Podcast | How Quantum Computing Changed Our Understanding of Science – with Lincoln Carr

While we await practical business advantage with quantum computing, has quantum information science already furthered our understanding of science? What’s the difference between a simulator and an emulator, and how does a physical quantum computer fit in? Join Host Konstantinos Karagiannis for a chat with Lincoln Carr from Colorado School of Mines as they explore these topics, along with everything from Tensor Networks, to thermodynamics, to complexity, with an eye to how the hardware timeline will make practical power a reality.

Guest: Lincoln Carr from Colorado School of Mines

The Post-Quantum World on Apple Podcasts

Quantum computing capabilities are exploding, causing disruption and opportunities, but many technology and business leaders don’t understand the impact quantum will have on their business. Protiviti is helping organisations get post-quantum ready. In our bi-weekly podcast series, The Post-Quantum World, Protiviti Associate Director and host Konstantinos Karagiannis is joined by quantum computing experts to discuss hot topics in quantum computing, including the business impact, benefits and threats of this exciting new capability.

Read trancript +

Lincoln Carr: Is there a fundamental science to be learned and maybe even some use cases in these prototype computers that are teaching us to make a future quantum computer? Absolutely, yes. There’s a lot of room, and there are a lot of things to do, and a lot of those things are not so much about quantum. They’re about reenvisioning classical computing.


Konstantinos Karagiannis: While we await practical business advantage with quantum computing, has QIS already furthered our understanding of science? What’s the difference between a simulator and an emulator, and how does a physical quantum computer fit in? We explore everything from tensor networks to thermodynamics to complexity with an eye to how the hardware timeline will make practical power a reality in this episode of The Post-Quantum World. I’m your host, Konstantinos Karagiannis. I lead Quantum Computing Services at Protiviti, where we’re helping companies prepare for the benefits and threats of this exploding field. I hope you’ll join each episode as we explore the technology and business impacts of this post-quantum era.


Our guest today is a professor of physics and quantum engineering at the Colorado School of Mines. Lincoln Carr, welcome to the show.


Lincoln Carr: Hi. So nice to be here.


Konstantinos Karagiannis: Thanks so much for joining. A lot of quantum information science discussions tend to focus on future use cases, which are important to prepare for. But QIS might be already teaching us a lot about science We’re hopefully going to get some current things, too, out of this session here. But let’s dive in here right now with something a little more general that’ll help the audience get oriented. When we talk about quantum computers, then we also talk about simulators and emulators, do you feel any need to differentiate those terms? Throw a stake in the qubit, as it were, about whether we need to change the meaning of these terms or if any of them mean anything specific to you.


Lincoln Carr: If you’re a computer science person, you want to use the word emulator, but we commonly use this word incorrectly: simulator. A simulator, generally, in the computer science world would be something that’s on a classical computer, and an emulator is like a wind tunnel. Instead of simulating a wind tunnel, you put your airplane in the wind tunnel and you run the wind over it and see what happens. All quantum computers are emulators right now. None of them are actually computers, because they’re not error-corrected.


This is a little bit complicated because right now, as you may be aware, classical computing — the stuff that’s supporting our conversation, in fact — is hitting a wall. The data centers are running out of room because of generative AI, among other major impact factors. We have to reinvent computing itself. We’re in the middle of reinventing even what we mean by computer, which is very exciting. Quantum emulators — what we casually call computers — have a major role in that reinvention.


Konstantinos Karagiannis: That makes a lot of sense. What would you say using emulation has already shown us?


Lincoln Carr: This story starts in 2002 with two major results. It’s been going a long time — 22 years now. The two major results are the following: One was done, by the way, by a master’s student who’s now a professor at Harvard, Marcus Greiner. The other was done by some outstanding people at JILA, right here in Colorado. One of them is, how do bosons become fermions? These are the two kinds of particles in the universe. Our body is made of fermions, protons, electrons and neutrons. That’s what makes up our body.


Those are qubits, by the way. They’re nonbinary. Our body is built of nonbinary things. Fermions are exclusive — they don’t like to be in the same state. They’re like two cars — you put two cars in the same place, and bad things happen. It’s like a crowd of people at a Greek party in Boulde — they all want to be in the same house, and it gets impossibly full, and then yet more pile in. That’s what makes lasers work: Light is a boson.


Now, it turns out, fermions can pair to make bosons. It sounds a little bit technical, but that’s what’s underneath superconnectivity, which is the big dream for quantum computing — that we’ll understand superconnectivity, for example. We didn’t know how fermions pair to become bosons gradually. We know that happens in matter, but this was an unknown thing. How does one basic kind of particle in the universe turn into the other kind of particle? This was unsolved until this project came along in 2002. Through these quantum emulators, they were able to solve that problem by causing this pairing to occur very gradually and discovering something totally new about the universe.


That’s one of the things quantum emulators are doing: They’re teaching us basic things about the universe, like, how does one kind of particle become the other? That’s a big result. The other one — I love this story because I like to encourage young students. We have a great quantum engineering programme at Mines, and we have a lot of master’s students in it. I like to tell them, “A master’s student actually started your whole field.”


That problem was, imagine if you froze water into ice, and then you had such incredible time resolution that you could watch it oscillate from water to ice to water to ice. Imagine if you saw it melt and refreeze and melt and refreeze. Now, that’s something hard to imagine with water and ice, but in fact, it happens in quantum matter all the time because of quantum fluctuations.


This master’s student was able to show that matter in a crystal of light would do that. That is called the dynamics of phase transitions. That was discovered, understood, observed. It’s still an ongoing field. It’s been going for twentysomething years, and it’s changed how we think about the basic building block of STEM called thermodynamics. That’s a huge scientific discovery. Both of those things are absolutely fundamental science started 22 years ago, and they continue and have blown up because of the new capabilities in what they call now quantum computers, like they have at Google and IBM and Quantinuum, etc.


Konstantinos Karagiannis: To do that level of work, what would be required? How many fake qubits? What would you need to do something like that now?


Lincoln Carr: There are many kinds of quantum matter, and qubits is only one example. Of course, it’s the one that’s best known in the press. The reason it’s best known is because we love to take the thing we know and put the word quantum in front of it. If you take bits — quantum bits. You do gates — quantum gates. Computers — quantum computers. It’s very convenient to take the thing we know and turn quantum into an adjective.


Konstantinos Karagiannis: Or, unfortunately, shampoo or vitamins or whatever.


Lincoln Carr: Let’s not forget quantum healing. There are a lot of great examples, and some of them are inspirational, like quantum healing for people, which is great. Metaphor is great. On the other hand, that’s not tech. This quantum-computing thing can be a little misleading because, in fact, many kinds of quantum elements come together to do a quantum task, and those elements could be bits. They could be what are called qudits, which are much larger quantum spaces. They could be continuous variables. We can think of them as pulses of light, for example, and all those can come together to create a quantum result.


Those early quantum emulators, they didn’t use quantum bits at all. They used something that was continuous. Imagine that you have some matter over here, you have some matter over there, and then this matter can interact in different ways. That interaction is modulated by the presence of this crystal of light. That’s what allows you to go through, say, a phase transition and see, by analogy, water oscillate into ice and back into water. This is literally quantum liquid and solid, by the way. It’s the quantum analog of this. But I didn’t call it quantum water and quantum ice, because I don’t want to do the same thing everyone else is doing. I would love to give you some quantum tea, but I don’t have any to offer over this podcast.


Konstantinos Karagiannis: Back in 2021, you worked on a paper, Quantum Simulators: Architectures and Opportunities, and it talked about and used the word simulator, of course. It talked about 300 quantum simulators in operation worldwide, which has obviously grown since then. How does that differentiate from what you were just talking about?


Lincoln Carr: Those are early quantum simulators. They are emulators, and they have become quantum computers. The idea of a quantum computer is, it’s much closer to a classical computer. You have discrete operations that happen in circuit layers. From the physics perspective, we would say it’s an interacting quantum system that is discrete in space and time and has local operations. Those local operations are the gates.


You can also think of a NOT gate — like, true, not true — or an OR gate or an XOR gate or an AND gate. Those are the building blocks of classical computers. For the general listener, those are nothing more than addition and multiplication, like 1 plus 1 versus 1 times 1 — it’s like an OR versus an AND. These operations are fancy names for what everybody does in first grade, and probably all human beings on Earth do naturally in their brains, and probably crows and dolphins and lots of other species. That idea is so simple. It would be great if we could turn that into a quantum device and make it do everything. That might not be true, but we’re trying very hard.


Those devices allow control over those gates, over those local operations, that we did not have before. Before, we did a thing to the whole system. We watched it evolve. We did another thing. We watched it evolve. Now we can get in and locally do something. It’s like if I could go in and reroute roads one by one, rather than saying, “Don’t tell too many people, ‘Come to the city today’” and then see what happens. But imagine if I could go in with little barriers and create a different path through the city. That could be an effective way to deal with traffic, rather than just saying, “Less cars on the road today.”


Konstantinos Karagiannis: That’s a good point. Is there a way to extrapolate some of these approaches to more everyday cases, like the ones that people are dreaming about? You brought up the example of traffic, for example, optimisation. What have we learned from this basic approach to more real-world uses?


Lincoln Carr: It’s my opinion, but many people would agree with me: The most important outcome of quantum computers so far is to reenvision thermodynamics. That might sound abstract, but thermodynamics is what makes engines work. Think about cars: They all run off engines. Our whole society, power generation, it all deals with some kind of information transfer or heat transfer, energy transfer — that’s all thermodynamics. Thermodynamics is our power grid. Ideas in thermodynamics are applied to understand human interactions and social outcomes now in what’s called statistical physics. If you’re rewriting those fundamental ideas, you’re rewriting the possibilities of tech.


I’ll give you an example. Imagine that you have a working fluid of an engine, and usually you think of gas, and you imagine heat and things like that in our car. Imagine if your working fluid is pure information. That’s a whole different concept of an engine. These devices are exploring, for example, engines that use information as a working fluid.


Of course, they’re very small, but when we think about nanodevices in science fiction, there’s always these nanobots that take over the world. Hopefully, they won’t take over the world. Hopefully, they do some good things. But if we want to make devices like that, for example, for medical purposes, to have individualised medicine, we need to understand the working principles of those devices. Those quantum computers, the most important thing they do is not that they solve traffic problems, like, maybe one day, they will. What they’re doing right now is rewriting the basic laws of thermodynamics at a small scale. That’s a big outcome.


Keep in mind that classical computers cannot go forward without understanding that. We cannot go forward with computing at all, and our whole society runs off computing. It’s fair to say that quantum computers are essential to the future of humanity — not in the sense of breaking all possible encryption or being superfast, superpowerful computers. Maybe one day. It’s not clear yet. But they’re rewriting the rest of things.


Konstantinos Karagiannis: They’re not rewriting the second law of thermodynamics, because there’s going to be a big problem if that happens.


Lincoln Carr: The second law of thermodynamics involves entropy, and entropy is a classical concept. When you talk about quantum entropy, it behaves very differently. Already, the second law of thermodynamics is modified, in some sense, at a very small level. One of the major discoveries is related to what’s called the Maxwell’s demon problem. Perhaps listeners have heard of it. It’s a fun thing to read about — and, besides, it has the word demon in it, so it’s exciting. Maxwell had this idea that you could somehow overcome thermodynamics if you had someone making some choices somewhere along the line with information transfer, and that was the demon.


It turns out that through quantum investigations, we’ve come to understand that there’s a cost for information creation and for information erasure, and the joint cost of information creation and erasure balances the information equation and allows us to solve these tiny information problems, like this information-based engine. Without that fundamental understanding, we couldn’t move forward. That’s not contained within the second law of thermodynamics in the obvious way.


Konstantinos Karagiannis: It was flawed from the get-go. People back then didn’t realise that that little demon sitting there had to know when to open the door to move one particle to the other side.


Lincoln Carr: And he has to forget things.


Konstantinos Karagiannis: He has to forget. Exactly.


Lincoln Carr: We think of forgetting as a loss, but it actually costs. My colleague Masutu Ueda is one of the people that solved this problem. There’s a few around the world, but I like to relate to his work, and he has good papers on this. He’s a superprominent guy in Japan at the University of Tokyo, and he’s an excellent communicator. I can highly recommend his work, whether you see his talks online or you read one of his papers, and his English is excellent, which helps, but he’s just a good, clear thinker, and solving problems like that is one of the reasons this foray into quantum computing has changed humanity permanently. It is a real next stage in tech.


Konstantinos Karagiannis: How do you feel about continuing forward using machines that aren’t full-fledged quantum computers? Do you feel like there’s still a whole unforeseen evolution to these types of machines we haven’t even thought of? We have roadmaps for how many qubits are going to be in a more traditional quantum computer. But do you think there are engineering tricks and even software tricks on the horizon for getting more out of classical emulation of quantum? Do you feel like there’s something there that’s still untapped that maybe we should be looking at?


Lincoln Carr: I’m going to first refer to the general situation we’re in, which is the Hitchhiker’s Guide to the Galaxy situation — we’re building the computer to teach us how to build the next computer. It’s the computer to make the computer to make the computer to make the computer, which then does the thing. A lot of this is early prototyping. That’s very typical with early prototyping — that you do what we call lower technology-readiness levels. Is there fundamental science to be learned and maybe even some use cases in these prototype computers that are teaching us to make a future quantum computer? Yes. There’s a lot of room and a lot of things to do, and a lot of those things are not so much about quantum. They’re about reenvisioning classical computing.


For example, to make a quantum computer work right now, you cannot just programme something and launch the programme. I worked with Google. I was one of their early-access users on their machine, and I can tell you I had beautiful theories that took into account all the noise and all the lack of error correction and all that and good equations. When I ran my simulation on Google’s quantum computer, the first thing I saw was just, this is nothing. That’s because the real computer doesn’t do what our models do. It has a lot of other factors in it you have to take into account.


In that paper, which was on quantum cellular automata — that’s about creating small-world networks and entangled complexity. Small-world networks are like airport networks, for example, or the internet or the brain. They’re very typical. It showed that they occur in quantum systems. To make that thing work for the first time on a quantum system, I have six or seven major corrections that have to happen that were not my original theories. It took a year and a half instead of three months, which is what I naively thought would happen.


That is because you’re not just programming with software. That’s my model for my code. You’re programming every part of the quantum computer from the top down to the bottom. They call it the computing stack: The bottom is the actual chip and the control of the chip and the material of the chip and how you interface with that material. Then you have all these layers between. Some of them are hardware, some of them are hardware blended with software and some of them are different abstraction layers of software.


Full-stack programming is the only way to programme a quantum computer. It will not work otherwise. Classical computers, we had so much room. It’s very rare you think about full-stack coding, but because we’re running out of energy and memory and bandwidth for computers, we absolutely have to start doing full-stack computing. Quantum computers are helping us to think about full-stack computing — every point of the stack.


Konstantinos Karagiannis: There was just a paper published about something like that that was classical, where you’re doing more parallel processing in the separate cores of the same task. They were getting up to a 1.9x improvement in performance or something like that. There’s still a lot to be figured out there on how well that’ll work. It’s very similar. It’s going right down to that level. It’s a whole new stack approach how they’re going parallel.


Lincoln Carr: Exactly. There are many such innovations in quantum computing that impact classical computing directly, whether it’s photonic computers or Shannon computers, which are probabilistic. Or it’s reversible computing. You can run a superconducting quantum computer cold enough that it doesn’t create more entropy — speaking of the second law — so the change entropy is zero. That’s called reversible computing, but on the other hand, it’s not so cold that you have to make it be quantum. It’s already quite useful. There are many interfaces between those architectures, referring to my paper earlier and the reenvisioning of classical computing.


Konstantinos Karagiannis: I was going to ask you about it in a moment, but we could dive in right now and then switch gears back. That’s the small-world effect for interferometer networks — that paper.


Lincoln Carr: I was referring to the one you asked about that was a roadmap on simulator architectures. But in my personal paper I did with the global quantum AI team and my colleague Elliot Caput — and a fantastic team of students who were obviously key to his success — that is on small-world networks. That uses quantum cellular automata, which is a fun area. When I was a kid, these cellular automata were called Conway’s Game of Life. With just flipping a few squares from black to white in a little grid — like a checkerboard or something — you would see these incredible, beautiful living patterns emerge.


That’s one of the ways they got kids into coding. They would do that, and they would do fractals. You’d see the Julia set or something. Kids would be, like, “I want to code for a living.” I got sucked in through those exciting examples. I still work on fractals and chaos, and I still work on cellular automata. Science communication works. That’s the moral of that one.


Konstantinos Karagiannis: That’s a great example. I’ve seen some quantum Game of Life simulations. There was a display in New York City here, where I live, and they were doing different things, like music and stuff. One of them was like a quantum Game of Life. It’s this idea that there are rules like when you have two cells next to each other — what that means, whether they live or they die. Then, after a while, you start to get complex patterns that emerge. Then they got their own names. People started naming these patterns that would emerge from the system. How does that complex-network-theory idea apply to what you did on the Google machine?


Lincoln Carr: To mention what those patterns look like, for listeners who’ve ever been to an EDM show, you see them all the time because a lot of those kinds of patterns, whether continuous or discrete, as you just described, they’re used to create the beautiful graphics that enhance your experience with music. They’re common. Then you ask how that relates to small-world networks. Small-world networks are a form of complexity, and in particular, this is pretty cool. People don’t ask themselves this. They take it for granted that if they want to get anywhere in the world, they have to change flights only maybe twice. But if you connected airports at random, you would change flights 30 times. It could be bad.   
That’s what happened early on, because there weren’t major airports. You would just go from airport to airport, and to get across the U.S., you’d do these barnstorming flights where you land in fields and you get on the next plane, and it’s similar to switching horses historically. It was time-consuming, but then you had big stables, so there’d always be a guaranteed horse. That idea that you’ve got hubs and that those hubs allow you to shortcut paths, one place to another, that’s one of the main concepts in a small-world network.


Of course, the internet does that. Biology does that throughout the body — the many biological codes, including DNA, but many other kinds of codes in the body: the immune system, etc. There are many kinds of small-world networks throughout our body. The brain uses this a lot. Remember, earlier, I was talking about those local gates and local access and how that’s been a real sea change from those early quantum emulators to what we currently call quantum computers, which are pulsed quantum emulators with local access.


Those current quantum computers allow us to create these local rules. Those local rules can then give rise to this global connectivity, and that idea that simple local rules give rise to global features that are common between human social interactions — the brain, DNA — it’s remarkable to see that in a quantum system. The reason I did that work is because at the time, people were saying, “Quantum systems are too simple. They can’t give rise to that kind of complexity.” I want to show that they absolutely can. That’s the same kind of complexity as we’re thinking about right now. That’s important because we don’t know where that kind of complexity comes from. There isn’t any theory of physics that gives rise to it — we have to cook it up — and yet it’s literally everywhere.


Sometimes, people think it’s a missing principle, like gravity. They call it the complexity principle. Or sometimes people think it might be a reinterpretation, a new understanding of these principles we already have. Either way, I want to show that quantum has to be involved, that it’s not a purely classical or large-scale phenomenon, which is what people had, as a whole, believed up to now.


Part of my personal thrust of my research has been to show that every feature of classical and biological complexity you can find in quantum systems has nothing to do with living beings. It’s nothing like that. It’s a basic principle: the universe. In some sense, you can say that the universe is doing something like cognition — something like the connectivity between airports, something like DNA. It’s doing that at many levels all the time. We notice the living level because we’re living beings. That’s what we like to focus on. We think living things are beautiful. But, in fact, the universe does that everywhere.


Konstantinos Karagiannis: Do you think that kind of approach and learning would lead to quantum systems influencing other systems — for example, in machine learning or something like that? Do you hope for any crossover there?


Lincoln Carr: Yes. We don’t even know what kinds of complexity arise in quantum systems, because the whole field is so new. We didn’t have devices that allowed us to look at things like that until recently. That’s the beauty of these quantum computers. We might not get, like, breaking Shor’s algorithm and breaking all encryption worldwide and hacking into government databases and all the things people imagine quantum computers are going to do. They might do that one day. In fact, it’s even likely they will. But right now, we can explore these basic principles.


That’s what people do with computers at first. Computers weren’t first used for EDM shows. First computers were used to look at basic things. I have a bunch of springs and masses, and they’re on a grid, and I pluck the system. Imagine a piano string or a guitar string, but now imagine that they’re in a square grid. Now, I pluck this grid and I ask, “Do I have a memory of my initial plucking?” It’s about memory in a system like that — one of the very first things people do with classical computers.


In fact, I mentioned fermions earlier. Fermi himself, as a much older person, was involved with this. It’s called a Fermi–Pasta–Ulam recurrence. It was one of the first scientific calculations done with a computer, in the ’60s or ’70s. They found out when they plucked this grid that it didn’t spread out — it actually recurred, and it recurred like crazy in this giant pulse. They discovered a whole new kind of physics that did not involve new principles, but was a reinterpretation of what we already had, and it could not have been discovered without the classical computers.


Then later, we developed the math to support it and all that. Why does that matter? I’ll give you an example: It turns out that in the ocean, every once in a while, an oil platform gets just shattered, just broken in half by a giant wave called a rogue wave. A rogue wave is related very much to those early computational experiments of Fermi, Pasta and Ulam — to understand that little waves all over the ocean can conspire to suddenly create this massive wave that has nothing to do with a storm that will just break your ship or your oil platform or whatever in half. How do you plan for them, and how do you understand them?


Those things occur in all kinds of physical systems, including the brain. That basic principle and that early computation does matter down the line. But it might take decades for that understanding to play out. People would love for quantum computers to solve the rogue-wave problem or some other kind of problem right now. But in fact, quantum computers are more at the stage of “I pluck a grid of strings, and what happens?”


Konstantinos Karagiannis: When I think of emergence and complexity, I’m worried about things like, is there a possibility for machine consciousness or something? I would think someone standing on an oil platform has a more immediate concern when it comes to emergence. There’s a potential for quantum to impact all this. That’s terrific.


To touch a little bit again on emulating these machines, I know you worked with tensor networks in the past. It was quite a while ago. Are you still active in that? Are you seeing any of those approaches bearing fruit? I found that the world of classical computing still protects this 50-qubit barrier. It’s weird. You try simulating 50 qubits on a supercomputer or something, and then, of course, every time you add a qubit, you double the resources. It becomes impossible to get too big there. Then, with tensor networks, you can put as many qubits as you want, but then you’d have to contract the giant mess that you create in the end. Then again, hardware seems to choke. Did you have any thoughts about that? Do you think there’s anything there, or are we going to hit the SAE limits?


Lincoln Carr: You’re asking the right guy, because my group supported the open source code for tensor networks used worldwide for about 15 years. We put it down because industry is doing a great job at it, and I don’t need to compete with teams of several hundred well-funded people. I can go off and do other things, which is great because I did it as a service. Now, I can set that service down and let other people carry it on.


But I do still watch the field closely, and I’ve worked a lot in it. I’ve done thousands of tensor-network simulations. Tensor networks are the idea that quantum mechanics is a big matrix problem. That is like a rack of numbers. Imagine you have a box, you have a grid on the box and at every point in the grid, there’s a number. By the way, every photograph is in fact a matrix because the values of the pixels are in a grid. Every video, every picture, that’s a matrix.When I teach my students matrices, I have them work with their selfie — literally, mathematical properties of their face. It’s a lot of fun.


Konstantinos Karagiannis: Got to keep them interested.


Lincoln Carr: Exactly right. Matrices are very approachable. The problem with quantum is, the matrices get too big. That’s the beauty about quantum. They can deal with very big matrices, and machine learning on images or video. That’s the hope with quantum, and certainly, with very large matrices in general, that’s one of the big computational problems.  
Now, it’s possible to write this giant matrix as a product of much smaller matrices. You can imagine in a face, a selfie, that you wrote your matrix as a product of a nose times an ear times a shoulder times a shirt collar. Now, that product might give you something pretty mixed up in the end, or it might be that you need only a few small matrices to make up an image. That’s about the information content of a matrix.


That is called compression. It’s information compression. You’re taking that giant matrix and writing it as a product over a lot of little matrices. You’re compressing the amount of information you need to support your selfie. Classical computers do that. They take a big quantum matrix and try to write it as a product of a lot of smaller matrices. That sometimes works, and it sometimes doesn’t.


For example, you actually can’t do that in white noise. If I took a selfie and then I randomised it till it looked like an old TV screen from my childhood — I’m old enough where I did see black and-white TV screens that looked like something in The Twilight Zone and were just white noise — if you try to do that, that’s called a random state. If you try to do that and you write that as a tensor network, only in some special cases is that possible. In general, it’s not possible.


Then there are things that have only a little bit of structure, and they’re also very hard to write that way. Then there are things that are super structured. For example, if I had just a grid of boxes, it would be obvious that I could write it as a product over some kind of something that tells me to write boxes, and it would be easy. Sometimes, that’s called algorithmic compression or information compression, but the idea is that you need only a small amount of code to produce this very big, complicated thing.


What you’re referring to is this neck-and-neck race between methods like that related to tensor networks. There are many, because people are very smart and they’re all working on this right now. It’s amazing. It’s going fast. They think a lot about information-compression methods like that and whether that can be used to beat a quantum computer. Why does that matter? Because you’re improving classical algorithms. The number-one effect of quantum computers on classical computers is to make the classical computers better, especially the algorithms.


What I’ve been arguing throughout this podcast is that it’s also going to improve the hardware. That hasn’t happened yet, but it’s coming very soon. But it certainly improved the software, the algorithms, already. Now, can a classical algorithm always beat a quantum computer at the 50-qubit level? No, definitely not right now. It’s easy to write down cases where that’s not true, but just a lot of times, they’re not the interesting cases. The big question is, what are the interesting cases?


I mentioned a wind tunnel a while ago. If I want to understand something like how an airplane flies, if I want to make a better airplane, that’s solving what are called Navier–Stokes equations. If I want to solve Navier–Stokes equations, the equations for fluid dynamics, there’s an X Prize for this problem. If I can solve that with a quantum computer more efficiently, then everybody’s going to buy the quantum computers. But right now, most of our cases are weird cases. They’re not cases that matter physically for applications like that. They’re more mathematical cases or computer science cases that are very theoretical.


Konstantinos Karagiannis: Great to hear your take on it. That’s terrific. They have a lot of potential to solve problems now, especially in the areas of compression, of course — things like SVD, other approaches. We can make things much smaller, especially with edge cases and edge computing.


Before I let you go, I know you were involved with NIST for 20 years. I wanted to get your take on what you did there. Was any of it involving cryptography, or was it purely more on the R&D of developing a systems approach?


Lincoln Carr: Exactly right. They’re both highly regulated application areas, it’s probably going to take about five years, even though, in a sense, it works. The navigation system is not accurate enough, but it’s more accurate than nothing. The MCG system creates real videos of the magnetic field of your heart. But more studies are required — clinical trials are required to map the images we’re generating to actual diagnoses. In a sense, the tech kind of works already, but the application has a lot of other complexities beyond the fundamentals of the tech.


Konstantinos Karagiannis: I want to give a plug for the national labs here because I worked at four national labs in the U.S., then at CERN. Those kinds of environments are fantastic places to get science done. It was my privilege to work at NIST. I was a NIST associate, so I was out there in summers and then continued to collaborate. It’s not like I was in NIST Central. But I like NIST. At some point, I had a job offer there, and I settled, for family reasons, in Colorado, but I still feel closely connected.


The mothership is out in Gaithersburg, but we have a little spaceship out here in Boulder, which has a few Nobel Prize winners. It’s a pretty powerful little spaceship with NIST Boulder. I get to go over there sometimes. NIST does a lot of fantastic things in quantum, from hardware to software, from cryptography to standards.


The part I was involved with is very much in the area of quantum emulators. There was a code at NIST created by one of the lifelong experts and early inventors of computational physics, Barry Schneider. Then that little code propagated its way into a slightly larger group of Charles Clark, and then they didn’t want to maintain it. Then I took that code and I rewrote it and rewrote it and rewrote it, made it very big, and, with their agreement and support, turned that into what’s called matrix-product-operator and matrix-product-density-operator codes. Those MPO and MPDO codes are what eventually went into my open source code. Those codes, they also do long-range problems.


I talked about those local rules. If you’re working with solid-state elements that go into a chip, it makes sense that their crosstalk is fairly low — a piece of your chip far on the left is not typically talking to a piece of the chip far on the right. But if you’re working with the building blocks of nature — atoms, ions, photons — those things tend to talk very long-distance because of electromagnetism.


One way to understand that is, radio waves, they’re everywhere. Microwaves, like for your phone, they’re everywhere. Electromagnetic things, spread out. Typically, they spread out more or less like one over the distance squared. If you remember something like how a sphere grows the surface of a sphere, for those people who may unfortunately recall their high school geometry class, you might remember that there’s the formula 4πr2 for the surface of a sphere. That r2, that’s telling you how those things are growing.


That means they’re very long-range. Solving long-range problems is very tricky with those tensor-network methods because before, I wouldn’t think about my ear and my nose as being close to each other per se in a face. But if somehow, my ear and my nose are interacting, then you get these long-range effects. Those codes were designed to do long-range effects and deal with what are called open quantum systems, interacting with an environment, and deal with going from states to operators, which is a little bit technical.


That was one of the big things I did at NIST. I also worked a lot on solitons, and solitons are like those rogue-wave examples that I gave. In fact, they’re everywhere. It’s the number-one thing you see when you look down on the Earth — like with Google Maps, and you look at the oceans, you’ll see these waves that look like lumps that are humps that are moving around on the surface of the ocean. Those are solitons.


Lincoln Carr: Exactly. NIST was a great place to do those kinds of things. I worked with lots of people there over the years, and I continue to collaborate with them. Also, in my government position, I worked a lot with NIST around national standards and international standards for post-quantum encryption. I can’t emphasise enough how much people there give to the country.


Konstantinos Karagiannis: Right now, as I mentioned, we’re at the post-quantum cryptography aspect. They’re taking on a pretty difficult concept there, too — how to get everyone to migrate over. Yes, absolutely. Super important.


With that, I feel like I could talk to you all day. Thanks for coming on. I know you’ve written lots of other interesting papers, too, and you’ve talked about things like the importance of universities creating undergraduate programmes for quantum and everything. What are two or three things that universities listening should be considering for training their future quantum workforce?


Lincoln Carr: There are six pillars to the National Quantum Initiative, and five out of six are a big success, and one is lagging. That is the workforce piece, unfortunately. When you think about workforce, it’s about educating the general citizen. It’s not just about educating toward a job. Educating people for careers, for 20-year careers, and not for getting just their first job, that’s what matters.


When you think about the quantum workforce, imagine, you have to educate people for the entire future of computing. You have to educate people to be able to talk to our legislators and our dedicated civil servants and our CEOs and our artists and writers. How do you create a person who not only can solve a quantum problem but also will be able to be flexible and adaptable in this rapidly changing landscape over the next couple of decades? That’s a big educational problem, and it’s one that we have some hints of how to solve. But there’s a lot of innovation still needed to do that properly. It’s about the future of engineering, actually, not only quantum. That’s something I work on a lot, and if folks would like to ask me about it, I’m happy to address those things. Feel free to reach out to me.


Konstantinos Karagiannis: Great, thanks. And your info will be in the show notes. Thanks so much for coming on.


Lincoln Carr: Thanks.


Konstantinos Karagiannis: Now, it’s time for Coherence, the quantum executive summary, where I take a moment to highlight some of the business impacts we discussed today in case things got too nerdy at times. Let’s recap.


In computer science, a simulator, or simulation, typically runs on a classical computer. An emulator, or emulation, acts like a copy of something. You can simulate winds on a computer programme and have a simulated plane fly through them. You can also emulate winds by building a wind tunnel and having a small physical model plane experience the airflow.


Except for in rare experiments, quantum computers are not currently error-corrected. This means NISQ machines are a type of emulator that tries to act like perfect qubits and gates. Lincoln Carr says we’re still building quantum computers that will teach us how to build better quantum computers, in a sense.


Quantum simulations and emulation have already taught us much about science. About 20 years ago, ultracold experiments showed how sociable bosons could act like solitary fermions. We also learned about the dynamics of phase transitions at ultracold temperatures. Think water to ice and back, but far colder. We’ve also expanded our knowledge of thermodynamics, which can be applied to information. For example, fluids in a car engine behave a certain way with heat. Information can be that fluid.


This isn’t a new concept. The Maxwell’s demon thought experiment showed that a mythical being can decide which particles of gas pass to one side or another of a system, thereby decreasing entropy. This turned out to be incorrect because the information learned and forgotten by the demon is part of the thermodynamic system. Entropy still increases, and the second law of thermodynamics is protected.


Complexity is a major area of Lincoln’s interest. Anyone who has seen Conway’s Game of Life knows about emerging patterns that appear out of relatively simple rules. In the real world, things like solitons, or rogue waves in the ocean, are potentially deadly examples. The hope is that quantum computing will help predict these anomalies.


He’s also working on smaller networks or interactions that could affect code down the quantum stack. Lincoln has created numerous tensor networks as part of his work. These are ways of handling large matrices of numbers and the math between them, such as dot operations. These are popular for types of compression but can also be used to simulate quantum gates on a classical computer. Such approaches have already improved algorithms and software and may help improve quantum hardware in the future. In fact, if there’s one point to leave you with, it’s that most of the discoveries you heard about that seem science-only in this episode could have real-world implications in practical applications as we build toward our fault-tolerant quantum systems of the future.


That does it for this episode. Thanks to Lincoln Carr for joining to discuss his work, and thank you for listening. If you enjoyed the show, please subscribe to The Post-Quantum World and leave a review to help others find us. Be sure to follow me on all socials @KonstantHacker. You’ll find links there to what we’re doing in Quantum Computing Services at Protiviti. You can also DM me questions or suggestions for what you’d like to hear on the show. For more information on our quantum services, check out Protiviti.com, or follow Protiviti Tech on Twitter and LinkedIn. Until next time, be kind, and stay quantum-curious.