Fault-Tolerant Quantum Computing

Foreign.

Welcome to our live stream. My name is Mads Barami from Academic Innovation team at Wolfram Research. We are very happy to host two leading researchers from Harvard and Quera, Dolev and Harry. Thanks for accepting our invitation. And today we'll be talking about fault tolerant quantum computing. There are a few other of my colleagues from Wolfram Research. We have John, Nick and Yi. So and of course like in our audience in the Zoom chat, feel free. Like you know, we have Q A, you know, put your questions there like you're not and if I remember correctly, you know, $Harry. You guys are open to any question in the middle of your conversation, right? Like you know, so by all means, like you know our audience, please interrupt us, please ask questions and you know we would love to hear from you guys. So let's go with a, you know, brief introduction Dole of Harry, you know, you know, let us know who are you guys? What are you up to.

So I can start. My name is Delev. I am a 5th year PhD student at Harvard and I am primarily an experimentalist. This is my lab that I work in with other colleagues. But I also like theory and specifically the theory of error correction. And my. The main focus of my PhD has been the kind of discovery and development of this movement based approach with atoms to quantum computing and in particular its applications to error correction.

Awesome. And we'll be discussing in much more detail. Harry.

Hi everyone, I'm Harry. I'm in a joint position between Harvard and Quera. So partly a postdoc, Polly, a research scientist at Quera and I work a lot on architectural aspects of thinking about how we take the nice experimental tools that are pioneered by the leg experiment at Harvard and also being further commercialized at Quera. Thinking about how we can turn them into full fledged for tolerant quantum computers and a lot of both the architectural and theoretical questions that surround that on the QEC side.

Excellent. So of course like you know, the elephant in the, in the room is you know, fault tolerant quantum computing. And you know, we want to discuss about that. But before jumping to the detail of like you know, quantum error correction and the fancy experiments that you guys did and published toward the end of 2023. So I have a generic question. There are a few candidates, promising candidates for quantum computing. We have superconducting qubits, we have trap atoms, ions, we have spin qubits, we have photonics. Why atoms?

Sorry, should I do this? Harry, do you want to? So, okay, so the, you should take the next one. So the, the. So there's many different approaches and many different benefits to the different approaches to quantum computing. My honest view is that this is an extremely challenging problem. And so at this stage of time, we should be kind of pursuing all of them. The reason that atoms are so special and this will be central to what we talk about in a specific context of error correction, is that there are a lot of them and they're identical. I think that that's, those are the two really, really central aspects. And then there's a third aspect. So there's a lot of them and they're identical. That really, I think, differentiates them from trapped ions and superconducting cubits. But then the third way that that gets combined in quantum error correction is that they all need to do the same thing anyway. And that's what kind of makes them so powerful for realizing in particular error corrected quantum computation. There's also some other really important features, like they have long coherence times, we can entangle them with high fidelity. We can move them around in the middle of the quantum computation, which has, you know, a lot of strong benefits as well. But if I really were to summarize it, it's that there's, you know, tons of atoms, millions of atoms. Every time we start one of our experiments, we trap in a cold cloud and they're all identical. And for error correction they just need to do the same thing anyway. And that's, I think, the thing that's so powerful about the atomic approach.

So, Harry, like, you know, talking about atoms, like, you know, what would be which of the elements in the periodic table are the best candidate for trap atoms and doing quantum computing?

Yeah, that's a great question. And this is actually something that I would say is still open in the community. So we work with rubidium atoms, which is probably one of the most standard atoms that people work with, very well understood. A lot of the atomic physics is very well worked out and people know very well how to control it. But there are also complementary approaches to this. For example, others use maybe cesium or also use a family of atoms, so called alkaline earth, which are things like strontium or atopium. And I think really there's a lot of opportunities. They each have their own advantages and disadvantages. We like rubidium for its simplicity and also we have demonstrated very good operations with it. But in the long run future, it's also possible that other approaches could be equally interesting and carry their own benefits for error correction as well.

Okay, let me ask like, you know, I'm sure You guys remember that. What was the atomic Number of Rubidium 87?

I need to answer this one or I'm not going to get my feet.

Excellent. Now, like, you know, for our audience, like, you know, what you see in the background of Harry. Yeah, that's a, you know, fake lab. Like, you know, he doesn't want to, like, you know, you know, show us the secret things that he's doing, you know, at Quera. And by the way, Quera, like, you know, one of our partners on quantum computing. And you would hear a lot, much more about, you know, our partnership with them. But what you see in Dollar's background, it's a real lab. That's where that, you know, fancy experiment and that, you know, famous publication happened. So would it be possible that we take a quick tour of your lab and see, like, you know, what's going on there and look at some of the.

I can give a small, I can give a small tour. The, the, the. I don't want to. So we're currently taking some data. I don't want to disrupt the other graduate students.

Oh, the already experiment is happening there already. Nice.

Oh, yeah, we're currently taking some data. So this is, I guess, what I had previously alluded to before the call. But. So this is the, this single box. Inside of it there is a laser and it does all of our single qubit control that, you know, across the entire system, there is, you know, one microwave oscillator right up here. This one microwave oscillator controls the single qubit state of all of our qubits. Again, because all of the qubits are identical. And so if you're kind of just trying to track the state of all of them, you can do this with one microwave oscillator. And then I unfortunately can't open it right now because we're in the middle of taking data. I mean, you can see some kind of various lasers here. There's also a high power laser here that we use for entangling our atoms. Inside of this big black box that we can't open right now because we're taking data, is where all of these experiments happen.

Oh, I see.

Yeah.

So inside that black box we have the rubridium atoms. They are there. They are trapped.

That's right. That's right.

Okay.

Yeah.

And how many of them already, like, what is the maximum numbers that you guys can trap?

So when we trap them before an experiment happens, we trap roughly 10 million. And this is very standard. This is using standard magneto optical trapping techniques. People have trapped things at the scale of 10 billion. So there's truly many, many atoms, and they're all, again, old and identical, and they're packed into the several millimeter region of space using standard atomic physics techniques. So that just makes this cold cloud of atoms. Then the question is how to control all of them. And then we turn on optical tweezers that are tightly focused beams of light that each of them snag exactly one atom, or with 50% probability, it snags an atom. And that we've done up to the scale of, you know, roughly a thousand atoms. There's also, for example, very nice recent work from the Caltech group doing this at the scale of, you know, 6,000 atoms. So this is something that can you know, pretty readily just continue to increase.

We have an interesting audience question already, which. So this is tied in with this phenomena of Ryberg blockade that I'm hoping you can also elaborate on a little bit more for the audience. But the audience question is, you know, what are some advantages on rubidium as opposed to other atoms? And connected with that, you know, can you talk a little bit about this really interesting phenomena of Rydberg blockade that allows you to use them for various purposes?

You want to do this one, Harry?

Sure, yeah. So Rubidium is, I guess it's in the first column of the periodic table, if you look at it. And what that means is that outside of the, of the core, you have one electron zooming around there. So you might imagine that a lot of its structure is actually very similar to the hydrogen atom, which we learn at the very beginning of the, say, quantum mechanics classes. Because of this, it has a very simple structure that is almost the same as the hydrogen atom, except with some differences in the actual numbers of the wavelengths and whatnot. And that's what makes it simple as compared to, for example, strontium or atopium, where now you have two electrons hanging out there and there's a little bit more complications in terms of singlets or triplets or other types of features in the structure. Those, of course, are still very interesting if you are able to control them. And there's excellent work in groups like Jeff Thompson at Princeton, Manuel Andres at Caltech, Adam Kaufman at Gila and many other places trying to gain better control of these types of systems. But for us, when we first started, we wanted to use the simplest atom with the best understood characteristics. And so that's why we went for Rubidium. Now, part of this gate operations uses the so called Rydberg blockade that you mentioned. And what this is, is basically when we want to have the atoms strongly interact with each other. What we do is we actually excite them all the way up to the so called Rydberg states. So the way you can think about them is that the electron gets kicked into an orbit that is very large. This large orbit means that if two atoms are next to each other, they'll now start to talk to each other very strongly. And so they actually can't simultaneously go up into this very big orbit. And what this means then is that you have interactions which then subsequently leads to the actual gate operation. Now another feature of the blockade is that if the two atoms are next to each other, as long as they're within some radius, the so called blockade radius, then as long as they're within this radius, they'll have this strong interaction and the gate will operate. And so it makes for a very nice and relatively insensitive gate to things like positional placement fluctuations. Because the gate works as long as you're within some radius.

By the way, like, you know, if Harry, like, you know, if you guys want to share a screen and like, you know, show any presentations that you may have, have like, you know, for audience, by all means, please go ahead. Now talking about like, you know, those atoms, like you know, what are the energy levels? Like you know, like, you know, because when we talk about qubits, qubits like you know, it's two level, right? Like you know, the up and down or 0 and 1. But those rubridium atoms, like, you know, if anybody goes through like, you know, your papers, they would notice, you know, there are actually three levels that you guys are manipulating. So how come like, you know, this three level, like you know, atomic reflects in two. So that's the first question. So let's discuss the first question and then I'm going to ask another follow up question.

Well, so there's the three, so there's qubit states 0 and 1, and these live within what we call the orbital ground state of the atom. So you know, these are low states, they're separated by a microwave transition. That's why we use a microwave oscillator to drive transitions between them. And this is very long lived. I mean it's really easy to keep track of the phase of this microwave oscillator and this microwave qubit. And because it's such a low energy separation and so the coherence is seconds in our system and can be even longer. But there are also, I mean one of their features is they're magnetically Insensitive and so they're so long lived, but it also makes them essentially very challenging to interact with. And that's why we excite atoms to these third levels that Harry had mentioned, these Rydberg states, where now we take this spin up state and then we excite it so that it's going to this huge orbital state. And now the atom grows tremendously in size. Its coherence is much shorter. It's still quite long, but it's much shorter. But now it interacts very strongly with its environment. And this can be used for entanglement. So we store information inside of this hyperfine qubit we call it. And, but we only very quickly go to this Rydberg state for generating entanglement and then we come back down.

So basically like that coherence time that you said, like, you know, they live much longer in that, in the excited estate. That's the main reason that they are a good candidate compared to the other elements in the first row of the periodic table. But why not sodium? Because sodium, like, you know, when it goes to the excited state, you know, it's going to decay very fast and rubridium is much longer. And that's why like, you know, that's a better candidate.

So, so actually, so it really depends on what you're, what you're looking for. So atomic physicists are inventive and have trapped and manipulated many, many species of atoms. Actually the atoms in the first row of the periodic table are the ones that we've manipulated the most because they're, they're like hydrogen, they're hydrogenic, they have a single extra electron. And this makes, all of their structure is actually pretty much the same. So actually sodium and, you know, rubidium and cesium, they all actually behave quite similarly. There's, and then there's, you know, subtleties between them, you know, and then, so, so actually you can do, you know, high fidelity operations with rubidium, cesium, sodium, all like potassium, all in very similar ways. And the Rydberg states are, you know, actually almost exactly the same because it's, it's, it looks like a hydrogen atom at that point. Now that this electron is so far away from the nucleus. And then there's just really slight subtleties between them in terms of what are the exact optical wavelengths that we use. Which optical wavelengths do we want to use? What is the microwave separation between the qubit states? So really, really nuanced decisions. And people have made so much progress in atomic physics using rubidium and also, you know, other atoms, but specifically A lot of it has been rubidium. And so it's just a very well developed atom that has, you know, nice wavelengths.

Excellent. So like, you know, from theory perspective, so we have a bunch of atoms that are trapped and then there is a laser field interacting with them. Rabbit drive, like you know, phase etc, the tuning. And if a physicist wants to describe that, you know, they would just set the Hamiltonian and then we evolved the Hamiltonian and that's like, you know, we basically start your time evolution. That's a very typical example. Like you know, physicists, they learning like you know, the elementary quantum mechanic textbook. But this is not like, you know, the typical paradigm of gate based quantum computing. But it seems to me that you guys like, you know, this is the underlying dynamic. It's a Hamiltonian evolution, but it can be translated, it can be mapped into a gate based paradigm. How that's possible?

Yeah, that's a good question. So first I should say that even beyond our system, in many cases, for example for supergnartan qubits, underlying the actual system is still Hamiltonian. It's just that historically they moved from this paradigm of thinking about this slightly more analog natured natural evolution of the system into focusing on gates a little bit sooner than our community. But underlying all of these gates is indeed some Hamiltonian evolution that we try to program and control. And I think for us, really a big change in our mindset and why we now have been doing a lot more work focusing on digital evolution is the fact that we can now have a lot of flexible control through the types of techniques such as atom moving that dollar pioneered, such that you can reprogram things into discrete blocks and you do some analog Hamiltonian evolution within the block. Actually this Rydberg blockade that we utilize to do the gates is actually almost exactly the same as what is used for these analog quantum simulation experiments that you might also be familiar from a lot of the Harvard work and from the query machine online. And so it really is using the same mechanism, but now with the additional flexibility of things like atom moving, you can then also do a lot more individual manipulations that allow you to use the same tool set and do quantum gates with it. So really underlying it is all the same mechanisms. It's just that now with this new suite of controllability, you can also then chop it up into discrete parts and do digital evolution.

Okay, so right now we have Aquila, which is accessible through a cloud service to all of the users. And the experiment that you guys did, the main feature is the possibility of moving the atoms using optical tweezer. Is it correct that that feature is not yet available publicly? So the users, they cannot do it themselves. They cannot have the possibility of moving the atoms. Right?

Yeah. Unfortunately, Kwara doesn't yet have a system that is capable or supports mid circuit coherent movement of the atoms around in the system. But I should mention that actually a lot of the same optical Tweezer tools that you use to do those mid circuit manipulations are actually the ones that we use for the initial sorting of the atoms. So a lot of the basic capabilities are there. It just takes a little bit of time to fully get all of the operations packaged and tuned up and well calibrated in a way that is available for broader usage. But definitely stay tuned about that and hopefully in the coming, coming time, you'll be able to also access that on the cloud.

Excellent, excellent. Looking forward to that. So Dolev, like, you know, you mentioned your PhD, was specifically about like, you know, this movement based, like, you know, atom manipulation for quantum computing. Why do we need that? Why we need to move atoms?

Oh, great. Well, well, first I should say that, you know, the way. So I mean, we, we have kind of been, you know, random walking around into these kind of various things. So I mean, the first, the first reason that we, you know, tried moving atoms around was for actually a completely different application. We were doing analog quantum simulation with another student at the time, Harry Levine. We were doing analog quantum simulation, and we wanted to measure entanglement entropy. And we made two copies. It turns out if you make two copies of a quantum state, you can actually interfere them by putting them on top of each other and doing a gate between them. And then we were trying to use this as a way to enhance our analog capabilities. And it was not working very well originally due to some bugs. And then we started having this vision of, well, can we program arbitrary circuits in this way and have a fully programmable processor with any to any connectivity? And it turned out that it was working quite well, and that's kind of what had. And then it turned out that was actually very powerful for error correction. So in terms of how we got here, in answering your question, I mean, it was kind of like scientific random walk. Okay, now that we're here, then, you know, like, why is it so useful? So, okay, there's two, maybe two different answers I would give. So one is that if you want to have, you know, hundreds of qubits and you want to run an arbitrary quantum circuit on them, it can be very constrained if you only have 2D connectivity. There are some problems that map to that, but there are many, many that don't. And what we would like to do are develop devices that with hundreds and many more qubits, you can just run any quantum circuit and any quantum evolution you can write down in that way. You can just, you know, directly program. Currently we're doing this, you know, manually by hand, but you know, in the future for, you know, like Quera, for example, like, you know, that's something that someone would be able to do over the cloud, which is amazing, right? Any quantum circuit you want, you know, any to any connectivity between qubits. So that, that's, you know, just very powerful for exploring quantum computation in the lab in terms of exploring error correction. So that's something that we, I guess, have been kind of, you know, talking around so far. But when we're building quantum devices, it turns out that to make them really, really large, we're going to eventually need to take our qubits and then entangle them into what we call error corrected qubits or logical qubits. And there it turns out that moving qubits around for this very central application is central. And I would, I would maybe summarize that in two ways and then we can talk about maybe why error correction is so important later. But one is that now what we do is when we make an error corrected qubit, we take this single qubit and then we spread it out. We take a single qubit of information we care about and then we hide it across many physical qubits. And now it's this big block. And if you have this big block and you have two of these big blocks and you're trying to interact them, it can be very hard to interact them through an interface. But now that we're thinking about error corrected quantum bits and we want to do operations on error corrected in an error corrected processor. If we can move qubits around, then now each of these blocks essentially just looks like one bigger qubit. And now we can take these two blocks, put them right on top of each other, and then interact them as if they were just two really big particles. And that's one of the approaches, one of the reasons that moving qubits around is so powerful.

I see, I see. So talking about like, you know, error correction from the onset of, you know, quantum computing, you know, everybody was saying, you know, look, you know, to attain quantum value, fault tolerance seems the only way, like there is no way around, like you cannot like, you know, find any alternative Solution, at least as of now, you know, all the community agrees, you know, this is the way. So why we need error correction and how we implement that in the lab.

Yeah, that's a, that's a very good question. I think fundamentally it boils down to many of the actual advantages that people have been able to show for quantum computing rely on error rates that are very low. So just as an example, typically nowadays we're thinking about 10 to the minus 2 to 10 to the minus 3 physical error rates for our qubits. And that is already quite impressive at the physical level. But if you think about, for example, for Schwarz algorithm or many really large scale quantum chemistry algorithms that you'd want to do for an actual application, you're then looking at an error rate that is something like 10 to the minus 12. And in some sense, maybe that shouldn't come as a surprise, because if we think about our classical computers, they're just doing perfect operations all the time. And typically the number of operations that we're doing is actually also something that is probably on that order. So we really want to be able to do that many operations without getting any errors. And this is just exceedingly hard to do. If you think about this massive gap between this 10 to the minus 2 to 10 to the minus 3, which means maybe 1000 or so operations, to these trillions of operations that you would want to do in these applications with provable advantage. And so this is where error correction comes in. And it really, when it first came out, was quite a surprise that you could really do error correction and you could really tolerate an error in principle in any component of your circuit. This is the concept of so called fault tolerance. And the basic idea is that by encoding your quantum information, your qubit into multiple degrees of freedom, you can really now be robust to any disturbance in a single location or in a few locations, because you can use the rest of the system to fix that and recover the actual information that you want. And so using this idea, it turns out that as you increase the system size, you can actually improve your logical error rate exponentially in your system size, as long as your physical error rate is below a certain threshold, this so called error correction threshold. And so this then gives us the path to maybe be able to achieve very low logical error rates with a resource overhead that is growing relatively slowly in terms of the physical qubits that you need. It is still in practice a pretty large overhead. So, for example, for the standard surface code schemes that people use, people are typically thinking about maybe a Thousand or so physical qubits per logical qubit, still a pretty daunting number. And we actually have some active work in collaboration between Harvard, Chicago, Ancura and some other institutions of coming up with new error correction schemes that can substantially reduce that overhead. But still, it is a very daunting challenge and definitely one of the core research areas that the community will need to continue making progress on as we go towards these large scale quantum computations.

We do have another audience question which I think both of you could elaborate on. And this is help them understand the difference between physical qubits and logical qubits, and then also the scale that you mentioned of needing, say, 1,000 physical qubits per logical qubit, or what are the things that we're hoping to get to both in the near and maybe optimistically near future terms.

You want to do this one, Harry?

Yeah. So I guess the first question was the difference between logical and physical qubits, right? Yeah. So fundamentally they're both encoding some qubit information, but the main difference is that for logical qubits, now this qubit information is spread over multiple physical qubits, so that now if any individual physical qubit had an error, you can still recover from that error. Maybe. Just to make an analogy that hopefully will help illustrate this in a more familiar setting, let's say we have a classical bit of information. So we just have a 0 or 1. And if we just had a single one of those bits, if someone comes along and secretly flips that bit, then we would by itself have no way of recovering of it, because maybe the bit was flipped in the first place before they even came along. However, what we can do is we can then take several of these bits. For example, you take three bits and now encode them into a repetition code. Then if someone comes along and flips one of them, you can still do a majority vote and recover the actual information by flipping that one back because the other two were still in the correct state. So the same idea is generalizable to the quantum case. It becomes a little bit more involved, but the basic idea is very similar. And so by using this redundancy, you can then recover from individual physical errors. And what was the second question again? Sorry?

So the second part of the question was, you know, where do you think things are going in terms of the number of logical qubits that can, or, excuse me, the number of physical qubits that are needed to encode a logical qubit. So both currently and then in the near and optimistic, right?

Yes, yeah. And so that's, that's also a very good question. So I already mentioned this roughly thousand qubit, physical qubit per logical qubit for the standard surface code architecture. And some of the work that we've been doing on these so called quantum low density parity check code or quantum LDPC codes, some of these new code families can actually have a higher encoding rate. And the way it works is that you encode many logical qubits into many physical qubits. So now the protection is shared across all of them. And what this means is that you can be much more efficient in encoding the qubits. We're not the only ones working on this. There's also some very nice work from many people in the community, both academic and industry. A contemporary work without proposal was for example, a paper from IBM proposing some certain architectures in their case which might be a little bit more complicated to implement, but nonetheless provide some very interesting code families. And so here what we're really looking at are now numbers that maybe you could perhaps have maybe on the order of 20 physical qubits per logical qubit rather than a thousand. And there is certainly still sustained research in this area, both thinking about better encodings as well as once you have those encodings, how to co design them with the logical gate operations that you obviously would also want to do for the computation. And so I think it's a very exciting and interesting area of research that will continue to see a lot of fantastic work of in the, in the coming years.

And this ties in with something that Dolev was mentioning before, perhaps we could elaborate a little bit more on, which is that being able to spread out the logical qubit in terms of these movable atoms so that the information is encoded not in a local place, but you can move it around so that you can interact them more easily later. I wonder if we could elaborate just on that detail a bit more for the audience.

Sure.

So, so yeah, when, when we do quantum error correction, what we're physically doing. So, so, I mean, it's actually, it's remarkable error correction is possible in the first place. So Harry gave this example of classical error correction where you copy bits, you can't copy quantum bits. It's one, it's a fundamental there's no cloning theorem. This is part of the reason why it was so amazing when Peter Shore and others kind of invented Quantum error correction 30 years ago. But, so what you use is entanglement. You take a, you know, qubit and then you spread it out such that if the environment comes in and it measures any given physical qubit. That physical qubit is so entangled with its neighbors that it will reveal identically zero information. So this is very fundamental and this is how we're kind of. Yeah, so that, that's how we do making these logical qubits. But now that they're delocalized, you know, and they're hidden and things don't locally contain the information. Now, if you want to, for example, do an operation between these two things, but they don't locally contain this information, how do you do it? It's actually very challenging. You need to do many different tricks. And for example, if things are on this 2D grid and you want these two delocalized wave functions to interact, you have to do techniques that we sometimes call lattice surgery or braiding things that end up taking a number of operations that scale with the size of this delocalized degree of freedom. But when we can move qubits around, what we do is we effectively just take these two blocks, put them right on top of each other, and then we can entangle the logical qubits using a type of operation that we call transversal. And transversal here, what it loosely means is to do this gate on the logical degree of freedom that's delocalized, just do that exact same gate on all of the physical qubits that make up the block. And it turns out that a lot of gates and a lot of error correcting codes, not all of them, but most of them can be done this way. And so, for example, if I have a single logical qubit and I want to do a Hadamard on it, just like we're used to doing with physical qubits, it turns out what you don't need to do often is something unique to each individual physical qubit of the block. You can do it transversely. You can just do the same Hadamard on all of the physical qubits that make up the block. And this is what's so powerful about, you know, the atomic approach, where all of the qubits are identical, the light to do a Hadamard on all of them is identical. And we effectively just now take one big beam and illuminate this, you know, big atom effectively, you know, big cubit with this big beam. And in this way do a logical hadamard by just doing the same physical Hadamard instruction on all of the physical qubits of the block. And remarkably, this can also be done for the entangling. We can do it in this transversal way to do a transversal CNOT where we just take these two degrees of freedom, put them on top of each other, and now do the exact same physical CNOT operation using a global entangling beam on all of the twins of these two blocks. And in this single transversal step, we can entangle these logical degrees of freedom. And that's part of what makes this approach so powerful. Again, the other aspect of moving that makes things very powerful is, as Harry mentioned, the ability to make exotic types of error correcting codes, like for example, LDPC codes that have, you know, very dense encoding rates. That's, you know, one type of, you know, really useful exotic code. In our work, we also made 3D error correction code. So we made both 2D and 3D where now we delocalize it over, you know, just like 3D block. And this actually also has some, you know, really powerful features. So the ability to have very flexible connectivity for error correction is actually very useful in many, many areas.

And this is directly reflected in the fact that you have, you know, one microwave or density rather than needing to have many for each physical qubit.

Exactly. That is exactly right. And so not. So it's already useful for doing physical qubit computations where now, okay, we simplify the control problem. We have one global oscillator. And you know, if you want to do a Hadamard on half of your atoms, then, you know, then you can do it with this one thing that's already useful right. When we're doing programming quantum circuits. And then there's one more remarkable fact that really comes together, which is that for error correction they only need to do the same thing anyway. And the combination of those two with the atomic approach and kind of using global, parallel and efficient controls is, is what has allowed us to so rapidly take off in terms of these advanced error correction circuits.

So we have another audience question which is a little bit more general, which is understanding the connection between analog versus digital quantum comput. So I wonder if we could maybe take a slight turn into that before getting back to error correcting in particular.

Yeah, so I guess there are many different modalities that you can imagine for when you're trying to use a quantum device. So as we already discussed, underlying these systems usually is some, in reality, some analog, Hamiltonian. Even in the case of supernatural qubits, actually there's also the same thing. And actually I think there's, for example, Google had some interesting work trying to do simulation by utilizing more the native Hamiltonian for us historically, the cold atoms community because of both what was most natural with the control and the fact that you could rapidly go to large system sizes, where now simulation of just the native Hamiltonian itself is suddenly already at least non trivial, if not actually completely intractable. Classically that meant that there was a lot of interesting work that you could already explore both on the physics side and starting to think a little bit about some heuristics on the application side, such as these maximum independent set problems that was explained, explored in some Harvard experiments, a science paper from, from a couple of years ago, you could already explore some of these applications in this setting. And so really in the analog case, what you're trying to do is to find natural mappings from a problem of interest. This could be quantum simulation or some application like optimization, mapping that directly onto the Hamiltonian of your system. In the digital case, instead of trying to use these very native encodings, you're trying instead to now use it as a universal computer where you have these discrete building blocks and you try to piece those building blocks together. The advantage is that now in principle you could do anything. You now have a universal quantum computer in principle. But of course it also comes with a cost where maybe you're encoding is now not as native in the other case. And so I think there's an interesting regime, especially with these near term devices where for some things the analog evolution is something that would still be more effective than just directly running the digital. And this is something that we are still continuing to do in our community. So for example, after the recent error correction experiments at Harvard, there was a little bit of a, a refreshing break in between where some back to our odd quantum simulation, analog simulation routes, where some interesting experiments were run there before we return to some more gate based operation. And I think the really beautiful thing is that it actually doesn't take that long to switch between the two modalities because as we mentioned, you're really using the same tool set. And so you could in principle even, and this was already demonstrated to some degree in some of the early experiments that Olav mentioned with this atom moving approach, where you could even take a hybrid approach of doing some analog evolution and then doing some gates afterwards. So I think that both, they're both interesting in their own aspects and complementary in many ways.

Very interesting. So regarding, like, you know, your work, you know, the error correction code is like, you know, basically like, you know, an error happens, like, you know, you detect that and then you correct it. And these three steps are Usually, like, you know, experimentally they are very complicated how, how you would implement that. And of course, like, you know, there is a zoo of like, you know, different theoretical approach for quantum error correction. Which one you guys pick and, and why? Basically like, you know, this question is related to your collaboration with theory groups because you guys are experimentalists. And then there has been lots of like, you know, research on quantum error correction, but theories. Which one you decided, oh, this is a good fit for our specific, like, you know, device and why you went in that direction.

So, okay, so here I would illuminate that, that the. So the path is very long and in terms of building a large scale device and we are really looking for as many shortcuts as possible. So that is, I think, a founding principle. And in that spirit, we don't want to just make error correcting codes, we want to study algorithms between them. And that is quite nuanced and quite uncharted even from a theoretical perspective. So there was a lot of back and forth between us and also theorists in the department that contributed to this work and also in theoretical collaborators at other institutions as well. And so in our work, we made three different types of error correcting codes. We made surface codes. We made the largest surface codes that have, have been made and then we entangled them. And here the feature is that the surface codes are the most tolerant to errors, at least in most contexts. And they're also very standard error correcting codes that are well understood. We also made things that are very similar to the surface code or this 2D surface code, which is a 2D color code. So it's similar instead of being on the square lattice, it's a kind of on a triangular lattice and it's colored. And this is very similar to the surface code in many ways. One of the ways it's actually very different for practical operations is that the surface code can't do as many operations. Conveniently, this 2D color code can do, however, all of the Clifford gates. It can do hadamard S&CNOT, and it can do them without requiring any lattice rotations, which is the kind of subtlety that makes it a little harder for the surface code. This from a practical perspective is so useful because now with our logical qubits, any Clifford circuit you would want to run with physical qubits, you can now do that exact same thing with the logical circuit. So we can run any Clifford circuit in this way with these color codes. That was a really big feature of choosing them. And then we, in our last experiment we made 3D color codes. And these have their own kind of quirks that are very useful. So they lose one of the Clifford operations. They can't do Hadamards. So a really important thing I've swept under the rug is that in order to error correct, you need to digitize and you need to have, you know, a digital gate set, and it needs to be a discrete gate set. Unfortunately, there's no way around it. This is very fundamental to the fact that you need to be able to be robust to, you know, small angles. So it's a huge difference than working with physical qubits. And so it constrains the problem in very different ways. And so you have to think, what code do I come up with that has a convenient gate set for whatever problem I'm trying to solve? So in the 2D codes, we can do, for example, all of these Clifford group Clifford gates, but we can't do small angle rotations. And in particular, we can't do a gate that we call non Clifford, like a CCC gate controlled. Controlled Z. And we need non Clifford gates in order to do things that are, you know, classically, you know, not, you know, you know, linear or quadratic time to simulate, you know, that. That are kind of exponential time to simulate. And so for our 3D error correcting codes, even though we lost one of our gates, we lost our Hadamard, what we do get are non Cliffords. And what we did is found a very specific circuit, like a scrambling circuit or a sampling circuit that, okay, these 3D error correcting codes to do a generic arbitrary quantum circuit will have some cost associated with it that, you know, requires some, you know, extensive compilation. But for this specific algorithm, it can be realized in a very efficient way. And that allowed us to explore really complex algorithms with logical qubits by, again, finding a shortcut that for this specific algorithm with this specific error correcting code, you can realize it in a very cheap way. So that's kind of a summary of the smorgasbord of experiments that we did. Nothing we did is perfect. Everything kind of has its own limitations. But together it kind of, you know, paints a picture of, you know, different features of error correcting codes. You know, like large error correcting codes, complex operations, you know, programmability and so on. And kind of where we see it kind of progressing into the future by kind of being able to combine all these various features.

Excellent. So, like, you know, given that. That paper, like, you know, because, like, you know, many different researchers, students like, you know, they would read it and of course like, you know, they would be motivated to work on, on, on this field. Basically like you know, quantum error correction plus quantum computing. From your perspective, you guys, as the, basically the co author, the guys who are basically behind the scene, like what do you think are the most important take home message for the reader of that works? Like, you know, how would you summarize that?

Maybe I can start and then Harry, you can, you can add your, your own perspective. So the. Okay, so what I would say, so I would maybe have two, two central lessons. So one would be to kind of people who are more, you know, interested on the kind of algorithm and error correction side as like theorists. And it would, it would be that when we do things with physical qubits and we do things with logical qubits, it can be very different. So something I just alluded to is that physical qubits, they can do any single qubit gate they want. It's very easy to do a small angle rotation, but entanglement is often hard. Logical qubits is a completely different space. Actually, it turns out almost all error correcting codes we're interested in can do an entangling cnot between these logical qubits in a simple transversal way. But actually arbitrary single qubit rotations are the hardest thing to do in most cases. So it's actually a very different problem. And the things we're used to thinking about in terms of what's easy and hard for physical qubits is a completely different world for logical qubits. And at least in you know, my view, this space of how do we find good ways to program error corrected quantum circuits, which is what we would like to do going into the future, is an extremely open space that is also extremely ripe for breakthroughs. And you know, we found a specific algorithm that can be realized in a very inexpensive way with error correcting codes. We would like to find more of these. You know, we can make a whole database of them, you know, different algorithms that can be cheaply found with different types of error correcting codes. And right now we're kind of, you know, finding shortcuts that are maybe interesting for these short term problems. But if we do it right, these kind of shortcuts we find now will scale into the future. And some of the, some of these will be applicable in the large scale. And that's the kind of goal. So poking around with these near term devices, what I would call these like early generation logical devices is what we currently have. Figuring out what is attainable and then figuring out, you know, which shortcuts that we found can be used in the future as well. I think that that's an. It's an extremely exciting time and there's so much that has not yet been done. So that is what I would personally, you know, that from a theoretical perspective, I think that's a really important takeaway from an experimental perspective. And also experimental, but also kind of like error correction theorist. I think this kind of co design of the experiment and theory is so critical where, you know, we're benefiting so tremendously from, you know, collaboration with our theoretical colleagues as well. But you know, for example, this observation that for error correcting codes we just need to do, you know, the exact same operation on all the qubits anyway. And then for our atoms, it's. They're all identical and they all do the exact same operation using the exact same light. And then that this works so well for realizing error corrected quantum computation. I think there's many more kind of lessons like this that we would like to keep learning into the future. And if I were to work on a different system, like superconnecting qubits or ions or whatever, every day I would wake up and I would ask how to do this in that system because I think it is really the central thing that has allowed us to kind of so quickly take off. So those are my kind of two lessons. I'm sure Harry has some other kind of interesting perspectives. Perspectives though.

Yeah, I think that actually also mostly summarizes what I would say. Maybe one thing to slightly rephrase the latter point is that one of the things that the community has really been discovering more and more, not just in our work, but in previous error correction work, is this concept of hardware efficiency. But I think what we put on the map is also this aspect of control efficiency. So not just that you want the error correction to be hardware efficient, but also a lot of the complexity, especially when you think about these large scale systems, comes from the control. So for example, our classical computer chips, they're doing billions of operations and billions of elements in there. But usually the actual external control that you have going into the CPU is actually Fairly Limited. Maybe 1000 or so control lines or wires going in there. And a lot of the other stuff is then run autonomously. Right now a lot of the systems that we have tend to be of the nature where you really have one or even several control lines per qubit that you're controlling. And I think that's the control efficient aspect is Also another thing that really is highlighted in our philosophy and for which I think other communities are also starting to make progress on. But that's also another aspect very related to what Dolev was just saying that really is highlighted by our work.

Excellent.

You mentioned in your paper that these methods you expect could be scaled to something like 10,000 physical qubits. So I'm curious, what sort of timeline are you all thinking for when you're going to really scale up the number of things that you want to do with these?

The field is broad and there's many kind of amazing groups working in it. And actually one can find a paper from just, you know, like a week ago from the Caltech group getting to 6100 atoms, for example, and so far just trapping them, not really doing manipulations on them. But, but I mean, so I think the scale of 10,000 atoms is, you know, impending. And I think so. I mean, yeah, I mean, so we're, we're currently working on various things and I'm speaking on behalf of Harvard. I don't know if Harry has anything he wants to say on you know, behalf of what's happening at Quera. But the, but I mean the scale of 10,000 atoms is, I, I can't give it, you know, I shouldn't say a number, but it's impending. I mean, it's really easy to have lots of atoms. That, that is I think clear. We also need to get to higher fidelities to really be able to use these atoms very well. We want to get to, you know, three nines gate fidelity, roughly. Currently we're at 99.55% gate fidelity. This is something that I think we also have a plan for and I would say is also impending. And I mean, in my broad view, in the kind of coming years, pretty soon we will have all of the ingredients that we need for making what I would describe as medium scale error corrected devices where you can do something like a hundred logical qubits that can do a million logical gates without having an error. And if we can create a device like this in the lab, in the kind of coming years we will have the ability to explore quantum computation and just quantum mechanics in a way that we've just never been able to touch. I mean it's, it's a completely different type of quantum computer to the ones that we have today. I mean it will not have errors, for example, for short circuits. You know, we will, it will just be flawless evolution. And that is, that is, I think, amazing. And so I think but, and I think it's impending. So that, that's, yeah, that's my statement. I don't know what Harry has to say.

So, so in terms of like, you know, the, the number of like, you know, qubits that you can trap and basically like, you know, as your physical qubits, what are the experimental limits? Like is there any upper limit? You would say, you know, look, you know, current like, you know, features that we have in the laser fields, et cetera, et cetera, we cannot go beyond this number for the next five, 10 years. Like what are those limits? Like you know, are we at the limit or there is still, you know, a lot that we can push.

So okay, so currently in our lab we have a roughly 10 watt laser that traps roughly a thousand atoms. It's actually one of the lasers that you briefly saw. But the. So if you came to the lab tomorrow and you know, tomorrow you at the same laser wavelength, you plopped in 100 watt laser, then you know, we would immediately have 10,000 atoms. We would just split the same laser beam into more spots using what one of our devices that we call a spatial light modulator takes a single laser beam and then splits it into, you know, our thousand individual tweezers. We would split it into 10,000 tweezers and then we would immediately have 10,000 atoms. So you know, in the sense it's, you know, you know, impending. And however, if you came into the lab and you plop down 100 kilowatt laser, it would destroy the lab. So you know, so what things we need to do to get beyond this. So okay, I would say the path to get to these like medium scale error corrected devices, at least the way that I would describe them, there's like a hundred logical qubits, million logical gates with like 10,000 atoms that have, you know, three nines gate fidelity that I think can be just done by just cranking the laser power knob essentially. Much beyond that to get to 10 million atoms, I think, you know, might benefit from some kind of greater creativity. And so it's harder to put, you know, a specific perspective from that.

Yeah, and I guess also there's active developments in the community, for example, for networking multiple of these models. These are still early on in the, in their development trajectory. But for example there's, there's very nice work actually in the lab right across the wall from where where Dolev is sitting, there's another lab working on networking. There's also active efforts in the community with many different complementary approaches. So that's Also a route that you could imagine then linking many of these 10,000 qubit modules together into a larger, much larger scale, full fledged quantum computer.

I see, I see. So Harry, I have a generic question for you. Like, you know, how was the transition from academia to industry?

Yeah, that's an interesting question. So I guess, as you know, in my position, it's still, currently, still a bit of a mix between getting some academic contact and getting some industry contact. And we are definitely still in a stage of the field where things are still fairly early on. There's still a lot of interesting research questions to be had and I think I've certainly benefited a lot from having both perspectives of some of the industry relevant questions and interactions, as well as some of the academic interactions. Actually some of the research ideas that we had on the, on these, for example, these LGPC codes actually came out of interactions that were more on the company side. So I think right now it is still a very fruitful collaboration where we are really just trying to push the frontier envelope of the research. And it really is these types of research breakthroughs that also make it possible for the companies to eventually deliver these, these large scale quantum computer systems. So I think it is actually very complementary and it's nice that there is still the opportunity to, to continue doing a lot of frontier research even in a company setting. Not just at Quera, but also at many companies across the ecosystem.

Excellent, excellent. A quick note that like, you know, at Wolfram Research, we always have a small quantum team and we have been like, you know, actively working on the very abstract level of like, you know, quantum error correction together with Nick. So I think like, you know, very soon, like, you know, I'm gonna push Nick to have a live stream together to discuss like, you know, a few fancy things that we have been developing as of now. It's very, at the very fundamental level, like you know, the direct experimental implications, like you know, we have to wait, wait for it. But that's also a very interesting thing. So just stay tuned. Like, you know, you may hear like, you know, some good noises from our regarding, like, you know, error correction, like, what about you? What's, what's the next step for you? Like, you know, I gather like, you know, you are about to wrap up your PhD in a year or so, so what's going to be next for you?

So I would, so I'm exploring, you know, broadly, but I would like to start my own lab. That's, you know, I don't know if I should be saying that publicly. But yeah, I would like to start my own lab. And you know, although, you know, I'm, you know, I'm exploring broadly, I'm still just a PhD student in the last year of my PhD, so I would like to kind of keep going in this direction. And I think that with clever innovations, we can still go very, very far with this technology. At the same time, we should also be trying to engineer things. And here again, collaboration between academia and industry is very interesting. You know, being able to engineer things and kind of in a way that people can actually access over the cloud is kind of amazing. But also I think, you know, being able to do, you know, exploratory work and see what ways we can still make, you know, breakthroughs that, you know, win us factors of 100 or a thousand is something that I'm pretty keen to keep doing with this technology. I think also what, what we're doing with, you know, building a large scale quantum computer, I mean, that's the goal and you know, building this large scale error corrected quantum computer, there are a lot of technical challenges associated with it that again, we're solving with both engineering solutions and also just breakthroughs like scientific breakthroughs, but they are not applied only to quantum computing. So I mean people, we are benefiting from 50 years of atomic physics research and that was benefiting from previous decades of NMR research. And if I think very far into the future, in 50 years we'll still be doing atomic physics. I don't know what exactly. Regardless of how quantum computing develops, I mean, people are not going to stop wanting to cool and manipulate individual particles and control them in individualistic ways and do different things with them. One example is fundamental science and precision metrology. The world's best timekeepers, the best clocks are atoms. And it's not only from the perspective of we want to keep tracking the second very carefully. It allows you, once you can start doing precision science so carefully, it gives you a different lens into the universe. You can start to, for example, understand gravity in different ways. You can even use them as gravitational wave sensors. It's remarkable. And I think the tools we're developing here for building, you know, quantum computers, we should kind of plow ahead, but we should also be keeping our head on a swivel because this technology we're developing here I think will also be, you know, very applicable to this broad field of atomic physics. And similarly, you know, we're benefiting from, you know, tremendous progress done in other areas of atomic physics and solve other problems that we then take to you know, try to use to build our quantum computers. So those are my research interests, broadly.

Excellent, excellent. So like, you know, best of luck, you know, to both of you. I'm sure, like, you know, we would hear much more from your success and like, you know, we will have like, you know, more chances to discuss more about your breakthrough. Special thanks to our audience, like, you know, for your, like, you know, engagement and very interesting questions. Dolev, Harry, any final comments, our audience, any final questions that you may have for our guests?

I have one final comment, if I can make this final, please. So the, the, I mean, one thing to say, I mean, so we discussed a lot of what we're doing here. What we're doing is obviously not in isolation. I mean, so there's in particular the neutral atom community. It's currently coming up with a lot of very different clever innovations and we talked about this Caltech paper. But there's also things, you know, you know, in kind of both in the kind of like, like ancient atomic physics, but also more contemporary in terms of like optical lattice simulators, you know, that, that kind of field of research, other areas of atomic physics that are kind of, you know, leveraging similar techniques. In the tweezer community, people are coming up with, you know, different types of atoms that have different types of features, different ways of doing the error correction. And it's a, you know, really unique area. Also, we learned a lot from other kind of quantum computing platforms. When we're building our quantum computer, we look at, you know, people have developed these techniques for super connecting qubits and ions, for example, and we think, well, what do they do and what did this look like? And that's amazing. And you know, I think that that actually, so, I mean, we benefited so much from all of this kind of different work and we hope that our work is kind of beneficial to the rest of the community as well.

Definitely, definitely, yes. All of us, we are standing on the shoulder of other researchers on many different field of research. And one beauty of quantum as a topic for research is its interconnection with many other field of research, from chemistry all the way to condensed matter physics, like computer science. And I think this is one of those areas that scientific communities and also the industry, all of us, we have learned that in order to tackle this very difficult problem, we should work together. And I'm sure our audience, they would hear much more about collaboration between the industry, academia and in our lifetime, hopefully we would see some of the big promises of quantum computing. Excellent. So thanks everyone, like, special thanks again to Dolev and Harry from Harvard and Quera for joining us and looking forward to another session in the future. Have a very good one.