number, and what I'm curious about is how many variables can be handled by the system, and is there a roadmap to add more on the analog compute side?
That's a very good question. Depending on the optimization problem at hand, the mapping that you have is not the same. It really depends on the problem itself, the overhead that you have. For the simplest optimization problem, you can have one qubit per one variable. But typically, when you have some constraints, additional things, the number of qubits necessary are larger than that. But all in all, what we find is that by increasing the number of physical qubits, you will be able to embed more complex instances as time goes by. That's really our roadmap, to try to be able to have many more physical qubits and as well, local control so that you can more easily accommodate for the constraints in the optimization problems, and you can solve it in a more native manner on hardware. That's really the target.
If I can just add to just that is the nature of how we work with our partners because we work very closely with them. As Loïc said, it is very problem specific. We keep on pushing to a point where we deliver value for them today. That is somehow a proprietary nature of the specifics of the problem that we are solving as well for our customers.
I do have a follow-up on the gate-based side. Some of the people in the room, I think, listened to QuEra's presentation a couple weeks ago, a week ago. They were talking about 1,000 logicals at nine nines, and they're using a similar approach. I'd love to hear, or just contrast, compare your approach in neutral atom to theirs. That's it. Thanks.
Sure. We've known the QuEra people for a while now. Of course, we are longtime friends in the academia. I think we have built this field also together, so it's very nice to see their progress and what they've done, and also what they plan on doing. First, let me tell you that. A few differentiators between Pasqal and QuEra, though. We are really building products that we are shipping and that we are operating with all those machines that are operating out there. We are not a research lab. That is quite clear. We don't want to be doing the job of a research lab. I think when you compare the technology, both companies are working with rubidium atoms. Relative, with quite a few commonalities between the hardware things.
All the things that you can do with the hardware from QuEra, you would be able to do that from hardware from Pasqal as well. We are working very deep right now and accelerating on FTQC as the commercialization phase of FTQC becomes closer. That was really our target, to decide on when to actually work very strongly on FTQC, depending on the advance of the field. Right now, we are accelerating, so our current roadmap is 200 logical qubits with 10 to the - 6 error rates by 2029. We will make significant efforts to map, to reach that results or actually be earlier than that.
I think, again, going back to from our very first slide, we do not focus on one-off results. Whatever we commit to, whatever we have delivered, is what we can deliver consistently as a compute platform. That is what we focus on. That is a big difference.
Hey, this is Troy from Cantor Fitzgerald. A couple of questions following up on John, too, on optimization. I guess from my perspective, I guess I know of two, right? There are differential equations, are there optimization equations? I thought you guys talked about both during your presentations. Can you just help me out with what are you guys best equipped to? I would assume it was more optimization. Are there others outside of those two?
Let me give you a high level. Again, we have to break out of the. We are not quantum annealing, right? Quantum annealing is small subset of analog. We can do optimization and material simulation and many other problems. That is why we can talk about all of those. With that, I will just hand it off to you if you want to talk more about this.
Sure. Using our analog approaches, solving QUBO optimization, discrete optimization problems, is something that we can do relatively broadly right now as of today. The showcase that I displayed here with solving differential equations is not done with the same kind of algorithm. It is done with a quantum kernel, so kind of machine learning-like algorithm under the hood. It is not a discrete optimization problem that we are solving. Typically, the things that we are solving right now, they fall into three main categories. First is quantum simulation. So when you simulate a quantum mechanical behavior, materials chemistry. Second is discrete optimization. And third is machine learning related, in particular when the data is structured under the form of graphs. So you have those three algorithmic primitives that are implementable on our analog hardware right now.
All the algorithms, all the use cases that you can see, they all fall within these three categories. And that is on what we are working on.
Okay. Thank you. Also, if you just look at the logical, physical to logical ratio, it looks like you guys are at about 500- 1 right now, right? 1,000 physical and 2 logical. Can you just talk about can you guys get that number, that ratio better for you? What is the ultimate goal that you guys think you can reach?
Sure, of course. The 1,000 physical qubits has been demonstrated on one particular quantum processing unit on which we have not implemented error detection or error correction procedures. If we would have done so, we would have a 2: 1 ratio, so 500 logical qubits. But it would not make sense. We would not be able to do anything with that because the number of logical qubits, as I said, is not the only thing that matters. The thing that matters is that you combine those number of logical qubits with fidelities and operations like magic state distillation and so on, everything, all the machinery that has to come. So we could have made a demonstration that would not have been very useful of 500 relatively low-quality logical qubits, but that is not what we decided to do.
On the other side, we used a smaller scale processor with better fidelity operations to actually demonstrate these two logical qubits and outperform on our benchmark, which was solving differential equation, logical compared to physical. To your question, I think there are many moving pieces. You always need to have number of logical qubits with the fidelity, this is really key, as well as what is the code, what are the things that you are using for that. Right now, what we are targeting is a ratio of 1: 100 on our roadmap in terms of overhead. There might be some improvements there. There is a lot of work going on, including from ourselves, but our target for the moment is 1- 100 in the relatively short term.
Just the last one for me. How important is error correction when you guys get to six nines reliability?
Yeah. Well, the six nines is when you're measuring logical fidelity. So it's at the logical level, the six nines, right? What you have to understand with the quantum error correction is that there is a threshold effect, right? What does it mean? It means that there is a fidelity that depends on the code that you're using. If you are below this fidelity, correcting error will not help you. The overhead that you have to pay is too large. It's not worth it. You should rather do it with compute with physical qubits, right? If you are on the other side, then the benefits start to kick in, and it's exponential the way you gain from error correction, if you are further and further away from that threshold. That's really the idea.
This 10 to the - 6 error rates is when we'll be able to reach levels of physical fidelities that are on the good side of the threshold to be able to lower the fidelity to 10 to the - 6 error rates. Why is that number of 200 logical qubits, 10 to the - 6 error rates interesting? Because it's what we call the MegaQuOp regime, where you can pile up a million or few million operations at the logical level. With that, we believe that we'll be able to have the first real meaningful quantum advantage applications of logical qubits. It's at that moment. I guess there is a relative consensus in the field about that at the moment. Of course, there are advances in algorithms, in hardware development, so we'll see in the future.
Hey, guys. Jesse Sobelson with BTIG. What is the current two-qubit gate fidelity on your machine today? Then what is the threshold that is needed for the Vela and Centaurus code to break even?
Right. 99.4% peak fidelity on our machine. It is currently under review. It is an archive paper, but you have measurements that you can find in the supplementary material of the paper about this 99.4% 2-qubit gate fidelity. I am talking about the most difficult one. The single qubit gates are better than that. Typically, what we want to be able to do is 10,000 physical qubits, 99.9% 2-qubit gate fidelities, to be able to be below threshold and reach this level that I was talking about, the MegaQuOp regime.
Thanks. Then, just back on the analog piece of things, can you give me an example of what near-term analog simulation problems we might be able to solve that would be commercially useful? Then how far analog simulation is expected to scale before we need to start incorporating error detection or correction, or if we even need to get to a point where we are solving molecules as complex as, say, FeMoco?
Right. I think FeMoco now is maybe not the right benchmark because of the classical advances that occurred a few weeks back. But leaving aside that problem, in material simulation, I would say that right now is actually already good enough to use our machines as a scientific and industrial quantum material discovery engine alongside CPUs and GPUs. Several hundreds of physical qubits is enough to be able to have something that is quite interesting and can be used commercially. We will expand. Materials, so that is the broad area, and we have demonstrated magnetism, like 2D magnetism. That is the baseline, and we want to expand, continue working on that particular field, and we believe that with Vela and the next generations of machine, we will be able to expand the span of problems that we can tackle using analog machines. This is on material science.
Of course, you can add error mitigation strategies, error detection, combination of analog and digital without needing to have full FTQCs, and that is clearly on our roadmap. That is what I meant when I answered the previous question that actually we believe that analog will continue to coexist, and we are investing a lot on that because of those particular tools that make it richer in the kinds of problem that we can solve.
Hey. David Williams from Needham. Just wanted to see if you could talk maybe a little bit more about your modular architecture. You talked about being upgradable and giving both platforms of analog and the digital.
Yes.
Maybe just talk a little bit about that modular platform, what it looks like, and how do you see that progressing over time?
Yeah. That is a very good question. So typically, what we have is that we have a modularity at the physical level as well as at the functional level. Here is the displays that we have the functional level, where you have some functions that can be addressed by given modules, and you can add those functions to the quantum processing unit. In real life, it is more at the physical level that you have the modularity, meaning that being able to have modules that have a set of interfaces that are well-defined between and one another, so that you can decouple the R&D timelines as well as the upgrade path for all of them. So that is typically the idea that we have started to develop and that we are continuing to invest on.
That is really something and, we believe it has both value from ourselves at the R&D level and also for our customers.
There is a question back there.
Hi. Suji Desilva, ROTH. To follow up on Dave's question, is that capability to have these modules distinct like that, is that relatively unique to Pasqal, or is that something other quantum companies can implement? If you could help us understand maybe what you did differently there that is an advantage for you guys, that would be helpful.
Right. Well, I do not know all the roadmaps and all the plans of the systems of all our competitors. But what I can say is that, of course, we have actually worked a lot on that problem to actually make sure that we can make it a reality. And that is something that might be also doable relatively easily with the neutral atoms, where you have this particular architecture, where you do not have a chip that is engraved, and if it does not answer to your specific ask, you have to build a new one. For us, we build the register depending on the computation that you want to do. So, for example, when I take the example of the demonstration that was done on logical qubits, solving differential equations.
For that, we needed several zones, like an entangling zone, a zone that was storage. The register was split in several kinds of zones, right? For that, it is a specific requirement for digital FTQC-related development. We were able to do that because actually the architecture is not fixed, the qubit layout is not fixed. You are able to do that to upgrade or to change your machine because there is a lot of versatility. We did that on the exact same hardware platform on which we did implement a QUBO optimization problem for which you do not need those zones. You do not need actually all the same sets of lasers. That is one key thing with the technology itself that enables us to do that.
Oh, hey, guys. Thanks for taking my question. Ryan Choi from Bank of America. You guys laid out a roadmap three years ago, hit every goal on time, or if not earlier, very impressive. When you think about 2029 and delivering your fault-tolerant computer, how should we think about that timeline potentially getting compressed, whether it be with using AI in your research process for it and whatnot? Broadly speaking, industry-wise, is that also something that your team is potentially anticipating? I have a follow-up.
That is a very good question. I have been working in this particular field for quite some time now, and I have been impressed actually by the pace of development of the entire industry, towards FTQC. Which is really, really fascinating to see, both on the academia and also in the industries, with many players that are really delivering great results every day. That being said, I think our estimates are being challenged in the good way now. There might be some way to actually accelerate. We are working on that on our roadmap, to try and see if we can do that.
That is very helpful.
And just on that, because there's overall development in the field, we benefit from that as well. So if everybody's accelerating, then we benefit from that as well.
Got it. And I guess on the flip side, when you think about risks and challenges that also lie in your path and that timeline of 2029 being elongated, what are the key risks for your team at Pasqal and what It'd be helpful to hear specific challenges that you've identified and have a plan to mitigate and address.
What kind of challenges are you referring?
Technical challenges.
Sorry?
Technical challenges.
Technical challenges.
I could name many technical challenges, of course. For us, I would say, one thing that has been top of mind for us, and I guess for most neutral atom providers out there, is the fact that this technology could be seen as slow compared to some other technologies. Why? Because you need to count photons when you measure the qubits, right? You have a camera, and you just count the number of photons that you collect, and it tells you if it is a zero or if it is a one. This is a slow process. That is actually what makes quantum computing, as of today, relatively slow with neutral atoms compared to some other competitors.
This has been top of mind for many people in the field, and there are ways to actually accelerate that, because when you think about it, the thing that actually matters is the gate speed or the time it takes to actually compute. This is really the final bottleneck as to what speed I can reach. When you think about the time it takes for a two-qubit gate on neutral atoms, it is actually quite competitive compared to some other changes. The fact that we were slow is related to the fact that measurement itself was taking the entire time budget available. Actually, measurement speed, clock rate, is one thing that was one of the main challenges. Still is. There are good results from Pasqal, from other teams actually working on that. This is one important thing to actually overcome.
I'm confident that we'll see results in the next years. Related to that is, being able to actually do quantum error correction in a fast way because you need to acquire results on cameras and feedback on the system very rapidly. This is kind of related issue.
It's more of an engineering.
It is.
Versus a basic scientific challenge.
On the scientific side,
There's no.
We don't see any roadblock. There are obstacles at the engineering perspective, of course. It's not an easy thing, but we're getting there.
Yeah. Hey, guys. Kevin Garrigan from Jefferies. You talked about being a full stack company, and we've heard a few other quantum computing companies use that phrase. Just looking at the software side of things, can you just talk a little bit more about how you differentiate there? I mean, is your plan to put a ton of R&D dollars towards developing software and be the best at a certain application?
You could talk about the low level, then I can talk about the high level.
Yeah.
Yeah.
We do have our own operating system, of course, for embedded software and so on, which is something that is proprietary that we built to assemble and to orchestrate all the magnificent equipment that we have on the hardware level. Then on top of that, you have software layers and middleware to talk to that hardware. On that, we have a specific modality in the way that there is this analog control that is not widespread, so we had to develop on our own the way to communicate with our hardware. This is a Python library, which is called Pulser. Open source. Many people are working on it, researchers from all around the globe. We are the primary developers of that, but it is open source. This is like the gateway to our hardware. Relatively low-level pulse level control, but not calibration dependent.
On top of that, we've built libraries that abstract away the complexity of the hardware layer by layer. You have Pulser, which is the API. You have algorithmic primitives, optimization, material, machine learning. On top of that, we are building application layer so that people who are using our hardware don't have to care about the hardware itself, the way to program it, but can input the domain problem-specific data. That's the target that we are developing right now in collaboration with our partners. Large part of our stack above Pulser is open source.
Nehal Chokshi, Northland Capital Markets. Look, you mentioned that there's a certain threshold at which you start to see benefits of error correction in terms of the physical 2-qubit gate fidelity. What is that threshold? Let's use 10 to the -6 logical error rate as the target for that.
Yeah. That's a very interesting question, but I'm afraid there is no definite answer to that question because it depends on the code that you're using. A threshold is attached to a code. The surface code, which is the most well-known code, typically the threshold is like if you reach fidelities that are above 99% fidelities for two-qubit for all operations, so including two-qubit gates. Surface code is like that. Okay? There are other types of codes for which the threshold is not the same. The field, what we are trying to do is to develop the codes that are interesting and good from this threshold perspective, right? So that it's relatively easy to be above this threshold, but at the same time can be implemented on hardware and the hardware architecture that we have. Right?
It's the co-design approach between the code and the hardware to try to find the best match so that we can have operations that are above this threshold. Right? On our roadmap, there is no specific code that is attached to this result. We are still working on finding the best match between the hardware architecture itself and the code that we'll use. There are many candidates for that, and it's still open.
As you explore these different codes, though, would you expect that threshold to be even lower or higher than the 99% on the surface code that you talked about just now?
Oh, we'll see. We'll see.
We'll see?
Yeah.
Okay. At the 99.4% fidelity that you're at with the 2-qubit gate fidelity, do you see a need to further improve that at this point in time?
Yes. Our target, as I said earlier, is to have this 10 to the -6 error rate that we can achieve with 10,000 physical qubits, 99.9% 2-qubit gate.
That 10 to the -6 is on a logical-
Yes
error rate basis, on a physical error rate basis.
99.9%
Got it.
3 nines.
Okay, thanks.
I think we are going to take one last question for this section, then Wasiq and Stéphane are going to do another section afterwards, but we are going to do a quick break after this question here. Okay?
Thanks. Julian Frost with Wedbush Securities. So earlier we were comparing modalities a bit. You talked about how currently with fidelities, trapped ion is best, then superconducting-
Yeah
then neutral atom, but you are closing the gap. You believe that neutral's on track to pass them both versus fidelity. So I am wondering if you could just expand on what do you think the key difference-maker or milestone is that will cause that leapfrog? If you believe trapped ion and superconducting won't have an answer to it, or just kind of what's going to cause that jump-
Yeah
if there's something specific you can point to. If this is for your existing analog architecture or the fundamentally new, more error-corrected-
Yeah
architecture on the roadmap. Thank you.
Yeah. That's a good question. So actually, I think going back in time, I can explain the fact that we had relatively lower fidelities compared to trapped ions, which is easier to compare with because it's. Above the.
Yeah, atomic species, laser kind of control and so on. No manufacturing defect. I would say there are two factors. First one is understanding the system itself, like error model. Understanding where the error was coming from, actually. That was something that was not so clear in the community 10 years ago to understand was it laser phase noise? Was it intensity? What was the thing that was causing this error to be relatively high compared to our competitors? That was 10 years ago. The second thing is that maybe in terms of the maturity of our equipment to drive those qubits, including lasers, was not as high because it was a more recent field, so the supply chain was also less robust, and there were things to discover. Going forward, I think now we understand completely our system.
I have not talked about that, but we have an extremely good understanding at Pasqal, as a field of the major error sources that are there. The rest will come from enhancing our laser systems, optical systems to be able to have homogeneous fields, strong intensity, low phase noise. All of this, I do not see any obstacle to 99.9%, as I said earlier.
Okay, that concludes this first Q&A session. Everyone, we have got a 15-minute short break, so maybe we will head back here around 10:15 A.M., 10:20 A.M.
Thank you.
Thank you. Okay. Thank you very much. I think we are reconvening. Just to recap what we have discussed so far, actually, we were having this informal discussion just prior to this session, and maybe I will just say it explicitly. There is a prevalent mental model that quantum computing can only be done in one way, which is FTQC. What we have communicated is that there are two completely different ways of doing quantum computing, which is full analog, which is a super set of quantum annealing and FTQC.
That is the first key point. Just like the brain is an analog system, it is not your computer, and it does not work. I mean, it does pretty well. There are completely different ways of doing computing. That is the first. The second is Pasqal, same hardware gives you best of both worlds. It is a really unique feature that we have.
We believe we are the company that has most properly explored the potential of neutral atoms by paying attention to both of these modalities of doing computing and by building well-engineered, commercially ready, commercially deployed systems. I just want to recap that part of it. That is how I want to start. This leads us to the next thing in terms of what we sell, how we sell, and why does it work for the customers. What we sell are three things. We sell our quantum computers, our QPUs, people buy it directly, or our systems are available through the cloud. Whenever I say we sell our QPUs, I mean it is the hardware and the software stack, the libraries that we talked about earlier. Same thing with cloud access. You get access to the underlying compute, to the entire software stack on top of it.
The third thing is built on top of the hardware, the software layer, we build solutions, and that is what we work on in conjunction with our end customers. Because remember, our focus is not to boil the ocean. It is to solve specific problems that are high-value problems today, which we can monetize today, and this gives us a ramp and a bridge to the future as well. How we sell this? Two ways. Mostly direct sales. When we sell our systems, we sell them directly to our end customers, who could be sovereign customers, large enterprises, and public sector customers. So they buy directly from us. Same thing applies to cloud. Cloud access is sold directly primarily to enterprises, and that is the lowest barrier of entry for them, easiest way for them to get in, and to ramp up their utilization.
We also have deep relationships with Microsoft and Google, where our compute, our quantum compute and the software stack is available through GCP and Azure. It is available today. We have OVHcloud, Scaleway, and multiple other venues also available in which you can get cloud access to our quantum compute. In fact, you can go to our website and sign up for your cloud account, and it will take you 15 minutes or less, and you will be playing with our quantum computers. We have literally taken all the mystery and the barrier out of this. What we showed in the previous example for the portfolio optimization, if we did not tell you that it was a quantum computer doing the compute in the back end, you would not know, you would actually not care, but you are just solving the problem.
That is the level of reduction of barrier of entry that we aim for, because in the end, it is all about the customer experience. Then once we have sold our systems, then we have to deploy at scale or integrate into various enterprises, or we have to integrate them into existing workflows. Then we utilize our partners like Capgemini, TCS, and so on, the traditional enterprise integrators. This is an example, pictures of some of our deployments, and as Loïc mentioned earlier, these are all our Orion class machines, all in different operating environments, all functioning, meeting the SLAs for our customers. We have extensive operating history here. One thing I would like to mention here is our ability of doing in-situ upgrades because we do not have to build chips. It means we can do in-situ upgrades in the number of qubits our machines have.
We just inject more atoms into the vacuum chamber, and voila, you have more qubits. That is, again, a unique capability that we have. I want to spend most of the time actually on this slide, which are the specifics of what we are working on. Remember, this is all on full analog quantum computing that is available today. On Saudi Aramco, which is a key reference customer for us in the area of oil and gas, there are some use cases that already are in public domain. There is a much longer list that we continue to work on. These use cases are around reservoir simulations, well placement optimization, rig scheduling optimization, and demurrage prediction. Demurrage is the amount of time a ship has to wait before it gets into port, and if you have a constant back and forth of ships.
You look at these four different problems, there is an optimization angle to it, but it is not a simple optimization, it is a very complex optimization angle. On the reservoir simulation, it is inherently a mathematical problem of finding underlying correlations in whatever data you have and reducing the error rates on that. All of this is possible and at the business value scale today using our analog quantum computing. That is what we work on. Our system is deployed in Dhahran, and we work hand in hand with specific teams in Aramco to build up applications and solutions in those areas and many other areas. That is the way we operate with all of our customers.
This again goes back to the concept of focus versus boiling the ocean, and we believe for us, this is the way to deliver value today to earn the customer trust today, build the ramp to the future. That is what we are doing at Aramco. A lot of this is on the upstream side. Upstream side, as you know, for all oil and gas companies, is a very critical part of the business. On financial services, there was a press release that came out earlier today with Crédit Agricole CIB. Let me read the headline of the press release in case you have not seen it. Crédit Agricole and Pasqal advance their strategic partnership to deploy quantum computing applied to finance.
This is based on the work we have done over the last three years, where we have shown value in credit default risk modeling, portfolio optimization, and what we are working on right now is on the capital reserve consumption, especially risk-weighted assets. This is something that we are progressing to the next stage to production deployment.
We believe this is a result of the hard work, the consistent methodical work we have done to identify where we can add value, again, based on the full analog quantum computing capability we have today, and now we are looking at how we start to integrate that into the workflows and scale it up. We believe this strategy for us of focused reference customer validation is an important strategy for us as a business, and we believe this also brings benefit to the quantum industry itself to be able to show real-world use cases.
We talked quite a bit about the high-value materials in terms of magnetic materials. Whatever we have shown over there is extensible to similar class of materials and other class of materials. It's a very powerful native capability we have, and we'll be talking more about that in the near future as well. I want to show you this slide. This goes back to our mindset of not just doing R&D, but delivering actual useful systems. The bars here show the number of quantum computers delivered or in production, and this is for various companies. At the bottom, you see the amount of funding that has been publicly disclosed, that has been raised by multiple players in the field. Within pure-play quantum computing companies, we are a leader in terms of the number of quantum computers either operating, deployed, or in production that are going out there.
In terms of the capital raised, this number is actually an overestimate of the amount of funds it took us to actually deliver that number of 10. We did it with less than half of that amount. The heart of that is it shows the incredible, I would say the distinguishing capital efficiency of our business. We believe that's a differentiator for us. We have two manufacturing facilities, one in France, one in Canada to serve the Americas. They're up and running with appropriate staffing levels without any extension. These facilities can produce up to 13 machines per year. If you need to add extra line, it's very capital efficient for us. We can add extra line, we can increase our capacity.
Commercially, if you look at it, the ingredients for us to build and scale this business based on the commercial traction we have, we have already put those foundations in place. Let me summarize, and then I'm going to hand it over to Stéphane. If you look at it from a business point of view, let's look at this series of steps. The foundation of that is to make sure you have commercial grade, enterprise grade, ready QPUs, and the associated manufacturing capability. Remember, we don't do lab equipment. Whatever we talk about is commercial grade, which can be deployed and operates autonomously. On top of it is the focus on specific high-value use cases, again, with the sector focus and delivering value and building that track record.
On top of that is our now our increased commercial presence across various geographies, and that is something that we'll be leaning much more into. On top of that, we have already established our cloud computing as a service as a very important access point for all enterprises. These are the four basic elements that form the foundation of our business, and this is also what we currently look at in terms of our business model and business plan. But with this new addition of our proof point on quantum advantage, which opens up the entire material sector, there is more drivers to our business growth that get activated.
And one very interesting one that I want to mention in passing is because of our capability to do this kind of accurate quantum level material simulation, we can use our computers to generate quantum data, which then, coupled with specialized AI models, is a further accelerator to our business and enables new ways of doing material simulation and other related areas. The heart of this, again, you cannot get to this point if you only have lab systems that do not perform reliably, repeatedly, and you must have enough of an operating fleet of systems so you can actually build a business out of this. And that is, at the heart of it, a core differentiator that we believe puts Pasqal aside from many other quantum companies. So with that, I am going to hand it over to Stéphane to talk about some more details about our business.
Thank you. Can you hear me? Yes, perfect. So, you understand we are not a lab shop. We are not an R&D lab. This is a real company. We have first-class clients, and you saw that. We are delivering real products, and we are generating actual revenue. So not just grants and subsidies, but actual commercial revenues. If you look on this graph on the left side, you can see that the overall revenues almost double year-on-year between 2024 and 2025 to reach EUR 24 million. Actually, and more importantly, the commercial revenues, they now account for more than 60% of the revenues of the company, and they have been multiplied by five compared to 2024. And so this is something that is really important.
And when you look at our bookings, where we have, as of the end of March, more than EUR 66 million of orders, we are really talking here about essentially commercial bookings. What is important is that these are revenues coming from multiple clients. It is not based on a single customer. And also these are revenues attached only to quantum computers. There is nothing else. This is what we focus on, as you understood from the presentation from Wasiq and from Loïc. Now we are about to accelerate. We have the hardware. We have the technology. We have everything in the engineering in order to deploy. We have the manufacturing capabilities, as you understood from the previous page, and we are now investing in terms of commercial deployment. And we have amassed a pretty significant amount of money in order to fund for this acceleration.
On the right side, you can see that as of today, we have $140 million of cash in our bank accounts. On top of that, we have secured a $250 million convertible note a couple of months ago. And then as part of this transaction, we have the money in the trust account, and so we could end up with at least $400 million and up to north of $600 million of cash in order to fund that acceleration. I will speak in a minute about the use of proceeds. If you go to the next page. Yeah, it works. These resources that we have now, these financial resources on top of the technology, the people, all the capabilities that we have, they are ample enough in order to fund our development, because you understood we have a very capital efficient model.
It is very capital efficient when you think in terms of OpEx, it is very capital efficient when you think in terms of CapEx. You can see here the numbers when you look at 2024 and 2025, anywhere between EUR 50 million- EUR 70 million of OpEx spent, which covers for both the cost of goods sold, of what we have produced, but also the R&D and all the staff that we have for research and development and also engineering. Some cost also for commercial, but that will, of course, increase in the coming years. Finally, G&A. These are all the OpEx that we are incurring. From a CapEx standpoint, you can see that it is quite limited. We are talking about EUR 20 million per year, and that caters for the spend in order to put in place all the manufacturing equipment, both in Canada and in France.
You can see that that would allow to produce 13 quantum computers per year. That has been largely done in 2024 and to some extent in 2025. Finally, when you look at the cash burn of the company, anywhere between EUR 30 million -EUR 50 million of cash burn per year. Of course, as we will scale, as we will accelerate, that number will probably increase a little bit, but we are not talking about spending a lot of money, and also we will start generating revenues, so we do not expect a very significant increase in our cash burn. What is sure is that we have ample resources with everything that we have in our bank accounts and that the transaction will provide us in order to fund the expansion of the company.
When you look at the transaction, what you have on the left here is the valuation of the company that has been agreed as part of the transaction. We are talking about a EUR 2 billion valuation. Of course, when you look at the competition and the players that are listed in the space, generally have a pretty healthy valuation. That means this is a pretty attractive entry point when you think about the valuation for anyone who would like to participate and be exposed to the quantum space. We are really happy to provide that, especially as we see a pretty drastic growth in our business in the coming years with the commercial scale and the footprint that we have today.
Also when you have in mind the balance sheet that we have, especially the cash on hand, which gives us security and solidity, which is important for the company, especially from a business standpoint, because of course, when you have clients like Aramco or Crédit Agricole, these type of enterprise clients, they want to make sure the company is going to be around in the coming years. The resources that we have on hand that you can see here allow us to make them comfortable about that, in addition to, of course, funding our development. Transaction overview. On that one, I will go relatively quickly. You essentially got already most of those numbers. On the top left, you can see the cash on hand that we have today and the cash that we expect from the transaction that will end up potentially north to EUR 600 million.
So again, something that puts us on the right foot in order to fund the rapid expansion that we expect for the business and for the company as a whole. Then the valuation elements. Finally, use of proceeds. Of course, we are going to continue to invest in core R&D, especially the strengthening of the analog technology that we have, but also the quick ramp-up of the FTQC technology and hardware and everything related that we have. That covers for R&D. That covers also for engineering and everything that allows to have equipment, including software and middleware and applications that are relevant for the business needs of our clients today and of course, tomorrow. We will invest also very much into our commercial expansion. So we will do that in a disciplined way.
We will invest in terms of geographies where we know the clients and the industries have business needs, and where the quantum solution can bring them solutions that are fitted to resolve their needs. So we will do that from a geo standpoint, then you understood also from an industry standpoint, we have been extremely focused on four industries, and we will continue to do that for the coming years. As we expand more and we get closer to full FTQC, by talking to our clients today, next year, and in the coming years, we will have exposure to many other problems and issues that they have, and therefore will be very well placed to design, especially using FTQC, what are the quantum solution that can help these people resolve their future issues that sometimes they do not even know today.
Finally, we will also continue to invest in what we call the deployment of the technology. So we are talking here about the engineering, we are talking about the manufacturing. We are talking about bringing down the unit economics of quantum compute, and quantum compute that is being sold to clients, either through hardware, through equipment, or through cloud-based usage. So this is something that we want to continue to spend money on. So this is what the proceeds will be used for when you think of 2026, 2027, 2028. Again, we have plenty of runway in order to fund the development of the company. So yeah, maybe a couple of words on this last page, which is the combination with the SPAC. So Bleichroeder is a great partner. They bring us a lot of benefits and network and capabilities that we need.
It is the right fit with Pasqal, and we think that is going to position us extremely well for, of course, business success, but also stock success, which we all expect. So thank you for your attention, and we are ready now for Q&A. Can always go back to some technology questions, but we are going to try to be more on the commercial and financial side. Thank you. Should we go three of us, four?
Three is all right. Any further questions?
Sure. This is Kingsley Crane over at Canaccord. I noticed on the production capacity slide that there's some variance between the on-prem, the cloud, and the R&D systems. I'm just kind of curious what may cause that variance, and to the extent that that's impacted by the modular architecture, I'm curious, does it create more engineering effort to implement the system, to upgrade the system? Is that all monetizable? And just color on initial ASPs, upgrade ASPs, and just thoughts on that kind of upgrade cadence. Thank you.
Okay. Do you want to talk about just the difference between different kinds of manufacturing and talk about the upgrades and stuff?
Yeah. Sure. Maybe we can find back this slide, and it will come back up. The idea is that we do have several manufacturing sites. And they have all their own throughput possible. Right? Now what we have shown here on this slide, maybe it's a bit earlier.
Yeah, this one, right? It is about the expected production capacity based on QPU type. You can see that there is an on-prem line, cloud, and R&D. R&D is for our own internal usage to be able to have our R&D team as a client of the manufacturing body, so that we can take those machines and continue to tune them up and boost their capabilities. On-prem is when we deliver a machine on site, and the cloud is when there is usage from the cloud, but the machine is ours and stay in our premises or data center. This is the split that we envisage.
As you can see, a key point here is that we do believe that cloud will take more and more of the actual percentage of machines, and we will see a market shifting towards cloud from on-prem at a commercial level before the end of the decade. That is our expected movement of the market. Of course, we can always decide to invest more in R&D and reserve some of those machines for ourselves if we want to accelerate more on the R&D side and be opportunistic about client deliveries as well. That is why there is some error bars on those numbers, if you wish.
This is basically summarizing our view in terms of how we want to engage effectively with the enterprise customers. Cloud access is the most effective way to do that. That is why we put the split this way. But it is exactly the same machines that are being built. There is nothing different in the machines themselves.
All right, guys. If we all went and used your financial optimization tool, would you guarantee our returns?
Well, clearly-
What's your conviction?
Well, clearly, risk and reward are not the only two parameters, right? In the example that we showed you, it only takes those two parameters in terms of-
I was just teasing anyway, but I just want to follow up on ASPs-
Yes
per quantum computer, and then your thoughts on how Quantinuum's pricing there is trying to capture X percent of the economic value they're creating.
Look, we have not-
What you guys can do?
We have not talked about our pricing at this point, so we have not shared that, so I will not be able to comment on that. Similarly, I do not want to comment about somebody else's value or how they price. But in general, what you have heard from us today is a couple of things. Number one, we have clarity and certainty in terms of what we provide, both in terms of the investment part of the ROI and also the return part of the ROI. So the opportunity is obviously there for us to monetize that. Let me just leave it at that. The most important point is to demonstrate that ROI, and that is what we have been focused on.
Great, thanks. Brian Kinstlinger at Alliance Global Partners. As it relates to the EUR 66 million of backlog, is that all on-prem? How many QPUs does that represent? Now that you have seven successful installations, what is the average sales cycle look like for that EUR 66 million of backlog?
Do you want to talk about a little bit of the breakdown, then I can talk about it?
Yeah. The backlog is a mix between some on-prem machines and, of course, in terms of revenue recognition, revenues will come when those machines are commissioned, so it takes a little bit of time because generally, and it is not exactly the sales cycle, but the procurement and commissioning cycle for an on-prem machine is over 12 months. We are talking between 12-18 months. Of course, as we work on the engineering, our ambition is to bring that down, not just in terms of revenue recognition, but for our clients. We also have a pretty significant number of bookings that is cloud-based. That is what we have right now in the order books. The sales cycle, obviously, much quicker when it is cloud-based.
What matters with clients is make sure that we can spend time with them about their use case, about their issues, and that we can see how that can be solved and addressed best with quantum solution that exists today, what we call the analog one. That always takes a little bit of time, and as you do it in a given industry, then it is quicker to do with other clients in that industry. What we have done already in the oil and gas industry and what we are doing right now in the financial services, they will help reduce the sales cycle. You are talking about, let us call it a few months when it comes to cloud-based. Of course, when it is a machine that is long, it is a longer time, it is a bigger commitment.
Thanks. I had another question about revenue scalability. For the on-prem sale, is that a one and done type sale, or is there a residual revenue element to it, like maintenance and support? For the cloud-based compute, how should we think about the linearity or logarithmic scale of the revenue per QPU? I am certain that a newer QPU is capable of generating more revenue, so maybe you can just talk about that.
Okay. Maybe I will take a crack. No.
Whenever you have a system sale, there is an O&M component to it, which typically has a lifetime. So there is a recurring component to that. There was a question earlier, which is if you have deployed a QPU, is there additional revenue possibility in upgrades? The answer is yes. So for the same asset, you have these two additional parts to that. On the cloud side, could you repeat your question again?
New generations. Are the new generations-
Yeah
of machine allowing higher revenues?
Higher revenue. The answer is yes. Obviously, as the compute capability becomes better or it becomes more potent and there's more of the application stack that's available as well, then we have that flexibility to be able to price it in a different way.
Can I just talk?
I think the microphone is coming your way. Microphone is behind you, right there.
Behind me. There you go.
Exactly.
Could you put the slide 33 online? I do not have a D-Wave System has annealers, right? IQM ships gate-based machines. You guys have 10 machines in production. Could you talk a little bit about the comparison
Seven operating.
Right.
Three in production.
Are those analog machines? Are they analog gate? Because it feels like this slide sort of is apples to-
Hundred-
oranges a little bit.
It indeed, there is a little bit of that. It is all 100 qubit plus, 100- 200 qubits.
Right.
All high complexity, commercially available machines.
I got it.
Right.
Those are 7 D-Wave annealers with over 100 equivalent.
Remember, annealers are not the same as annealing. As you said, it is an apples to oranges comparison.
Right.
The way we look at this is as pure quantum computers, which is a superset of an annealing machine. We would compare ourselves to companies that ship pure quantum computers. But of course, we are just counting the number of machines that are shipped.
I got you. I have the most boring question that will be asked today, I promise you.
Why do you look at me?
For SPACs. What is the fully diluted share count if you include all of the warrants, and options, and any dilutive instruments?
I think we have that on the cap table page.
It is in the Form F-4.
Yeah, let me check that.
I will take that question. It is Marcello from Bleichroeder. This slide that you see that is on the screen does not include the dilutive effect of the warrants and
Right
the other components. If you go to the Form F-4, all that is baked into that. The number right now as you see up there on the top right is 264, it is probably closer to 300.
300?
Yeah.
Okay. Thank you. It is just for comp tables and stuff like that.
Yeah. No, of course.
You help me with the math, appreciate that.
Reach out anytime, we can help you.
Thanks. This is Julian Frost with Wedbush Securities. I have a two-part question. When we think about pricing, given these are kind of early products and early projects, how do you approach these sales conversations with customers? Do you meet them where they are in terms of pricing, project scope, and budget, or do you have more of a set price for machines, cloud time solutions?
We have a set price schedule. Remember, our first commercial machine was deployed more than four years ago. We have had time to build that track record, and this is, again, a differentiator for us is we are not putting lab equipment out there, right? These commercial machines, based on an actual comparison between what the pricing landscape looks like and what value we deliver, we have a set price schedule, both on the cloud side and on the machine side.
Got it. That makes modeling easier for all of us.
Exactly.
I guess on that note, how do you view, I guess, the on-prem and cloud economics evolving over time? Like the pricing, the margin profile, at what point do you think there will be kind of, I guess, we might already be there, but mature levels of unit economics?
Right. You have a couple of points in there. I will just take a crack at that. As we discussed earlier, as we have later and later generational machines, then obviously we reserve the option to set the pricing both for the on-prem as well as through cloud access. In addition, because of the large fleet we have and the manufacturing capacity we have, we also have the additional lever of further optimizing our total cost per unit. So we can control the cost basis of that as we ramp up, as our learning curve continues to progress. On that side, we have this openness on that point of view. But we believe that we will maintain a competitive edge in terms of pricing and performance in the market. I think that is the key statement I want to make, and that derives from our approach itself.
This is a structural advantage that we have. We have seen some indications of that in terms of the financials, the OpEx, the CapEx, the free cash flow. So you have seen some indications of that, but a lot of this derives from the structural advantage of the approach itself, and that will continue to accrue.
Thanks. David Williams again from Needham. Wanted to ask maybe on the M&A front, as you kind of think about the opportunities to scale, are there areas of the business today that you could maybe accelerate the business? Is there any assets in the market you see, whether it is IP or even other companies, other technologies, maybe supply chain things that could help you?
At a high level, obviously, that's a toolkit that's available for us for inorganic growth and acceleration. At a high level, again, anything that is accretive to our technology roadmap, which is complementary and accretive, obviously, that's a target. We pride ourselves to be able to try to look around corners. We have done some acquisitions in the past, so we try to look around corners. Obviously, that will never go away for us. The second is on the commercial side because we have focus in terms of the problems we are solving for specific industries. That gives us another avenue in terms of accelerating that market entry, the customer acquisition, in a sense. So that's another thing because of our commercial maturity as well. Those are at a high level, two areas we can look at.
Then maybe lastly, just do you think your customers understand the real differentiation between the analog component that you bring as well as the digital? Do you think they understand the power of that and how it does differentiate you in the market?
In the end, they don't care. In the end, they just want their problem solved. In the end, I think a lot of the discussion around analog, FTQC, which modality versus not, it is a topic of today because of the general state of the industry. But in the end, the customers just want their problem solved, and that's what we are focused on. Just like today, we don't argue about the specifics of the GPU or the CPU construction, or which kind of memory is being used, and so on. We feel that's the way quantum industry will evolve. We stay focused on the customer and delivering value.
Hi, Tyler Anderson from Craig-Hallum. I have a boring question as well. Is the revenues and just financial statement, are those going to be in USD or EUR when you file?
Okay.
They are going to be in USD, right?
Yeah.
We do euros.
Okay
You will have euros financial statement. That is what you have right now in the F-4.
It will be euro-based financials, IFRS, PCAOB.
Yeah.
IFRS, okay. For
Remember, part of the transaction is they're going to remain FPI, foreign private issuer. They'll be French-based as part of that over the years, yeah.
For your 99.4%, is this post-selected fidelity?
We're talking about the fidelities of the physical qubit gates. There is some amount of post-processing indeed, in terms of our measurement errors in particular.
Okay.
You can see all of the details in the paper if you wish. We describe all the procedure there in great detail.
Yeah, I have to go back and look at that. Thank you. For your analog, I was wondering, you say that annealing is a subset, and annealing can do quantum tunneling within optimization problems. I am just wondering what other features your QPU enables users to have to give better advantage using analog.
Sure. Yeah. Well, when you think about annealing, the idea is really that you want to follow the path in the energy landscape, right, and follow the ground states all the way to where you want it to be at the end. So that's the assumption, and that's the idea behind quantum annealing. The thing with analog is that you can be out of. So this implies that you are always following the ground state, so you are going slowly, and there is only one path that you can follow. Using analog computing in general, you can be really abruptly out of equilibrium. There is nothing that prevents you from exploring the phase space, really with all the different paths that you can take. You have various knobs available to you on the hardware, and you can tune all of them arbitrarily if you wish in a continuous manner.
Really, it's about the way you program the machine. It's continuous compared to discrete gates. But the things that you can do is you can do annealing, adiabatic, you can do out-of-equilibrium quenches. You can do whatever you like. You're not constrained by one kind of computing. You just have a different way to control thermodynamics compared to gates.
Right, that makes sense. Thank you. I just have one more for your gate-based system. I just want to ask, you have qubit rearrangement and you have pulse shaping that is helping you with this material simulation and whatnot. How much of an advantage do you think that is? Is this less steps as compared to somebody with a planar architecture
Yeah
namely, like a superconducting?
Yeah.
I just want to talk about all the different ways that you can
Yeah
do that a little bit differently.
Yeah, that's a very good question. So actually, it boils down to describing the power of analog and register reconfigurability compared to fixed digital architectures. The register, you can tune it so that you have the geometry or the topology of your problem itself can be mapped down onto the hardware so that you don't have to pay the overhead of having swap gates or things like that to actually compile down your problem topology to the hardware that you have, which is fixed. This is something that is actually quite native on our platform. And then when you have analog and digital, if you were to actually simulate the dynamics of a spin Hamiltonian using digital gates, what you would have to do is to Trotterize your Hamiltonian to break it down into sequences of gates, and what you find is a huge overhead in the end.
If you wanted to do what we did, like simulation of out of equilibrium Ising model with gate-based, the overhead that you would pay in terms of swap gates plus totalization is huge. You would need something like a 10 to the - 5 error rates and 10,000 gates to be able to achieve the same level of performances. It's really a great change compared to. If you wanted to do what we did on the material science use case with digital, you would not be able to do that with the current hardware. You would need a lot of progress on the digital side.
Hey, Loïc, can I have one more?
Are you able to take logical qubits, let's say the data qubit within the logical qubit, and then place it in the arrangement of what the problem is, but then fix the placement of those and then perform nearest neighbors? Are you performing nearest neighbor gates at all within your architecture? Or is this always movement to perform those two?
Typically in the current architecture that we have for digital error-detecting code, when we perform gates, we just move the qubits close and shine a laser so that there is a gate between those two, and then we move them back in the original position. That is the way it is done. You have an entangling zone where you shine very strongly a laser in an homogeneous fashion, and when you have pairs of qubits that are very close by, they feel a CZ gate, so an entangling gate. That is the way it is done right now. There are ways to do also other kinds of gates if you want, without moving the atoms. This is something that is open to us. This you can do. Really what it comes down to the end is you have an algorithm that you want to implement.
How do you compile it down in terms of instructions on your hardware set? And this is an interesting problem, yeah.
Thank you.
Hi, yeah. David Bolocan. I was wondering if you can talk about your manufacturing and supply chain partnerships, how that will evolve as you guys start to ship more and better systems, and maybe especially regarding your most critical components, like the vacuum chambers and the laser tweezers and yeah, anything else.
You want to take it or should I?
Sure.
Maybe you can-
Okay
You want to take the first crack?
I'll take the first part. In terms of the key components, there's some key components, we actually acquired those. So we actually did the vertical integration on those, like the vacuum chambers and so on. On key systems like lasers, we have very close partnerships with those companies and these are multi-range, multi-year partnerships. So in fact, we are also driving the state of the art in a sense because of our leading-edge requirements. In terms of supplier dependency, because of the inherent design of the system outside the vertical integration, we have made sure we don't have a single supplier dependency, and when we have few supplier dependency, we have very deep relationships. Plus, we have forward inventory that we have for long lead items. So our supply chain from that point of view is lower risk and not single-source dependent.
That is part of the construction of the supply chain. To what Loïc had mentioned earlier, if you look at the overall system design, this goes back to our engineering focus for the last many years, there are some aspects to it that are truly key and proprietary that are either in-house or with key close partners, which we control. Other stuff is, effectively it is off the shelf as much as we can. That removes that part of the risk as well. Do you want to add something more to it? I think this is all, we are able to address this and this then enables us for scale up because we have control over the key points of that. We can ramp up our vacuum chamber. We have access to the laser systems, the optics, and so on and so forth, and everything else is rampable.
In fact, if we wanted, we can outsource a couple of these mechanical assemblies as we do to contract manufacturers and so on. There is no supplier risk from that point of view.
Hey, just an easy question. Can you help us out with timing of the transaction? When does the deal expected to close, when we find out the redemptions, and then the de-SPAC date, or roughly?
Correct. Marcello, do you want to take a?
Yes
crack at this, please?
Here you go. Thank you. In terms of where we are in the deal, on June 26, so last Thursday, we filed the Form F-4 publicly. That was our second public amendment. Sorry, it was our first public amendment. Ideally, we should get effectiveness in early July, which puts us at a close date of around end of July, beginning of August. In terms of the dates for the EGM, right now we have it tentatively scheduled for July 28, but more to come just because we cannot set the date until we have the effectiveness from the SEC.
Thanks. Hi, guys. Suji from ROTH again. On the chart you have with systems, I would be curious to know, I am assuming it is cloud-based and on-prem, commercial, non-commercial. If we did just commercial on-prem, that chart would look starkly, I think, toward you guys.
Right
versus other. First of all, is that correct? Second of all, the comment about it being cloud longer term, more units than commercial. Is commercial the use of these by guys like Aramco? Is that maybe a more near-term phenomenon because the cloud is not available? Or do your ability, the zero ability to translate these systems to what they need, is that only uniquely deliverable on-prem versus cloud?
The way we look at it is whether we deploy on-prem or cloud, there's a special class of customers that, let's call them public sector or sovereign customers. Outside of that, everything is commercial. Even those are effectively commercial for us because they buy under normal commercial terms from us. The difference between cloud access versus on-prem is more about what is easier for the end customer. We believe for enterprises to use them for use cases, in general, it's easier for them to start to access it through the cloud. The ramp up, the barrier to entry is very low. Just like with any cloud access, you can ramp it up as your demand goes up. That is why we emphasize a lot on the cloud access. I don't know if I answered your question.
No, mostly. With the on-prem sales then, would you expect that to diminish over time as customers are doing it now because that's the only way to access?
The proportion would diminish, the raw numbers would, we believe, will go up. But the fraction of sales that are cloud versus on-prem, that will shift because we feel that that fraction will shift more and more towards cloud.
Fair enough. Thanks.
Any final questions here? Okay.
I think we are coming to a close at this point.
Yep.
Fair enough. First of all, we just wanted to say a big thank you for being here, for listening about Pasqal, and to learn a bit more about this remarkable company that we have been building. We are happy to entertain more questions and so on you have, but really, thank you very much for being here and for all of your great questions today.
Thank you.
Thank you.