The quantum physicist Charlie Marcus — a principal researcher at Microsoft Quantum Research and a professor at the Niels Bohr Institute of the University of Copenhagen — is engaged in one of the most ambitious quests in modern technology: the creation of a true quantum computer. In this episode, Marcus talks with host Steven Strogatz about why facts are never complicated, what working in a music store taught him about doing science, and the parallels between the use of knots in early Mesoamerican culture and his quantum computing work today.

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Charlie Marcus: I want to tell a story about how man is able to create things that never existed before, and that the study of science is now not just the study of naturally occurring phenomena in the absence of a human mind creating them.

Steve Strogatz [narration]: From Quanta Magazine, this is The Joy of x. I’m Steve Strogatz. In this episode, Charlie Marcus.

Steve Strogatz: You’re singing the song of the triumph of human imagination as expressed through science. So, it’s not just wild, untamed imagination. It’s imagination constrained by observations, by experiments, but ultimately … imagination.

Strogatz: Charlie Marcus is a quantum physicist who I think is doing some of the most exciting work today on the effort to create something that doesn’t exist yet, a quantum computer. Actually, Charlie and I started our careers together back when he was a grad student and I was a postdoc. We worked on something pretty esoteric called the dynamics of charged density waves.

Strogatz: You know, I think it’s about half a lifetime ago that we worked together scientifically.

Marcus: It feels to me a little bit like — especially since I have sort of a poor memory of my childhood, in a way it feels like more than half of my scientific life ago.

Strogatz: Has your memory gotten more detailed?

Marcus: For my life, let’s say half of my life ago, because that first half sort of barely counted. I don’t have this vivid childhood that a lot of people do, except for the music store.

Strogatz: Okay. Maybe you better tell us, what is this music store? What were you doing?

Marcus: Oh, boy. Yeah. So, when I was in high school, I got a job working in a music store, and I was selling guitars and fixing guitars. I was playing a lot of music then. And it was really hands-on. It was like people coming in with broken musical instruments. And it was kind of the end of the hippie era, and it was all filled with hippies, and I completely latched onto it. And the weird thing was that I had incredible responsibility for a high school kid. Like, I would open the store on Saturdays, and go to the bank, and get the money and put it in the cash register, and run the whole store until closing time.

Strogatz: That makes me think that this is… When you say music store, it’s partly the job that you were doing when you were helping people is partly electronics and partly mechanics.

Marcus: Mostly mechanics. I don’t think there was any electronics involved. It was kind of acoustic instruments that was being focused on.

Marcus: Yeah. But at home I had an electric — I was already doing electronics at that point.

Strogatz: That just to me feels very emblematic or representative of your can-do attitude about making things work, fixing stuff. And it’s not that you were doing that back in the music store.

Marcus: I think what was great about our working together — and actually, there’s a part of the story, which I don’t know whether you remember, but it has become, as you say, for me, emblematic of something else entirely. And with other good friends later in life. I’ve used this idea over and over again, but it comes from you. But you said we should collaborate on something. And I said, “Well, what?” You said, “Oh, I don’t care.” Like, who cares? What a dumb question. It doesn’t matter what we work on.

Marcus: Yeah. It was sort of like, let’s collaborate on something, and we just — it’s like an arbitrary choice. The fun is in the collaboration. It’s not like there’s any great problem that needs to be solved that your skills —

Marcus: — and my skills will solve it. It’s just, “pick something, work on it for the sheer pleasure of working with somebody on something.”

Marcus: That was a new idea to me, and that came from you. And I really liked the idea. The idea is that somehow what we’re doing here in this activity is such a human enterprise that it’s not like there’s this God-given list of problems that needs to be solved, and by hook or by crook we’re going to get to the bottom of the list. There is no list. There’s only us. And that you can just… Once you have a friend or a partner, you can say, “Let’s just jump in and do something.” And it turned out it was a really great problem. But it arose not because this was some problem out there that needed to be solved. It arose because it was a friendship that needed something to fool around with.

The problem that I got interested in was delay, and how would delay affect dynamics, and whether it would create chaos or whether it would always create oscillation.

Strogatz: So, “delay” meaning…? Here what would that mean?

Marcus: Well, let’s say you have this massively interconnected complex system that contains elements that, in the parlance of the field, is called frustration. Meaning that there are loops of interconnection. So, A connects to B, B connects to C, C connects to D, and D connects back to A again. And that they may be doing something in which A is trying to turn B off, and B is trying to turn C off, and C is trying to turn D off, and D is trying to turn A off. But if A is off, then B goes on.

So, the whole thing just runs around in some circle where everybody’s trying to flip the other one to the opposite sign. That kind of thing, which is called frustration in these complex circuits, is really at the essence of why, for instance, neural networks can have complex dynamics and an infinite number of ground states. A lot of the richness has to do with loops that contain frustration.

Strogatz: For people that haven’t thought about frustration, of course it’s an ordinary word that we all kind of know what that means.

But imagine you’re friends with a couple, they’re a married couple, and then they have this bitter divorce. It used to be that all the relationships were positive. You like each of them, and they liked each other. But after the divorce, when they now hate each other, it’s often difficult. That’s a frustrated triangle. Because you can’t really stay friends with both of them, because they don’t want that. They usually want you to choose sides.

Marcus: Right. Exactly. Perfect example.

Strogatz: That triangle has gone from un-frustrated to frustrated after the divorce.

Marcus: That’s great. That’s a great example. Now, there’s a new element, which turns it from being a frustrated static problem. Who are your friends going to be for the future of the relationships, to a dynamics problem, meaning something like, how on a weekly basis do I manage my friendship with the exes, when the information that you get about he said she said is delayed in getting to you?

And you get these runaway conditions, where you keep picking loyalties, and you get some piece of information. You say, “Now she’s a jerk. I’m going to hang out with him.” But then a week later, you get some other information that proves that, no, no, no, actually, he was the one that said that. So, you say, “No. Sorry. I was wrong. He’s the jerk, and I’m going to hang out with her.” You can get situations where, because of the delayed propagation of information —

Marcus: — what ends up being frustration, ends up being something oscillatory.

Strogatz: Yeah. So, you’re doing an electronic —

Marcus: That was a problem —

Marcus: — and it’s a hard problem to solve on a computer, because you need to know the whole time history before you can solve how a delay differential equation, differential equation system with delays in it works. And it was just easier to just build it. So, there were — in fact, the funny thing is, this connects us back to the music store, because there were electronic chips that are used in the music industry to create the sound of, like, a concert hall with echo.

Like, if you didn’t have an acoustic room where you’re being recorded right now, or I didn’t, and instead you were in a great church or something like that, it would be echoey. And they make chips that you can buy that create the part of the microphone circuit. They create the sound of an echo. So, I bought a bunch of these chips. I just wrote to the company, and I said, “Can I have a whole bunch of these echo chips?” And I built the neural network, and then inserted the echo chips into the neural network circuit. And then it has a little switch on it; you control how much echo there is in the circuit. So, I could make the circuits show these oscillating patterns just by turning on the church sound.

Strogatz: I never really appreciated that. So, you’re not pulling my leg. That something about what you learned through your music store experience did directly come in handy in this work.

Marcus: Yeah. Absolutely. Those chips were the… Like an electric guitar, you can think of some songs where it sounds — there’s some echoing sound, and they do it with those chips.

Strogatz: Charlie eventually combined this very hands-on work that he was doing in the lab with something that people tend to think of as incredibly abstract and theoretical and kind of bizarre: quantum physics. Quantum physics deals with tiny particles. Particles the size of atoms or even smaller and how they behave. It turns out that they behave in a way that’s really hard for our macroscopic human brains to understand.

When we try to come up with language to describe what’s going on down there, we end up saying almost nonsensical things. Like, it’s as if particles aren’t really one way or another. It’s like they’re both. Things aren’t just black and white in the quantum world. You can be alive and dead at the same time, or on and off. It’s all sort of indefinite.

Marcus: When I tell people what I do and say, “I work in quantum computing,” or, “I work on quantum physics,” the standard answer, it’s almost like people are preprogrammed to give this answer is, “Oh that’s really complicated. I never understood that.” Okay. But then let’s say instead your wife says, “I’ve got great news. I’m pregnant.” Nobody ever says, “Oh that’s really complicated. I’ve thought about that, and I can’t understand how that could possibly happen.”

Strogatz: That’s so complicated.

Marcus: If you want to talk about things —

Strogatz: How does that work?

Marcus: — that are complicated, there’s a lot of complicated stuff out there. Like, where do babies come from? And how do brains work? Forget about brains. I mean, how does your liver work? Those things are really complicated.

Strogatz: Well, with the babies, is it because it’s happening all around us every day? It’s so commonplace, we just confuse familiarity with simplicity, or something like that?

Marcus: I think there is something else. I think that there’s a kind of intentional mythology created within the scientific community. It’s like this kind of declared profundity or declared complexity or declared — it’s just declared. That’s right —

Strogatz: That’s part of the charm, right?

Marcus: You just declare it as, “oh, only three people in the world understand it” or “nobody understands it” or whatever. You just declare that. But it’s just not true. And in fact, I know that it’s not true, because I know that I’ve said things to people where I know what I’ve said isn’t very hard, and I know what I’ve said could be understood. Let’s just say relatively like I know that I’ve said a lot of harder things. And at the end they’ll still say, “Oh that’s so confusing.”

It’s frustrating. What? Which thing that I just said was confusing? There’s no fact that’s confusing, and it’s not that confusing.

Strogatz: Okay. Wait a second here. I have to push back. For all those folks out there who are thinking, “Look, I know quantum mechanics is confusing, people talk about it. It’s a wave, and it’s a particle. It’s up, and it’s down. It’s alive, and it’s dead.” So, there’s this counterintuitive —

Marcus: It’s just [BLEEP]. It’s just [BLEEP]. It’s just a big no.

Strogatz: A big no from you.

Marcus: Someone shows you a squirrel, and you say, “Is it a rat? Or is it a cat? I don’t understand. Is that a rat? Or is it a cat?” The answer’s it’s not a rat or a cat. It’s a squirrel. Someone says —

Strogatz: Yeah. I’m with you there.

Marcus: “Is it a particle? Or is it a wave?” It’s neither one. Who told you you have to force it into being something like a cat or a rat? It’s neither one! Why are you putting it into some box that you have to put it in? It’s some new thing that you haven’t seen before. I go to a new city, and someone says, “Is this Paris? Or is this Berlin?” You say, “It’s neither one. It’s a different thing.”

Strogatz: Hold on. This is a little bit glib here. I mean, I want to agree with you.

Marcus: I don’t think I’m being glib, as long as you’re willing to learn that something exists that you didn’t know about before. That’s the only thing that’s being asked of you.

Strogatz: Wait a second. Your squirrel sometimes acts very much like a rat.

Strogatz: I mean, like light, which can be both a particle and a wave sometimes, really seems like a particle, and sometimes it really seems like a wave. But sometimes it seems like this third thing.

Marcus: Exactly. It will eat cat food.

Strogatz: Is that the point?

Marcus: If you put cat food in front of it, it will eat the cat food. You say, “Oh, well, it must be a cat. Look. It’s eating the cat food.”

Marcus: But it’s not. It’s just eating cat food. Or if you put it in a maze it will run through the maze. You say, “Oh, it must be a rat. How could it be going through a maze if it’s not a rat?” I really do think that it’s this new thing, and as long as you’re willing, as long as you’re willing to say that “I can have a new experience. I can see something that I haven’t seen before.” Then there’s nothing hard.

Strogatz: What’s your manifesto here?

Marcus: What I would say, at a sort of manifesto level, is what is our process in general for distinguishing truth from falsehood? First of all, do we accept the idea there are some things that are true and some things that are false? This is a tricky time for such a notion. But let us say that there is a notion that something can be true and something else can be false, something else is wrong. How do we decide? Well, we observe it, and we just see what it does. And then we try to describe it.

And I think this is what’s happened in quantum mechanics, and people — even as recently as within the last few months, have people said that they just don’t believe quantum mechanics. They think that it goes in the category of false ideas. They think that there’s essential aspects of quantum mechanics which are not captured by our physical description of quantum mechanics, that there’s things missing.

And invariably what this conversation — how this conversation evolves into something like, “Well, there are very abstract experiments that can be done with Bell inequalities and measurements and entangled.” And I usually say, “Stop. Stop. Stop. Stop. Stop. If quantum mechanics didn’t work, that stop sign wouldn’t be red.” Red paint works because of quantum mechanics.

Strogatz: Tell us a little why you’re thinking. I mean, I can guess. But what do you mean?

Marcus: What I mean is that our understanding of everything in the world, those things that we’re able to understand — red paint. Why is red paint red? Because there’s some chemical in it, and that chemical has a resonance, and if you want to understand how that resonance comes, you’d better understand that molecule. If you want to understand why that molecule has a resonance in red, you better solve for the eigenenergies of that molecule. And if it’s a small enough molecule, you could do it. But even if it’s too big for you to literally solve that molecule, you certainly believe you understand what’s going on. And the origin of its red color is fundamentally quantum mechanical.

And if you didn’t believe in quantum mechanics, you don’t have to do a complicated experiment in order to verify quantum mechanics. You can just say, “How do I possibly understand anything that I’m experiencing?” And more even than red paint, because red paint would exist even if we didn’t understand quantum mechanics. But let me give you an example. Like an LED. That shines every time you turn around, there’s another LED blinking at you.

Strogatz: Sure. I’m looking at one right now.

Marcus: That thing doesn’t occur in nature. There are no LEDs in nature.

Marcus: Someone had to understand —

Marcus: — how to build an LED and make it work, and make it red, and make it green, and make it blue, and make all those colors work. And that’s all quantum mechanics. It all works. It all works just fine. And that’s why it’s actually more interesting to look at an LED than it is to look at red paint because you don’t need to understand aerodynamics to see a bird flying. You don’t need to understand quantum mechanics to see red paint.

But you do need to believe in quantum mechanics if you think that someone designed that LED, and they did. So, what is the simplest problem where quantum mechanics would show up? And it would be something that could be in one of two states. Not everywhere. It can’t be a position in place because then it’s an infinite number of states.

So just reduce it to its simplest element. It could be in one of two states, which you could call on or off, but there’s nothing particularly on or off about them. They’re just A and B. They’re just two different states. And then what quantum mechanics says is that the state that that system is in is not determined until it’s measured. That it will be in a state that is described quantum mechanically as a superposition of those two states.

Strogatz: It reminds me of your squirrel and your rat and your cat.

Strogatz: Superposition is a third — it’s like something can be not on or not off.

Marcus: I don’t want to say on and off because on and off sounds a little — I want them to be sort of similar to each other like the two states. On and off are kind of different. Let’s call them A and B. The essential element of classical mechanics says that if something can only be in the state A or B, then even if you don’t look at it and you don’t know; it is in either A or B. Those were the rules. The rules of the game were that it had to be in either A or B. So, if you accept those rules, then you say, “Okay. Now I’m closing my eyes, what possible states is it in?” And you say, “Well, you just told me. It can either be in A or B.” Good. So, nothing complicated there.

Quantum mechanics introduces a new possibility to that list. So, I guess you would say it’s a third thing, although it’s a third thing composed of the first two, which is that you can say that it can be a little bit of A and a little bit of B. And so far, so good. I don’t know that anybody is now having a heart attack listening to this. I mean, do you? Do you think if I say, “Well, it could be a little bit of —.” Like new rule is, it can be a little bit of A and a little bit of B. And maybe if you’re the kind of person who likes to force it into things you already know, then think of things that can be a little of something and a little bit of something else.

Strogatz: Oh yeah. What are those? Can you think of any?

Marcus: What’s an example of something? Orange is a little bit of yellow and a little bit of red. An Arnold Palmer is a little of lemonade and a little bit of iced tea.

Strogatz: That works very well.

Marcus: Nobody’s going to say, “What, an Arnold Palmer, I don’t understand.” How could it be iced tea and lemonade? Everybody understands that. Okay. Good. So, it’s this new category of thing. But now there’s something — there’s a new rule, and you have to accept the new rule, and this is something, it’s called apostulative quantum mechanics, which means it’s not really derived from anything. It just appears to be a fact.

And when you say it appears to be a fact, it means if you do a whole bunch of experiments and you take this fact to be a fact, you keep getting the right answer to all of these experiments.

And so, it’s not something which is supposed to make sense. That’s not how we got it. We didn’t get it because it makes sense. We got it because if you say this is true, then the predictions of all of your outcomes will be valid, and here it is. That if you measure something with an apparatus that is capable of giving, let’s say, only one of two answers, then the quantum system will give you an answer to that particular question. The simplest case that’s familiar to us is polarizers. Like polarizers, that your sunglasses can let light through. If you take polarized sunglasses, half the light gets through.

I don’t know whether it’s ever bothered you to ask the question, which half? Light’s on its way. It’s coming to the glasses, and half of it’s going to get through, and the other half is, it’s not going to get through. Now, I’m one little particle of light — well, I’m using language again, but I’m saying some bit of light that’s going to try to get through. Am I the lucky guy who gets through or the unlucky guy who doesn’t get through?

Now here’s the postulate of quantum mechanics, which is if you ask a question — like “Do I get through or not get through? Or am I oriented north-south, or am I oriented east-west? Or am I in A, or am I in B?” — that the apparatus will determine what answer the system will give. So, the system can have many answers available, an infinite number of answers available.

The simplest case is this orientation business of the polarizer. Orient it north-south, and it’ll answer, “I got through that.” Orient it east-west, and it will answer, “I got through that.” So, the quantum mechanics system is one in which it will answer the question that’s asked of it. But it doesn’t have a gigantic dictionary on board to look up, “If you ask me this question, I’ll give you that answer. If you ask me this question, I’ll give you that answer.” It just kind of makes up an answer irrespective of what question you ask.

Strogatz: I’m just having a little bit of an eastern philosophy moment here as I’m listening to it. Because it’s very cool, this whole thing. This is partly I think why you get books like The Tao of Physics. Once, when I was giving a lecture about Taoism and its relation to chaos theory, I happened to meet a scholar of Tao, and he said, if you ask, “What is the Tao?” he said, “It’s undifferentiated potential. It’s all possibilities wrapped up.” It just seems like that’s a close notion to what you’re talking about. This idea that this quantum system has all these possible — I can’t say it like that.

Marcus: No. Look, I think that we’re aligned.

Strogatz: It’s got this —

Marcus: We’re aligned, Steve, in the following sense. My statements up until now have been that the difficulty that people have with quantum mechanics is that they bring a certain world view to the problem. And it certainly is the case that other cultures might’ve gotten it righter. That we can now in hindsight say, “You know, this view of how the world works is actually much closer to how we think quantum mechanics works than the other notion of everything being causal and everything being predetermined.”

Maybe the American idea of “if you slip and fall on the street, it’s somebody’s fault.” Nothing just happens. Everything is causal. You wouldn’t have fallen unless some other guy would’ve … put his hose, and it would’ve frozen overnight and made the ice, and you could trace it back. And then you could sue the bastard. So, the idea of there being causal relationships between everything that happens is a philosophy. And you’re saying that Taoism may just release that causal change. I’m okay with that. I think that that sounds right to me.

Strogatz: After the break, Charlie tries to untangle the Gordian knot of building a quantum computer by actually using knots themselves.

Strogatz: So, why are scientists like Charlie trying to build a quantum computer? Well, you have to think about what an ordinary computer does. It operates on zeroes and ones. Its transistors are on or off. It’s just one state or the other, binary. And an ordinary computer just chugs along, one calculation at a time, with this kind of binary information.

But a quantum computer wouldn’t be limited like that. It would have a gift of being indefinite. That would mean it could explore many possibilities and do many calculations all in parallel at the same time, which would give it the potential to crack currently uncrackable codes and solve enormous problems that have been completely out of reach.

Marcus: These are problems that are just impossible, or they’re past their exponent, where it’s age-of-the-universe type characteristic times to solve them, and you just can’t solve them. There is no machine that will approach them. So, you’re back to experiment again. You could ask the same question, is there a room temperature superconductor? Wouldn’t that be nice? Wouldn’t it be nice to have all of our levitated railways have to be operating at room temperature?

There’s certainly no theorem in physics that says that all superconductors have to be ultra-low temperature and a pain in the neck to achieve. There’s no malicious god who’s preventing us from having a room-temperature superconductor.

But then you say, “Well, where do I start looking?” I don’t know. You have some general principles you might want to use to motivate you, but you can’t calculate any of that stuff. It’s too complicated. So, there are —

Strogatz: You mean, if you’re trying to design one in the computer, since we know the basic principles.

Marcus: You design one in the computer because there’s a big periodic table, and it’s not going to be pure elements, and it’s not going to be the binaries. Those have all been checked. Then again, it’s just too hard to start trying everything in the laboratory. There’s this crazy and funny and interesting story about magnesium diboride. I don’t know if you’ve heard this.

Strogatz: That one? Of course, I haven’t heard it.

Marcus: It doesn’t go that well at cocktail parties. There was a chemical called — and there still is — called magnesium diboride. And you could buy it from the Alfa Aesar catalog. It was just a chemical. It was on everybody’s shelf. Every chemist had —

Marcus: — magnesium boride on their shelf. But it turned out it’s a high-temperature superconductor. Look, it’s magnesium diboride. It’s two borons and a magnesium. It’s not that complicated.

Strogatz: Sounds almost as simple as something can be.

Marcus: That’s like water.

Marcus: Right. So, here’s this high-temperature superconductor that’s been sitting on every chemist’s shelf for 100 years.

Strogatz: Yeah. And besides high-temperature superconductors, there are lots of other problems that only a quantum computer could solve. Like, what kind of material absorbs carbon the best? Or what would make the best fertilizer? Or, as Charlie explains, what if there’s something that could replace a rare metal that we’re currently using all over the place in our electronics?

Marcus: Capacitors that are… Most of our electronics contain tantalum. And tantalum is a great element for — you probably spend your whole life not appreciating the value of tantalum.

Strogatz: No. I have never even thought about it.

Marcus: Right? It’s just some dumb thing in the middle of the periodic table that you skip over, unless you’re listening to Tom Lehrer or something.

Strogatz: In his song about the periodic table?

Marcus: But tantalum, but if you lived in some of these war-torn areas in Central Africa where mining is — sort of the analog of blood diamond is blood tantalum.

Marcus: Because it’s used in capacitors that are inside of all these microelectronics.

Strogatz: So, you’re saying the world’s supply —

Marcus: There was an effort — this may be slightly old news. Forgive me if it is old news, because I think that there was an effort to get tantalum out of these capacitors, and maybe industry, since the last time I read about it, has been successful in getting tantalum out of these capacitors. And it’s no longer part of it. I don’t know. I actually don’t know about that.

Marcus: Here’s a material that has been the basis of wars and that’s part of our capacitors in all of our modern electronics. Is there another element or combination of elements that we could replace tantalum with that works just as well? I don’t know. And these are hard, hard, hard computation problems. So, here I can make a very clear statement. There are some problems that it’s not known whether they are beyond quantum computing. But problems that are intrinsically quantum mechanical, where, for instance, whether something becomes a superconductor or not is a quantum mechanics problem.

Marcus: Whether or not this molecule is red is a quantum mechanics problem. These are intrinsically quantum mechanical problems.

Marcus: And so is building a machine that is, at its heart, a quantum machine. And exactly how it works and exactly what algorithms it works on, that’s not known. But these are problems, which are quantum physics problems.

Another way of saying it is that they live in the very high-dimensional space that quantum mechanics occupies. This is maybe getting a little abstract. But they live in this very high-dimensional space that quantum mechanics occupies instead of living in the classical three-dimensional space that we normally inhabit.

Strogatz: The big obstacle of building a quantum computer starts with something called a qubit. Qubits are the building blocks of quantum computers, and they are very delicate, very fragile little finicky objects. Any little noise or jiggle from the environment can ruin them and cause them to collapse into a normal, classical bit. Something binary, meaning something that’s A or B. And then that ruins the whole quantum system. You’ve got to stop them from getting accidentally measured into being either A or B.

But, unfortunately, there are all kinds of things that can lead to this sort of accidental measurement.

Marcus: What you can say is that any encounter — it could be simply that when an atom gets near an atom, or when something gets near something — that it raises its energy a little bit. Like, let’s say two balloons, that you rubbed them on the wall, so they’re staticky. Okay. And I bring them near each other. You can say that’s not an encounter because nothing happened. But, if the electricity on one felt the electricity on the other, so that the overall energy of that two-balloon system was raised because all those charges were then put near each other. That would be enough of an encounter that if you took them back apart again. The quantum mechanics would remember that encounter. So, all of a sudden, everything gets out of phase and out of whack. They know that they encountered something.

Strogatz: So, let me give a little visual here, because I have something in my head, and I bet you have something similar in your head. But unless we say it explicitly, it may not be in our listener’s head, which is that when you speak of phase, I’m picturing a point running around a circle abstractly.

Marcus: Exactly. On a clockface, a hand of a clock.

Strogatz: Yeah. And so, when you put the balloons near each other, that little abstract dot runs around faster and makes more laps than it would’ve otherwise.

Marcus: If it raises the energy it runs faster, and if it lowers the energy it runs slower.

Strogatz: Okay. So, it’s like if that thing were a clock, actually — like the hand of a clock winding around, you’d see the change in phase as a change in time. That’s what you meant by getting out of whack or out of sync.

Marcus: Absolutely. They would get out of phase, proportional to how long they spent in that encounter. And so, almost anything that constitutes an interaction — that needn’t be one electron jumps off of one balloon and goes onto the other balloon. That’s also such an example, but it’s more than what one needs. We’ll create when those two things are separated and remain in some quantum mechanical state, something which is entangled. So, entanglement became this kind of known phenomenon about what happens when two parts of a system were at one time interacting.

Marcus: And then, even if you remove the interaction, they have a memory of having done that. Now, what happens in quantum mechanics is just like putting a picture of yourself in a compromised position: the e-mail to a friend saying, “Whatever you do, don’t share this picture with anybody.” That’s how long it takes for the picture to be all over the internet. And it’s the same situation with entanglement. You say, “Well, this photon, this electron or photon or whatever, are entangled.” But then that photon goes and gets entangled with somebody else, and that one gets entangled with two more. And pretty soon, in about a nanosecond or something, the whole universe knows and can download the picture when they want to.

Strogatz: Oh wow. I never knew this. It’s Telephone, a big game of Telephone.

Marcus: It’s a big, uncontrolled, runaway entanglement —

Marcus: — that is unbounded, and suddenly, quickly cascades out as far as it can, and that’s what I mean by measurement.

Strogatz: Thank you. Beautiful. So interesting.

Marcus: You need to make some system, which when you’re not — when you intentionally don’t disrupt it, it’s hands off. But when you do want to adjust it, you can adjust it pretty fast, and that the figure of merit of how good of a qubit it is, is the ratio between how long it remains unmeasured by the environment when you’re trying not to measure it divided by how quickly you can manipulate it when you do want to measure it. If you can get that ratio up into the range of 10,000 or something like that, then it becomes possible to do something called fault tolerance.

Fault tolerance in a quantum mechanics context is, if you can achieve this number — say 10,000 or whatever it is. It depends a little bit on the qubit. Then you can make a system of, say, two qubits or three qubits or four qubits or five qubits, more qubits that last longer than the constituent parts. There’s a crossover, a threshold, and I think that most of us have experienced in our lives something in which — you know, we’ve been on committees, faculty committees or whatever, our work committees. And sometimes having six or seven people on the committee makes the committee better and sometimes having six or seven people on the committee makes it worse.

Marcus: Generically, it makes it worse. It’s harder to get to answers. You wish all those people would just leave the room and just decide it on your own. But sometimes having four or five people in the room actually lets you get places you couldn’t get otherwise.

And that’s true with qubits. When you get to that threshold, then you can scale your system into the realm in which you can have an arbitrarily long-lived effective logical qubit. And what’s amazing is, this is all kind of verified math. It’s not controversial like quantum mechanics itself, but nobody’s done it.

Strogatz: Nobody’s succeeded in making it yet.

Marcus: No one has succeeded in making —

Marcus: Has achieved fault tolerance. It was a little bit like in Terminator 2 when the thing achieved consciousness. Nobody has made a fault tolerant system that is better when scaled.

Strogatz: So, when we hear about the occasional report of this or that person has made it, a quantum computer, which those reports go back —

Marcus: Those are true. Those are true.

Marcus: And those are all great.

Strogatz: — in a certain sense but not in this sense.

Marcus: Not in this sense. Not in this sense. They’re true in a certain sense. By the way, I would like to come down very much on the side in favor of those efforts. Because I would say anybody who says anything negative about, “Oh well, it’s not a real quantum computer,” they don’t understand how lab life really works. Lab life really works where you build a little thing and you learn, and then you fix those problems. Then you build a little bigger thing, and you learn more, and you build a little bigger thing, and then you learn more. And so, these exercises to build small quantum computers, find out how they work, program them, see how hard you could push, this is the way to approach experimenting. This is the way to approach technology. I think that it’s absolutely great and perfect.

Strogatz: So, is it that you and your colleagues have a particular strategy for how to try to get to this threshold?

Marcus: About 20 years ago now, a group of people led by Alexei Kitaev, who’s now at Caltech, and a number of other people, including Mike Freedman, who was with Microsoft at the time, thought about ways using the analogy to knots, you can dig up financial records now that are 5,000 years old. And the way they were kept is by taking string and tying knots in the string.

Marcus: Yeah. So, there are these pieces. They even used a decimal system. This is Mesoamerica.

Strogatz: This is crazy. I never heard this. Mesoamerica. What are you talking, like Mayans or something?

Marcus: So, look up — another thing to look up. The Quipo: Q-U-I-P-O.

Marcus: Yeah. And these were records that were kept by tying knots in string and —

Strogatz: The string itself hasn’t decomposed because it’s somehow in an oxygen —

Marcus: It’s buried in the dirt, and it was —

Strogatz: It’s in the dirt. Yeah.

Marcus: — low oxygen or something like that. But I mean, a lot of them fell apart. The string fell apart, but the ones that the string didn’t fall apart, you better believe the knot didn’t accidentally come out.

Strogatz: Right. The knot didn’t untie itself.

Marcus: The knot didn’t untie itself. Maybe the entire system melted or whatever, or fell apart.

But we can say it in the following way. The environment that measures a system isn’t very intelligent. It doesn’t know how to untie a knot, and if you can encode quantum information in a topological structure, then that information will also not be subject to measurement by a dumb environment. What’s happened in my lab since then is asking the question, where in nature can you find states that can be tied in knots? And it’s very interesting because if you look around at most of the particles that we encounter in our everyday life, they fall into the category of bosons and fermions. And neither bosons nor fermions can be tied in a knot. But that’s not the only things there are.

Strogatz: Those aren’t the only games in town.

Marcus: They’re not the only games in town.

Strogatz: This is really the crux of Charlie’s work right now. He’s saying that there are particles out there that could be candidates for the ideal qubit. These are particles that Charlie’s calling topologically nontrivial. They’re not the particles you would’ve learned about if you took physical chemistry or quantum theory. All of us who took those courses were brought up on things called bosons or fermions. This would be a new class of quantum particle with this strange property that they can encode information in knots.

If you picture a particle as a point, you could almost think of these particles as having a little string hanging down from them. They’re more like strings than points. And so, when you move them around, it’s as if there’s some string hanging under the table. So, as you manipulate these particles, those strings below the table and in a certain sense get braided together, get tied up and tangled in knots. That’s the topologically non-trivial thing that Charlie is hoping to exploit in a future quantum computer.

Marcus: Imagine now a table with — I’m looking at my table here. I’ve got three coffee cups, two pens, and a mouse. Let’s imagine that I do the following. I move them all around the table. Okay. You can probably hear me —

Strogatz: Good. That’s good.

Marcus: — moving things around the table, right?

Marcus: And now I’m putting them back exactly where they were. Exactly where they were.

Strogatz: I see. I see now. Okay. So, in your third dimension, you actually got — you’re imagining the string to have moved so that if I looked straight up from the string at that time corresponding to the depth or the change in the Z, the vertical change. I know what — geez, it’s not easy to say in words. I see. But you’re keeping track of where everything was at every time with time being the third dimension.

Marcus: Yeah. The string totally tangled under the table. In fact, I made a whole sweater. You can really say that the sweater that you’re wearing right now does record the time history.

Marcus: Of every needle that went around every other needle.

Marcus: In a plane, and this was the sweater that emerged in the third dimension out of the problem. That sweater is now the computation. Okay. So, if you can make a non-Abelian particle, a non-Abelian particle. A particle that is non-trivial and degraded.

Strogatz: Okay. That’s your task, now. It’s to make —

Marcus: And then you can say, “Boy, that seems like a hard way to make a quantum computer.” And I think the answer to that is, yeah, it is hard. It’s cool. But it’s also hard. But that tells you how critically important it is to prevent accidental decoherence.

Strogatz: Yeah. Decoherence meaning this —

Marcus: Inadvertent measurement is so profoundly difficult to get yourself to fault tolerance that, if you can invent a particle that allows itself to be braided and that the braiding is invisible to a dumb, unstructured and local environment, then that qubit will last arbitrarily longer. Now comes the question of how quickly can I move these coffee cups around the tabletop?

Marcus: I mean, this is something that happened in Copenhagen just about the time that I was moving here is that a materials scientist named Peter Krogstrup was able to grow that semiconductor, that particular semiconductor, and the superconductor that together produces this excitation in a single crystal. So, the crystal’s like half superconductor, half semiconductor, but with perfect registry, like atomic registry. And that had never existed before. That material never existed before. And that material actually made this first generation very good. Materials that had these — we believe had these excitations in them.

Now, what we’re in the middle of right now is turning that excitation in a qubit, which involves moving around each other and seeing that you’ve done it, braiding them if you want to call it that, and verifying that you’ve braided them, and then unbraiding them and seeing, when you do trivial operations, you get one kind of answer, you do nontrivial operations you get another kind of an answer.

You better believe that we’re not as far along as some of these spin qubits or superconducting qubits. Qubits that have been basically they were existing technologies for manipulating spin or manipulating electric —

Strogatz: These are competitors you’re talking about, other —

Strogatz: You don’t want to be —

Marcus: Let’s say alternatives.

Marcus: They’re alternatives. By the way, they’re alternatives that we think about every day, and they’re alternatives that they’re probably thinking about. I guess they’re just … different people put their money on different bets. But you swear that the one you’re working on is going to win out…

Strogatz: So, listening to Charlie talk about what’s happening at the edge of knowledge in quantum physics today in this quest to build a quantum computer, I was really struck by a couple things. He talks about not feeling quite in competition with these other teams. That they’re all learning from each other. They’re all thinking about ways they could incorporate the best ideas of their friends. And it sort of reminds me that science is this long human story, very long.

When you think of the pre-Inca civilization that was storing knowledge in knots and braids, it’s sort of emblematic of science in general — that we can learn from ancient peoples 5,000 years ago and in a way there’s nothing new under the sun. And yet there is something new under the sun, because if we do have quantum computers someday, based on these topological ideas, they will absolutely change the world. That’s the kind of paradox that quantum theory itself is all about. There’s nothing new, and there is something new.

Next time on The Joy of x, neurobiologist Eve Marder, on the quirky things that set us on our scientific path.

Eve Marder: And she came back from the first day of class saying, “Eve, you’ve got to come take this course.” And I said, “Well, why?” And she said, “Because the professor’s really cool. He’s got a British accent, and he’s got a dueling scar, and he wears three-piece suits.”

Strogatz: A dueling scar? You mean like he got slashed by somebody?

Marder: He had a scar on his cheek.

Strogatz: The Joy of x is a podcast project of Quanta Magazine. We’re produced by Story Mechanics. Our producers are Dana Bialek and Camille Peterson. Our music is composed by Yuri Weber and Charles Michelet. Ellen Horne is our executive producer. From Quanta, our editorial advisors are Thomas Lin and John Rennie. Our sound engineers are Charles Michelet and at the Cornell University Broadcast Studio, Glen Palmer and Bertrand Odom-Reed, who I like to call Bert. I’m Steve Strogatz. Thanks for listening.

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