Daniel Gottesman

Daniel Gottesman

Brin Chair of Theoretical Computer Science, University of Maryland;
Fellow, Center for Quantum Information and Computer Science

By David Zierler, Director of the Caltech Heritage Project

January 28, 2022

DAVID ZIERLER: This is David Zierler, Director of the Caltech Heritage Project. It's Friday, January 28th, 2022. I'm delighted to be here with Professor Daniel Gottesman. Daniel, it's great to see you. Thank you for joining me today.

DANIEL GOTTESMAN: You're welcome.

ZIERLER: Daniel, to start, would you please tell me your titles and institutional affiliations?

GOTTESMAN: I am a Brin Chair of Theoretical Computer Science at the University of Maryland.

ZIERLER: Now, there is a joint appointment with the Center for Quantum Information and Computer Science, if I have that correct?

GOTTESMAN: Yeah, QuICS is like an interdisciplinary center for quantum computing at the University of Maryland. I'm a QuICS fellow as well. I should say I also have a part-time job with the company Keysight.

ZIERLER: Are you the inaugural holder of the Brin Family Professor?

GOTTESMAN: I believe so, yeah. It's a new chair. There's supposed to be another one, I think, but they haven't appointed that yet, so at the moment, I'm the only one.

ZIERLER: Is it Sergey? What Brin is the leader in this effort?

GOTTESMAN: It's the Brin Family Foundation. But Sergey Brin's father, whose name I would have to look up, was actually a math professor at University of Maryland.

ZIERLER: Oh, wow.

GOTTESMAN: I think Sergey Brin did go maybe for undergrad here, so they have like family ties to Maryland.

ZIERLER: Just to clarify, there's no connection with Google, obviously. This is strictly the Brin family.

GOTTESMAN: Right. It's a family charitable foundation.

ZIERLER: This is a recent move for you, right? When did you come to Maryland?

GOTTESMAN: Just this past summer, so in July.

ZIERLER: I wonder if you can explain a little? I'm just following developments. There seems to be a tremendous amount of growth at Maryland in quantum information generally. What's behind that?

GOTTESMAN: It's not just Maryland. There's a lot of places that are recognizing quantum information as a kind of hot topic at the moment. There's a lot of industrial investment and government investment in quantum computing, so a lot of places want to hire in quantum computing. Maryland is one of them. Maryland has had a big quantum computing effort for quite a long time, but it's expanding.

ZIERLER: Your home department is Computer Science?

GOTTESMAN: Yes.

ZIERLER: Do you have a courtesy appointment in Physics, or how does that work interdepartmentally?

GOTTESMAN: Honestly, I'm not completely sure at the moment. I seem to have some sort of connection to Physics. They were happy, say, to discuss incoming grad students with me, and give me access to the files. But I'm not sure exactly what its nature is. I haven't quite figured that out yet.

ZIERLER: I wonder what we might read into the fact that obviously, your education is in theoretical physics. You're in computer science now. What does that tell us about the academic home of quantum information circa 2022?

GOTTESMAN: It remains an interdisciplinary field. It's found in many different departments. Physics and computer science are kind of the main ones. You'll find lots of people in both of those departments in different kinds of universities. There's some math, different kinds of math, pure math, applied math. There is different kinds of engineering. Seth Lloyd at MIT is in the Department of Mechanical Engineering, which he likes to call quantum mechanical engineering. There are people in chemistry. It's a very diverse field, and so there's a lot of different departments represented as well. Somebody like me that's been kind of in the field for a long time move between departments relatively easily.

ZIERLER: Daniel, I'm curious if the partnership with NIST is relevant for your research.

GOTTESMAN: Yeah, it's very relevant. A lot of the people here are actually kind of primarily NIST employees. They may have some partial appointment at Maryland, but kind of their root job in some sense is a NIST job. A majority, I would say, of the people in QuICS are coming from NIST.

ZIERLER: Since you're so new to Maryland, are you in the process of building up a research group?

GOTTESMAN: Yeah.

ZIERLER: What are some of the goals? What are you trying to accomplish at Maryland? What are the kinds of postdocs and graduate students you're looking to recruit? What are the big things to work on right now?

GOTTESMAN: One topic that I've been interested in throughout my career is fault-tolerant quantum computing. This is also, of course, a topic of interest in industry. I would say the most industrial efforts tend to be kind of more focused in the short term of kind of optimizing existing fault-tolerant protocols, whereas I'm much more interested in coming up with new protocols and new principles, and kind of a better general understanding of how fault tolerance works. But I'm not restricted to just fault tolerance. I also have a long-standing interest in quantum complexity theory, kind of understanding the power of quantum computers and quantum information to do things that classical computers can't. Another topic that I wrote just one paper on but I think is a promising one is using quantum information to build better telescopes.

ZIERLER: Oh, wow, that would be exciting. What would that look like?

GOTTESMAN: The one paper that I wrote, the idea is to improve optical interferometric telescopes using quantum repeaters. A telescope is limited in its resolution by kind of the size of the dish. Because light is a wave, it diffracts, and so the bigger the telescope, the kind of sharper an angle you can see because you have waves from a wider range of things. But one way around this is to have multiple telescopes so you're connecting up. In that case, the resolution is limited by the distance between the telescopes. For instance, this technique was used a couple of years ago to make these pictures of a black hole with the Event Horizon Telescope.

But that's radio telescopes, and the radio telescope is basically kind of combining the light from different telescopes. It's basically a classical problem. Whereas in the optical regime, the telescope is usually getting to kind of like one photon at a time, so a single particle of light, and that's a quantum object. What you're supposed to do is measure the relative phase from one telescope to the other, and that's not a well-defined thing when you're just getting single photons. No, that's not true. The phase at this telescope is not well-defined. The phase at this telescope is not well-defined. But the relative phase actually is well-defined because that's telling kind of what you're seeing in the sky. To do that, you have to do an interference experiment between the photon that could arrive at this site, and the photon that could arrive at this site. When the telescopes are far apart, that's very hard to do. That's where the ideas of quantum information come in because we have done a lot of thinking about how to transport quantum states over long distances. That was the idea of that paper.

ZIERLER: To clarify, you don't need a quantum computer to make a quantum telescope? We don't have to wait for a breakthrough in scalable quantum computing before we have these telescopes?

GOTTESMAN: Yes and no. Quantum repeaters don't necessarily require a quantum computer. They kind of—you—teeny little quantum computers. But they have other technological aspects that are hard. There are people working on quantum repeaters but they're not at the level of performance that we would need for these kind of quantum interferometric telescopes.

ZIERLER: Daniel, what I'd like to do is some quantum information 101 just to get some nomenclature understood from your perspective, and also to get your perspective on your approach to the research and the science. First, what aspects of your overall research agenda would you say are fundamental research basic science, and where do you have a more industrial perspective where you're thinking about applications like telescopes?

GOTTESMAN: I would characterize the telescope work also as basic science. It's not something, like I said, that's a short-term project. It needs a lot of development in terms of getting the repeater technology better to make it practical. I do have some work with Keysight that's kind of a bit more applied, so understanding how to characterize quantum errors and stuff like that. But the bulk of my work, I would call basic science. Even when it's kind of developing protocols that are useable for building quantum computers, a lot of it is focused on understanding kind of the underlying principles, and what's possible and what's not possible.

ZIERLER: Just to get a sense of definitions, do we yet have a quantum computer? If not, what would that look like? What are you waiting to see before that declaration is made?

GOTTESMAN: No, I would say it's fair to say that we have quantum computers. They're right now not big enough and not reliable enough that we can do anything that's kind of really useful. We have quantum computers but they're not really useful quantum computers yet.

ZIERLER: Is usefulness or utility, are you defining that both in terms of their promise for physics research itself, or do you mean usefulness in an economic or a commercial sense?

GOTTESMAN: In either sense. Today's quantum computers are kind of just getting to the stage where they can do stuff that's hard to simulate on a classical computer, and whether we're kind of like just before that or just after that is sometimes a little matter of debate. But, basically, that's where we are, right at that borderline, today. The problem is that—this is something that John [Preskill] called quantum supremacy. But you may have heard there's some controversy about that particular term.

ZIERLER: You mean controversy in the sense that "supremacy" has odious connotations elsewhere?

GOTTESMAN: Yeah, that's exactly this, yes.

ZIERLER: Which is very unfortunate, of course.

GOTTESMAN: Yeah. But in order to do that, you kind of have to tilt the scales as much as possible in favor of the quantum computer [laugh] by making—the job of the quantum computer is basically just to do anything that's hard to do on a classical computer. The thing is that if you do that, basically, like do some sort of random circuit, who cares about the outcome? The only reason you're interested in that is because it shows that quantum computers can be better than classical computers. Now, there's a nice idea by Scott Aaronson that maybe you could actually use these experiments to generate random numbers in a way that you couldn't really do classically, but, basically, the main purpose is just to demonstrate that your quantum computers have passed this kind of break-even point.

ZIERLER: Is part of the challenge that it's difficult to determine what quantum computers will be useful for, and then, as a result of being fuzzy on that, it's difficult to actually go ahead and build a quantum computer?

GOTTESMAN: I would say it is true that it's difficult to determine exactly what quantum computers are good for. We know a number of specific ideas, and there's a number of other ideas that are out there that are kind of hard to fully test right now because we don't have big enough quantum computers to do that. There's probably many more things that we haven't thought of it, and that's obviously a very interesting topic of research constantly. But I don't think that's the main obstacle to building big quantum computers right now. In fact, I'm not sure I would say that's an obstacle at all. The only sense in which it's an obstacle is it's useful if you go to funders to be able to say, "This is what we'll be able to do if we had quantum computers, right?" The better evidence you have of that, and the more applications you have, the easier it is to get money. But as far as technical obstacles, there's many other technical obstacles that have nothing to do with not knowing the best applications for them.

ZIERLER: We hear the terms quantum computation and quantum information. They're always used in the same sentence. From your perspective, where are they essentially interchangeable, where is it a Venn diagram where there's a shaded area, or where is perhaps quantum computation a subset of the larger field called quantum information?

GOTTESMAN: The last one. Quantum computing, quantum computation most specifically refers to: you have a quantum computer; you want to know how to build it; you want to know what it can do. Quantum information is a broader field. First of all, it includes some applications that don't necessarily involve quantum computing like quantum cryptography and quantum sensing. It also includes kind of some contextual stuff where you're thinking about quantum mechanics in an information theoretic way. But you're not necessarily imagining having an actual quantum computer to do anything. Now, the boundaries of what counts as quantum computation and doesn't count are kind of fuzzy because—for instance, there's a bunch of work on using quantum information ideas in high-energy physics, in AdS/CFT. Those don't necessarily—you don't need a quantum computer to do those. Thinking about information theory is already a big help there. On the other hand, if you have a quantum computer, you can maybe do some simulations of holographic systems, and that might give you some insight as well. Just because it doesn't necessarily involve a quantum computer, it doesn't mean that it's not kind of part of the same thing. The people that work on them don't really make a distinction. We move back and forth between things that are quantum computation, strictly speaking, and things that maybe are not so clear that they are.

ZIERLER: You mentioned quantum cryptography and quantum sensing. Do we have those yet? Are those in the here and now, or those are off to the future as well, even if they don't require quantum computers?

GOTTESMAN: Yeah. Those are both applications that exist in useful ways today. None of them are really big business yet, but there are companies that sell quantum cryptography devices. Quantum sensing, I don't know quite as much about, but I think there's many things that kind of are doable today with today's technology. I'm not sure what there is in terms of actual products there. But there's also things that can be developed further. For instance, quantum cryptography in its current version has kind of a range limit of how far you can do it. That's actually the original application of this quantum repeaters idea that I mentioned for the telescopes is to kind of extend the range of quantum cryptography. The quantum repeaters are basically like little, small quantum computers that are doing some sort of error correction. Again, those exist in the lab but they're not kind of practical commercial things yet, so there's still room for development in both, in quantum cryptography and in quantum sensing both from the full range, from purely basic research to a very applied engineering development.

ZIERLER: Daniel, it's a basic question but perhaps it's the question. What is so difficult about quantum error correction?

GOTTESMAN: There's a couple of different possible answers. The main obstacle right now is getting quantum computers that have low enough error rates that the error correction is helping. The reason there is because in order to do the error correction, quantum error correction, you're encoding your qubits using extra qubits. When you do gates in a fault-tolerant way, you do a lot of extra gates. All these things involve some extra steps, and those extra steps can have errors in them as well, right? When you enlarge your quantum computer and enlarge your circuits, that means more opportunities for errors. At the same time, you're correcting the errors. It's kind of a race between these two things. If the error rate is high, then the extra errors that you're adding just overwhelm the system, and it's not actually helping. It's making it worse. If the error rate is low enough, then it does help, and then you can improve things in principle indefinitely, depending on how many qubits you're willing to spend on doing it. The error rates in the real devices are just not quite at that level yet where we can get that improvement. They're kind of around the right level. Again, that's something that we should be seeing experimentally soon.

ZIERLER: Given how long you've been involved in quantum error correction, how do you measure progress over the years, even over the decades? What are the benchmarks to say, "This is where the field was 20 years ago. This is how far we've come in those 20 years"?

GOTTESMAN: Most of the progress has been theoretical. There have been experimental demonstrations of quantum error correction. I guess there's some people that doubt whether quantum error correction would work in real devices. I'm not sure the experimental demonstrations are big enough to convince them. I was not really one of those. The theory is very clear about quantum error correction. The progress we've made, the biggest results were already kind of in place by the late 1990s. We knew that there was a threshold for fault tolerance, which means that, yes, what I just said before, that if the error rate is below this threshold value, then the error correction will work, and you can do long computations reliably. We knew how to do fault tolerance. We knew how to do arbitrary quantum computations even when there's noise in the system. Those are kind of the big results that are still central today. What's happened since then is there's been a lot of progress in getting better protocols that are more practical. One big development there was—Caltech had a huge role in this. Kitaev—actually, this was before he came to Caltech. But—

ZIERLER: It's why John brought him to Caltech.

GOTTESMAN: Well, one of the reasons—

ZIERLER: Right.

GOTTESMAN: —was he came up with this toric code, and then John and—well, I guess it was Dennis, Landahl, Kitaev and Preskill, all of whom at the time were at Caltech—Landahl I think was a grad student then. I'm not 100% sure about that, but certainly a recent graduate if not—showed that this code was actually reasonable for fault tolerance. Then there were some later developments by Raussendorf and Harrington—Raussendorf had recently left Caltech as a postdoc, and Harrington was still there, I think, maybe as a grad student as well—where they showed kind of substantial improvements in this surface code protocol, and that it actually had a lot of good properties. There have been further optimizations since then, but those were kind of the biggest steps in showing that this was a really good way to do fault tolerance. It's now pretty much one of the leading candidates. I personally have another approach that I like a lot, but that one is not nearly as developed.

ZIERLER: Do tell. What is that approach?

GOTTESMAN: The biggest problem with the surface code is that it's not very efficient in how it uses qubits, so you need a lot of extra qubits to correct errors and to make the computer reliable.

ZIERLER: Why is that a problem, lack of efficiency, using so many qubits? What's the issue there?

GOTTESMAN: It just means that the devices that you build, you can't have as many logical qubits, right, for the same sized device. If you have a million physical qubits because by today's standards, it's a huge amount, but it takes 1,000 physical qubits for one logical qubit. It's only 1,000 logical qubits, which is getting to the stage where you can do some interesting stuff certainly. But it doesn't sound like a lot of qubits. You'd like where if you could that down to a factor of 10 then that would be 100,000 logical qubits. That's starting to be a lot. My idea is to use codes that are kind of intrinsically more efficient than the surface code. They share one property with the surface, which is that you can measure whether there's errors or not by just looking at a few qubits at a time. The disadvantage that they have relative to the toric code and surface codes is the surface codes, it's easy to lay them out in a flat, two-dimensional arrangement, whereas these other codes, you can't do that, as far as we know. Basically, you can't do that, so you have to have some way of getting longer range connections. But it turns out that in principle, this approach can drastically, greatly, greatly decrease the number of extra qubits you have. But we don't yet have practical protocols to do that.

ZIERLER: Now, these doubters that you mentioned who are looking at the experimental data, and are concluding quantum error correction is not possible, is that tantamount to then saying scalable quantum computers are not possible, or is there a distinction there?

GOTTESMAN: First of all, I wouldn't say the doubters are looking at the experimental data. The experimental data is on the other side that suggests that it is possible. The doubters definitely are saying that scalable quantum computing is not possible. I think they frequently go from kind of a gut belief that that is true to saying, "Well, that means that quantum error correction must not be possible. Let me look around for things that might go wrong." They come up with ideas, and some of them are not good ideas. Some of them are just wrong; things that we've already dealt with. Some of them are things are that, in principle, I guess that could happen, but there's very little evidence that that would be true. Sometimes, they come up with things that are genuine holes in our arguments that might or might not be a problem in real systems, and sometimes we can later patch those arguments. There are still maybe one or two places where there's maybe some question marks there, but, by and large, we have some very broad results to say that quantum error correction is possible, and that leaves the doubters without too much to work with.

ZIERLER: If you're willing to name names, are there some doubters whose critiques are sufficiently cogent that it's actually exerting a positive influence on the field?

GOTTESMAN: In the past, Robert Alicki has, I think, filled that role to a certain extent, and Gil Kalai maybe to a slightly lesser extent—I don't—but to a certain extent. Those are the ones that have kind of taken the time to learn about the subject, and understand it well enough to make sensible critiques. There's others that make critiques, like I said, that are just wrong.

ZIERLER: The phrase "fault-tolerant quantum computation," so is the idea to make a quantum computer fault-tolerant. Do you need fault tolerance in order to achieve a quantum computer?

GOTTESMAN: If you want to have a really big quantum computer, we're pretty sure that you're going to need fault tolerance.

ZIERLER: What does that mean? Is it tolerant of faults? What does that phrasing exactly refer to?

GOTTESMAN: Technically speaking, a quantum error-correcting code is a way you encode qubits using more qubits in such a way that if there's an error that occurs on some number of qubits, that you're able to identify that and correct it, but a quantum error-correcting code assumes that you can do this encoding in a perfect way, and it assumes that all you want to do is store the quantum information and not do anything with it. Fault tolerance puts on top of the quantum error-correcting code kind of additional protocols that tell you how to create an encoded state even when errors are present; show you how to do error correction even though there's errors in your error-correction process; and show you how to do computations on quantum information while it's encoded in a quantum error-correcting code. A fault-tolerant protocol, so, like, a quantum error-correcting code is useful if all you want to do is quantum communications, and all you're worried about is errors along the way. Whereas a fault-tolerance protocol is what you need for building an actual quantum computer where all of the pieces are necessarily not quite perfect. We think that that's going to be necessary because quantum computers are not going to be perfect. Building things at the level of single atoms is very hard. Quantum information is just inherently more delicate than classical information. That combination of things just means that kind of the physical error rates per gate are not going to be low enough to do really big quantum computations without some way of dealing with those errors. Now, over the next decade or so, people are imagining that we'll have quantum computers that are not big enough and not reliable enough to do error correction; that either the number of extra qubits needed to do that is just too much, given how few qubits they have, or the error rates are not low enough. People have been looking into what's called NISQ algorithms—again, this is a coinage of John's—N-I-S-Q—for Noisy Intermediate-Scale Quantum. There's a number of ideas for algorithms that will work, even though you don't have fault tolerance, so even though those actual errors are correct in the computer. There's maybe a few of those algorithms that can be scaled up to very large sizes, and will still work even if you have many, many qubits. Some of these ideas just won't work though; that once you get to big enough sizes, the accumulation of errors gets to be too big, and that kind of overwhelms your algorithm, unless you have error correction.

ZIERLER: Two last definitional questions, both of which maybe you can clarify some perhaps misperceptions. First, quantum complexity. The layman's observation would be, well, it's all complex. What specifically is quantum complexity?

GOTTESMAN: Quantum complexity is kind of the quantum analog of classical complexity theory. Classical complexity theory is the study where you try to classify computational problems based on how hard they are. There's some problems that are, for instance, easy to do on a classical computer, and there's other problems where we don't know how to do them on a classical computer but we know how to solve them on a quantum computer. Then there's problems—those are complexity classes. The first one is known as P for polynomial time. That's what we mean by doing things efficiently. Next one is BQP. The Q tells you it's quantum. Then there's problems, for instance, where it might be hard to find the answer, but if somebody tells you what the answer is, you can check that efficiently on a classical computer. That class is known as NP, and it includes problems like the Traveling Salesman Problem. There's a famous open problem whether P is equal to NP or P is not equal to NP. For instance, this is one of the Clay Millennium Problems that you can get a million dollars for solving. Then you can kind of get analogous quantum problems, like QMA is kind of the quantum analog of NP. QMA problems might hard to solve even on a quantum computer. There's some piece of information that somebody can give you that would let you check the answer, but you needed a quantum computer to do that checking.

ZIERLER: Then, finally, a fun one, can you explain why quantum teleportation is science and not science fiction?

GOTTESMAN: Well, it's been done experimentally in the lab many times. The thing that's maybe worth noting about quantum teleportation is that what you're teleporting is a single quantum bit, a qubit. You're not teleporting people. You're not teleporting big objects, unless you break them up into individual quantum particles, and teleport them one-by-one. What it does, in some ways, it's very surprising and mysterious. In other ways, it's just a matter of sending information from one place to another. That doesn't seem controversial. What's special and kind of amazing about quantum teleportation is that it breaks up the process of sending a quantum bit into two pieces, one of which is kind of a quantum piece but doesn't involve any communication at all. You need a disentangled state to do quantum teleportation. The other is a communication part, but that doesn't involve anything quantum. It's a purely classical communication. You send two classical bits. It's kind of surprising that you can break up a quantum communication task into these two separate pieces.

ZIERLER: Does the work on quantum teleportation yield new insights into quantum mechanics itself?

GOTTESMAN: I would say, yeah, the fact that it's possible, by now, it's old hat, right. This is from almost 30 years ago. Maybe it is 30 years ago now. I don't know. We're used to it in that sense. But certainly, at the time, I think it was pretty surprising, and it had a deep insight. It's also kind of intrinsic in kind of understanding the relationship between classical bits and quantum bits, and the different—there's this mindset, which was started in large part by quantum teleportation but has been built over the years, of thinking of different kinds of quantum resources, different sorts of things that you can use to do tasks, and the idea that classical bits are one resource, and quantum bits are another resource, and that there could be a trade-off between these two. Quantum teleportation had a big part in creating that idea.

ZIERLER: Was this relevant at all for your work on stabilizer code formalism using quantum codes?

GOTTESMAN: Quantum teleportation is somewhat relevant. Developing the stabilizer codes, it was not directly relevant. The second part of that was kind of understanding like the behavior of what's known as the Clifford group, which is a set of unitary operations which are kind of good for encoding quantum error-correcting codes, stabilizer codes, and good for manipulating them, for doing fault-tolerant gates on them. Understanding that and in particular the relationship of measurements with the codes, quantum teleportation was, I would say, fairly important kind of conceptual background for that. Now, I have another paper which is like 100% quantum teleportation, which another well-known paper. That's the one I did after I left Caltech, which is using quantum teleportation to do quantum gates. Obviously, that would not have been possible without the aid of quantum teleportation at all.

ZIERLER: Daniel, some questions about the state of play in an industrial setting, particularly because you have a current affiliation in private industry. First, among the behemoths in the field—the Microsofts and the Googles and the Amazons, Honeywells, and so on—to the extent that you're following their individual approaches, first, do you see this as a race, and a race to what, and are they using similar or different means of getting to a scalable quantum computer?

GOTTESMAN: There's certainly an element of being in a race here. That's primarily the business side in the sense that I think if one company gets too far ahead of the others, then maybe the other companies will decide it's not worth competing anymore, and so they'll stop trying.

ZIERLER: It's an arms race in that sense, you mean?

GOTTESMAN: Well, I don't know. An arms race is kind of the opposite, right, but there's an element of that as well, which is that because the other thing is that if one company kind of comes out with really useful quantum computer products, they get this first-mover advantage, and their brand name gets associated being the best quantum computer. Whether or not it's actually the best or not, it doesn't matter so much. If it's the only one at that time, then they can retain kind of a branding advantage in later years. It's not the be-all and end-all. If there's other companies that can be not too far behind, they can still share the market, and probably the advantage is not that big. Now, there's many different companies, and there's kind of a few different approaches as well. You have companies like Google and IBM are building superconductor-based quantum computers. You mentioned Honeywell. They have an ion-trap quantum computer. But actually, the big player in that space is a startup, IonQ, which actually just recently went public, the first kind of quantum computing startup to go public. Then there's another approach using just photons, where another startup called PsiQuantum is probably the leader in that space. There's a race between the individual companies, but there's also a race between these different approaches. Again, if one of them gets too far ahead, then maybe the money will dry up for the other ones as venture capitalists or whatever want to put their money in the one that seems most likely to pay off. But, right now, I don't think anybody has a decisive advantage in terms of either the technique of how to build a quantum computer or which company is clearly going to come out ahead.

ZIERLER: Now, is your sense that the different approaches are leading to the same goal, or are the different approaches suggestive of the idea that there's more than one thing that we call a scalable quantum computer?

GOTTESMAN: Well, I definitely think that there's more than one way to build a scalable quantum computer. I don't think that it's the case that one of these will work, and the other ones won't work. It may be in the end that one of them is a little easier than others. They also could end up having different applications and different advantages and disadvantages. For instance, photonic quantum computers would probably very easy to integrate with communications, which is going to be harder with the other ones.

ZIERLER: Like the quantum internet, for example?

GOTTESMAN: Yeah, and that's useful for quantum cryptography, for these quantum telescopes ideas, but also other ideas that some of them may have not been developed. But if you have quantum computers in different sites, and you want to send quantum information around, you have to figure out some way to do that. The superconductors and the ion traps are kind of a little more conventional. They have qubits embodied in some sort of physical object as opposed to more the ephemeral photons. The superconductor is kind of intrinsically faster than the ion traps, but also intrinsically a bit noisier. Of the two of them, the ion traps are, again, kind of easier to interface with communications, which could be useful while scaling up. In the long run, it's hard to say. There may be specific applications that need high speed, where superconductors are going to win out; specific applications where you want kind of—the superconductors also definitely need to be refrigerated, whereas ion traps maybe not, although it probably helps, so you're kind of trading off different things.

ZIERLER: Among the different approaches to quantum computing, is there one that you see as most promising for physics research itself to the extent that we're a little more advanced in our imagination and our thinking for how quantum computers are going to be useful in physics?

GOTTESMAN: The whole point of the quantum computer is that once you have one, you can run any quantum algorithm on it. I don't think that one particular kind is going to be better for simulating physical systems than another kind. Whichever kind is the best, has the biggest system and the most qubits and the best error rates, that's the one to use.

ZIERLER: All right. Now, let's go back to undergraduate days at Harvard. To clarify, when you were an undergraduate in the early mid-1990s, was there such a thing as quantum information, and you had not known about it, or was there no such thing as quantum information yet?

GOTTESMAN: Yes, there was definitely such a thing as quantum information. Richard Feynman and David Deutsch were talking about quantum computers in the mid-1980s. Definitely by the time I got to college, they existed. I just had never heard of them.

ZIERLER: What was your major as an undergraduate? Was it physics?

GOTTESMAN: Physics, yeah.

ZIERLER: Was it theory? Were you always gravitating towards theory?

GOTTESMAN: Yeah, definitely.

ZIERLER: What kind?

GOTTESMAN: For me, the borderline was between doing physics and doing math.

ZIERLER: What kinds of physics were you excited by as an undergraduate?

GOTTESMAN: I was interested in high-energy stuff. I was interested in quantum gravity. That's what I thought I wanted to do.

ZIERLER: What was the state of play for string theory at Harvard at that point? Was it exciting then?

GOTTESMAN: Harvard was kind of slow to get into string theory. Either just before I got there or shortly after, they hired their first string theorist, which was Cumrun Vafa. It was not a big thing there. My undergraduate advisor was Howard Georgi. He's kind of older-school particle physics. String theory was only just really becoming a big thing at all then. Kind of the first string theory revolution was maybe the mid-80s. I guess Harvard, they figure they don't need to get involved in this newfangled stuff. They're Harvard. They can hire whoever they need to later.

ZIERLER: Sure. [laugh]

GOTTESMAN: They're also kind of a bit slow to get involved in quantum computers. They have some people now but not a lot.

ZIERLER: So, as you said, even though people like Feynman and David Deutsche were thinking about quantum information, this did not register with you as an undergraduate?

GOTTESMAN: No, that's right. It certainly wasn't a big thing in the popular media. At Harvard, obviously, there was no one doing it. Even when I was at Caltech, I was working with John, who definitely knew about quantum computing, I don't recall ever discussing it with him until Shor's algorithm came out.

ZIERLER: Oh, wow. OK. What kinds of graduate schools did you apply to? Did you have a specific focus in mind who you wanted to work with?

GOTTESMAN: No, not really. I just applied to the best schools, and Caltech was the one that kind of seemed the most attractive to me.

ZIERLER: Why? What was it about Caltech?

GOTTESMAN: It was a combination of things. Princeton actually kind of turned me off by just like assuming that they were the best, and that everyone wanted to go there.

ZIERLER: [laugh]

GOTTESMAN: But I had a good time there. They put me up in a professor's house, who was a future Nobel Prize Laureate. He hadn't won it yet. It was a good visit, but it still kind of turned me off in that respect. Caltech, it was a good visit. I remember talking to John about density matrices. Anyway, it was an interesting visit. I had some reservations about Berkeley and Stanford, the way they approached the graduate requirements, and stuff like that.

ZIERLER: What year did you arrive at Caltech?

GOTTESMAN: 1992.

ZIERLER: Now, at that point, as you said, you hadn't talked to John about these things. Was your sense, retrospectively, that he was already starting to think about these things at that point?

GOTTESMAN: Well, you probably should ask him, but my understanding is that he had talked to Feynman about quantum computing, back when Feynman was alive. He was gone by the time I arrived. It maybe informed his thinking a little bit, but at the time, he was mostly interested in the black hole information loss problem, and so that was what I kind of started working on. While that does have a very information theoretic aspect, and, nowadays, there's a lot of quantum information, and people that are studying that problem, it was a separate thing. It didn't involve a lot of what we talk about today in quantum computing. Then, Shor's algorithm came out, and, at the same time, I was kind of like feeling that, for me at least, quantum, the black hole information loss problem was not the right thing to work on.

ZIERLER: What would that have been understood at the time, black hole information loss? Would that have been more like cosmology, theoretical astrophysics? How would you have categorized it?

GOTTESMAN: No, I would call it quantum gravity, and still would do that today. The idea that the quantum—the information loss problem is that you make a black hole, things fall into it, but then Hawking says that black holes evaporate. The radiation comes out of the black hole, and over a very, very long period of time, the black hole can disappear completely. The question is what happened to the information about the stuff that went in? The analogy is if you burn an encyclopedia, the information is gone in practice, but in principle, if you could track every single atom, and trace it all back, the dynamics of the fire and the smoke and all of that stuff, then you could reconstruct all that information in the encyclopedia. It's not really gone; it's just kind of mixed up a lot. Black holes are different because they have this horizon, and information can't get out once it falls in. How do you reconcile that with this idea that physics, microscopically speaking, seems to be completely reversible? If it's reversible, that means you can get back to where you started. That was the tension, and there's different schools of how you could resolve this, but all of them seem to have problems of one sort or another.

ZIERLER: What kind of interaction was there between quantum gravity and the string theorists at Caltech? For example, was John Schwarz part of this effort?

GOTTESMAN: I don't think there was much interaction. John certainly was knowledgeable about string theory, and kept track of stuff that was going on there. I don't recall any of the, like, serious string theorists thinking about this problem at all back then. Nowadays, that's very different, of course, but string theory was a much less mature field, and they were focused on different kinds of problems back then.

ZIERLER: They were not so close to asserting that string theory is the most plausible path to achieving a theory of quantum gravity?

GOTTESMAN: No, they were asserting that even back then, but they didn't have as many tools to study different kinds of problems. I think it was not until somewhat later that black holes started to play a big role in string theory. Actually, a lot of that came from ideas from the information loss problem. The black hole holography and AdS/CFT kind of grew out of that. I'm not so knowledgeable about the string theory history, but I think the big insight there was Juan Maldacena's work, which was like kind of mid-, late 1990s. That was after I had already moved into quantum information.

ZIERLER: When Shor's algorithm came out, '94, did that register immediately with you? Did that put you on a different course?

GOTTESMAN: Well, it registered with John. I was not aware of it directly. But like I said, at the time, I was kind of dissatisfied with working in this black hole information loss problem. He suggested that maybe this would be something good to work on, this quantum computing. I started thinking about it then.

ZIERLER: The people that are going to be reading these transcripts, these interviews, they're coming from a lay perspective oftentimes. Can you explain why Shor's algorithm was just so foundational to making quantum computation not just an idea?

GOTTESMAN: The idea of a quantum computer, obviously, is that you can build it out of individual atoms or other things that behave quantum mechanically that lets you run different kinds of programs, different kinds of algorithms that you can't run on a classical computer. Actually, there was already a very good example of something that it seemed like a quantum computer was good at that we didn't know how to do classically, which was Feynman's idea that you could use it to simulate physical quantum mechanical systems. I think that didn't make such a big splash because it's something that seems obvious, even if it's only obvious in retrospect, but once you know about a quantum computer, then, OK, sure, it makes sense that you can simulate quantum systems. Shor's algorithm was very different, right, factoring large numbers. What does that have to do with quantum mechanics? It has nothing to do with quantum mechanics, apparently, and, yet, a quantum computer can do it. The other side of it is that it has immense practical importance—well, sort of—because the most common cryptosystem, even today, in the world is called RSA, and it's only secure if it's hard to factor large numbers.

So, that meant that there'd been a lot of work in classical computer science about how to factor numbers; how to do it. There's obvious ways to do it where you try dividing everything into it, and then there's much more sophisticated ways using elliptic curves and various kinds of advanced math, but none of them are really that efficient. They take a really long time. A quantum computer can do it much, much faster in a way that's considered efficient. It's polynomial in the size of the—polynomial in the number of bits of the number—the length of the number that you're trying to factor. That was fairly strong empirical evidence that quantum computers could do something that was hard on classical computers; that people had tried really hard to do it classically, and, yet, we know how to do it on a quantum computer. It was something that, obviously, the NSA [National Security Agency] was very interested in knowing whether it was going to be possible to build quantum computers or not. Also, the fact that it was something that's so different from quantum mechanics was maybe a hint that there were lots of other applications that we would not have imagined out there. That created a big incentive from the theoretical side to investigate. I should say that, at the same time, there was also experimental progress that was really important that made it not just a theoretical idea but something that you could actually imagine building, which is—in that era, people were able to manipulate single atoms, and start to do interesting things with it. There were proposals for how to build quantum computers, like concrete, you could imagine doing it. The basis of the ion-trapped quantum computer comes from about the same time. I'm not sure if it's 1994 or 1995, something like that, but it's around the same time. The combination of this theoretical breakthrough with experimental advances that made it actually plausible that you could do this, that's kind of what ignited the field.

ZIERLER: How does this filter down to you from John realizing that this is an exciting development, and he says, "Go work on this"? Work on what exactly? What was the plan for you?

GOTTESMAN: Well, basically, I went out, and I read every paper in the field, which was like five papers.

ZIERLER: [laugh]

GOTTESMAN: That's not quite true. There were some older papers that I didn't read, but there were a relatively small number of papers there. It was kind of relatively straightforward to get up-to-date on what was going on.

ZIERLER: What were the ideas? What were you getting from these papers?

GOTTESMAN: I read about Shor's algorithm, of course, so I understood how that worked. There were a couple of papers on quantum circuits, and how to kind of put together smaller quantum gates, and some more complicated quantum operations. The one thing that we had at that time as a sense of infinite possibility. We had no idea what was possible for quantum computers. One of the first things that I worked on was I had an idea for an algorithm which, if it worked properly, it would've solved NP complete problems. Basically, what I was doing was trying to solve what's now known as the database search problem, which is what Grover's algorithm does. This was before, obviously, Grover's algorithm came out. Although one of the papers that I had read was actually the paper that proved—maybe I need to give some context for the non-experts.

Grover's algorithm does this database search, which you can imagine you have some giant list of numbers, and you want to know somewhere in this list is the number 534, but the list is totally unsorted. Classically, how would you do this? Well, you'd look at the first number, and say, "Is that it?" You look at the second one, "Is that it? Is that it?" You keep on going through the list until find 534. You go through all of them, and you say, "It's not there." So, if there's N items in the list, you have to check roughly N things before you find it in general. Whereas a quantum computer, by taking advantage of quantum superpositions—and Grover's algorithm uses only about square root of N times looking at the list. It has to be a quantum list—a list that you can access in superposition, but that can be a huge speed-up when N is very large. It's not as dramatic a speed-up as Shor's algorithm but it's also useful in a huge variety of problems because it doesn't have to be an actual list. It can be anything where your strategy would be to try this, then try that, then try that; try a long list of things. You can go down to the square root of N as many things. It turns out that square root of N is the best you can do for this problem on a quantum computer. There was actually a paper that proves that—that square root of N was the best you could do—before Grover found an actual algorithm that did in square root of N, but it was written in a very computer science-y way, and I read it, and I didn't understand it, and I didn't have any idea it had to relate to this problem. I tried to solve it. Of course, it didn't quite work. Now, in retrospect, I think that a more careful analysis of my approach might've gotten that square root of N speed-up as well, but it wasn't what I was looking for, it wasn't what I was expecting, and so I didn't see that. That's what I was thinking of to start with. That was something I kind of mostly was doing by myself. I talked to John about it but it was an idea that I had had. The next thing to look at was there was a paper by Bill Unruh that said, "Well, I don't know about this quantum computing stuff. What about errors, right? The errors will definitely be a problem in quantum computers."

I think we already knew that error correction was necessary, but that helped to kind of crystallize the sense that it was important. John and I and some other people around thought about, talked about how could you do quantum error correcting codes. We couldn't come up with a way to do it. Then there was this paper by Peter Shor. So, arXiv back then existed for high-energy. It did not quite yet exist for quantum mechanics, quant-ph. I don't remember its exact start date. It was around this time. John got a hold of Shor's paper on error correction through some other method. I don't think it was on the arXiv. Then the arXiv kind of got up to speed, and all the papers from then on were pretty much on quant-ph.

ZIERLER: Now, had John put other grad students on this project as well?

GOTTESMAN: Yeah. It's hard for me to remember exactly who appeared when. Dave Beckman was in my year, and he was also working on quantum computing sort of stuff at some point. I don't remember exactly when. Then, in the following years, Andrew Landahl and John Cortese joined, and they were doing quantum computing kind of from the beginning. Then there were some undergrad students that were working on stuff, the most notable being Debbie Leung, who nowadays is a well-known researcher in the field of quantum information. At this time, at the time we were talking about quantum error-correcting codes is probably—I'm not sure Andrew Landahl and John Cortese were there yet. I think it was probably just me and Dave Beckman and John and whichever students were around at the time.

ZIERLER: Daniel, just the three of you or four of you, looking back, did you see that those discussions had a momentum that naturally was leading to what would become the IQI?

GOTTESMAN: No, I think that was later. At that time, Caltech was not really on the map of quantum computing back then. I guess Feynman had kind of put it on the map, but he was gone, right, so none of us that were there had written anything of significance in the field. It was not until a bit later that the momentum started to build. There was a grant proposal—maybe not completely true. Jeff Kimble was doing quantum computing-related experiments, and he had some papers, including one of those kind of early foundational ones, which said, well, OK, maybe you can actually build a quantum computer out of light—although that technique turns out to be just too hard, so a bit later than what I'm talking about, like a year later or something, John and Jeff Kimble and Steve Koonin put together a grant proposal.

ZIERLER: Koonin was provost at this point?

GOTTESMAN: No, this was before he was provost, I believe—

ZIERLER: Okay.

GOTTESMAN: —although maybe just right before. Again, I don't remember the exact chronology. They put together the first kind of Caltech grant pro…well, I don't know. Maybe Feynman had had one earlier. I don't know. It was the one that first kind of created a quantum information funding source at Caltech, and enabled them to hire postdocs, and kind of build up the number of people there. That was maybe a better point to set a new creation of IQI, which was a later, bigger grant.

ZIERLER: From these early ideas, what would come to be your dissertation, your thesis research?

GOTTESMAN: Like I said, we were thinking about quantum error correction. We couldn't figure out how to do it. There was this paper by Peter Shor, so there was more interest in thinking about quantum computers, quantum error correction, and understanding, like, how well could you do it. Could you do more efficient codes? Then came the papers by Calderbank and Shor and by Andrew Steane that showed this class of codes now known as CSS codes, which is a big, big, important class. It still wasn't clear that that was the best you could do, and it's not the best you can do, in fact. John and maybe—I don't remember who. It might've been Andrew Landahl by then, anyway, or it may have been some of the undergrad summer students. I don't remember. They came up with some idea for a quantum error-correcting code, and I was able to show that it didn't work, that they had not—because this was before we had these quantum error-correcting conditions that make it easy to check if a quantum code works or not. That led me to thinking about kind of bounds on quantum error-correcting codes, and how good could a quantum error-correcting code be? I came up with this idea of what's now called the quantum Hamming bound, which is probably not worth describing technically, but the thing is, there's analogous classical Hamming bound, what is called the Hamming bound. The quantum Hamming bound is actually, it turns out it doesn't necessarily work for quantum codes because they have this property called degeneracy, where you can have two errors that do the same thing, two different errors that nonetheless do the same thing on code words of a quantum code—and that doesn't happen classically. I realized that this was a problem with the bound that I wanted to come up with, and so then I kind of didn't really know what to do with this. I thought about it a little bit. I didn't get anywhere. Then a paper came out by Ekert and Macchiavello where they proposed a quantum Hamming bound and another bound, but they didn't mention this problem of degeneracy.

So, of course, I found that very frustrating because this was something I'd figured out, and realized was wrong, and somebody's putting out a paper that says it, without noticing that it's wrong. What I did was I got back to thinking about this again, and I said maybe I can actually prove that this bound is correct in general. To do that, I have to understand degeneracy better, and so I tried to come up with an example of a quantum error-correcting code that had a lot of degeneracies, had a lot of cases where the errors kind of clotted with each other. Whilst studying this thing, I realized, very surprisingly to me, it was actually pretty good at correcting errors. All I put in by hand was the fact that two different errors did the same thing. There were some totally different errors that it was just automatically correcting, but I didn't do anything about that. While trying to understand why, that's how I came up with stabilizer codes. That's the story for me.

ZIERLER: Looking back, this idea that there was exuberance, infinite possibilities, what was naiveté and what was just really forward thinking?

GOTTESMAN: Well, it's hard to distinguish between the two.

ZIERLER: [laugh]

GOTTESMAN: Back then, because it's just a very new field, there was the sense that not only did we have no idea what was possible and not possible, but that, actually, you could do something very simple, and come up with a great new idea. Sometimes, that was just total nonsense, right, like my idea for solving NP complete problems. Nowadays, we think that it's not possible. The stabilizer code, that's also a pretty simple thing, and it's just no one had looked at it yet because there hadn't been time. When I came up with it, error-correcting codes, quantum error-correcting codes were only a few months' old. While the field was growing explosively, it was still only a handful of people. Compared to today, it's nothing similar in size. There's other examples, of course. Another famous thing from about the same time was there was this proposal for a cryptographic protocol known as quantum bit commitment. It's not really important what it is, but what was discovered also in the mid-90s was that, actually, that protocol didn't work and, moreover, it couldn't work; that there was no way to do this using quantum mechanics. All that stuff we were discovering back then—what you could do and what you couldn't do—and, again, it was unchartered territory, so there was a lot of low-hanging fruit, things that are relatively straightforward and, yet, very impactful. but sometimes you'd try to get a low-hanging fruit, and it turns out not to be fruit at all.

ZIERLER: Now, I've been looking forward to ask this question because for so many of John's students who came through later, after the field, after IQI was much more developed, the theme that keeps popping up about his style as a mentor was that he was interested, he was accessible, he was supportive, but he was really hands-off in terms of not handing you a project. I wonder, given that the field was in the infancy, that you were sort of present at the creation, if he might've been more hands-on with you simply because the whole thing was new, or not necessarily.

GOTTESMAN: No, I would not say he was hands-on with me at all. Suggesting I look at quantum computing is not at all the same as giving me a project. Sometimes, we had discussions, and that of course led to ideas, but I didn't actually collaborate with him. I certainly didn't write any papers with him until I was already gone from Caltech, until I was a postdoc elsewhere. I think in later years, he kind of, of necessity, became even more hands-off because, back then, there were four or five students working on different things, not all quantum information thing, but it was kind of a reasonable group size, whereas in the later IQIM years, it just kind of blossomed out of control with many, many students wanting to do quantum computing, and John was like almost the only one to go to back then. There's now many faculty. Back then, there was him. Kitaev was maybe not even appointed yet. If you're a theorist wanting to do quantum computing, he was the only one. They had a bunch of postdocs. Back then, it was IQI probably. There were just too many people. He couldn't manage them on a day-to-day basis, but he was still hands-off. I think for some of the other students, he was more involved. I was kind of relatively able to come up with my own ideas, and so he just let me do that.

ZIERLER: Besides John, who else was on your committee?

GOTTESMAN: [pause] Probably it was Steve Koonin and Jeff Kimble, I think, pretty sure because those were kind of the ones interested in quantum computing. There was one more that just kind of got drafted, who I think was Pines. Now, I tried to get McEliece, who's a classical error-correction guy, but he was like on sabbatical or something, and not available.

ZIERLER: Thinking about possible career paths, was this risky at all? Was quantum information a field that you could apply for in faculties, or how might that have worked out?

GOTTESMAN: It was extremely risky but, as a grad student, I did not know that. I had no idea. I was very naïve in that respect. I thought, oh, this is an interesting new field. There's grant money coming in. Surely, people will want to hire in quantum computing. It wasn't too hard to find a postdoc. There weren't that many postdocs at the time but there weren't that many students graduating either. I had a nice result that I could present, so I didn't have trouble getting a postdoc. When I started to apply for faculty jobs, I realized it wasn't so straightforward.

ZIERLER: [laugh]

GOTTESMAN: Nobody was advertising for quantum computing jobs, certainly, and you applied to these relatively open ones and, of course, there's a ton of people applying. Probably a lot of those departments don't have anybody who knows anything about quantum computing, and they wonder why they should hire in that area. They want to hire in their area. I didn't know any of that stuff at the time.

ZIERLER: I know you went to Los Alamos. We'll talk about that in a second. Where else could you have gone? Who would've been a peer of John's at that point that you might've worked with at a university?

GOTTESMAN: Let's see. Seth Lloyd had been hired at MIT by the time I got graduated. I did write to him to see if he had a job. He had some grant money but he wanted to use it to—in his words, I believe—to hire Murray Gell-Mann as a postdoc, as a visitor, basically.

ZIERLER: [laugh]

GOTTESMAN: What else was there? IBM certainly, even back then, was a powerhouse. David DiVincenzo and Charlie Bennett were there. I don't remember if I kind of communicated with them to try to get a postdoc. Los Alamos was a big place then, so that's why I chose Los Alamos.

ZIERLER: What was going on at Los Alamos?

GOTTESMAN: Oh, and Berkeley, there was Umesh Vazirani at Berkeley, who was also there.

ZIERLER: What was going on at Los Alamos at that point?

GOTTESMAN: Manny Knill and Raymond Laflamme were there. They had written a number of papers on error correction and fault tolerance. They were one of the groups that came up with this idea of the quantum error-correction conditions to check whether codes worked. They had a bound on the performance of quantum codes that actually was correct. With Wojciech H. Zurek, who was also at Los Alamos, they were one of the groups that came up with this idea of the threshold theorem. It was a good place to be for quantum computing back then. Then, when I applied, I think Ike Chuang was a postdoc there. He left at the time that I arrived, so we didn't exactly overlap there, but Michael Nielsen was also there as a summer student. No, he was a grad student. I'm not exactly sure what his arrangement was. He was a grad student with Carl Caves at University of New Mexico, but he was spending a lot of time or maybe all his time at Los Alamos.

ZIERLER: The field is so new at this point. Were the questions being raised at Los Alamos different? Were you being exposed to new ideas than at Caltech?

GOTTESMAN: Yeah, I guess so. It was a little bit of a different perspective, just working with different people. At that time, again, the field was much smaller, so you would go to a conference, and you'd meet everybody in the field.

ZIERLER: Right.

GOTTESMAN: I knew everybody in the field, basically, back then when you could go to conferences, pre-COVID. It was a global community. Being at Los Alamos was worthwhile but it wasn't—all you needed was enough money to travel, and then you got to talk to everybody. By then, arXiv was in full swing, so the papers were available.

ZIERLER: Obviously, it's fundamental research, but just being at a national laboratory, was there a sense at that point that quantum information was responsive to the DOE mission with the national labs?

GOTTESMAN: Well, sense by who? Los Alamos is a very big and bureaucratic institution.

ZIERLER: Sure.

GOTTESMAN: Quantum computing back then was not considered its primary mission in any sense. I think it was reasonably well supported in the scope of these things, but definitely being there, I got the sense that it was kind of a side thing. It was not really that they were interested in this; just that there happened to be a bunch of people that they hired for other reasons that became interested in it.

ZIERLER: I'm thinking along the lines of like supercomputing at Oak Ridge, for example, if people were thinking that this might be really exciting at some point in the future, and this is a space where DOE can lead.

GOTTESMAN: Well, supercomputing was important at Los Alamos back then, but remember, quantum computers of that era were not good enough that that was a viable—what they wanted them for was nuclear weapons simulations, and quantum computers were not at that time a viable option for that. It's not clear that quantum computers even today would speed up the types of problems that they want to do. Now, of course, Los Alamos does have a lot of—and a more established kind of quantum computing effort. Nevertheless, it was supported. The people that were doing it—Raymond and Wojciech were in the theoretical astrophysics group. Manny Knill was in a computing group. I don't remember what it's kind of main purpose was. There were people that had basically changed from other areas to work on quantum computing because they thought it was interesting.

ZIERLER: What was your key work during the Los Alamos years?

GOTTESMAN: At Los Alamos, I got interested in quantum cryptography. I wrote a couple of papers about that. One on quantum secret sharing, I think, has kind of ascended to be one of my more cited papers by now. Let's see. Let me look at my publications from back then. [pause] That's probably the most important one. There was a sort of pedagogical paper about stabilizer codes that's somewhat influential. That's probably the most important one.

ZIERLER: The Heisenberg Representation paper, that was done while you were at Los Alamos?

GOTTESMAN: Yeah.

ZIERLER: What is that? What is the Heisenberg Representation?

GOTTESMAN: Let me explain the name. In quantum mechanics, there's kind of two representations, a standard like 1920s quantum mechanics. One of them is the Schrödinger picture where you follow what's called the wave function. It gives you kind of the probability of different types of things happening. It's actually a quantum amplitude rather than a probability. The other's the Heisenberg Representation where instead of kind of looking at the wave function, you look at the operators, but kind of the properties, the things that you can do to a quantum state, and you let them change over time. The stabilizer formalism for quantum error-correcting codes, instead of looking at the states of the code word, you look at operators on it, and so you define a code by some of these properties that's not changed by certain actions. In that sense, it's analogous to the Heisenberg Representation of regular quantum mechanics. That's why it's called that. Again, what it is, is basically a kind of an expository paper of kind of explaining how this works. It was written for the proceedings of a conference that I gave a talk at, which was not a quantum conference. It was a conference on group theory in physics.

ZIERLER: Now, to go back to the job market question, were there academic positions? Was Microsoft specifically a place you wanted to go, or was there not really opportunities in an academic setting at that point?

GOTTESMAN: I didn't really finish in Los Alamos. I was there for two years. My position was extendable for a third year but, after two years, I thought, well, I should apply for faculty jobs, and if it doesn't work out, then I still have another year. I applied for a bunch of faculty jobs. Although, again, like I said, nobody was advertising for quantum computing specifically. [pause] Yeah, I think that's right. I don't remember. Yeah, I had some leads on academic jobs, but nothing that panned out. Of course, there were companies even back then that were interested in quantum computing—not as many. IBM was one, and Microsoft had Mike Freedman, who was interested in quantum computing. I thought I'd apply for like a research staff job there. They didn't want to offer me a permanent position, but they did offer me a postdoc, which was not my original intent to move to another postdoc, but I had such a great time visiting them that I decided to go there.

ZIERLER: This was a postdoc with Freedman, or was there a group that you joined?

GOTTESMAN: Yeah, so I joined the theory group, which is theoretical computer science group. Although it was kind of an eclectic group with Mike Freedman as more of a mathematician, and the group leaders were Jennifer Chayes, Christian Borgs. They were basically mathematical physicists that were doing kind of computer science-related stuff. Then there were some more traditional theoretical computer scientists as well. In some sense, I was Mike Freedman's postdoc, but I was attached to this theory group, and it was kind of a little bit broader.

ZIERLER: What was Freedman working on at that point?

GOTTESMAN: Well, he was working on topological quantum computing. He had some ideas for building a topological quantum computer. I don't remember exactly the chronology. He had some papers. The time that I was there, also Kitaev was there. He was a visitor in the group. He wasn't a permanent employee there. They eventually wrote some papers on kind of the equivalence of topological quantum field theories in quantum computing. I don't remember whether that was after I left or during the time I was there, but it was kind of around the same time. Maybe that was a little bit after I left.

ZIERLER: This would've been so early, but from the business side, was anybody talking about applications, or this is really all just pure fundamental research?

GOTTESMAN: Obviously, we had the application to cryptography, and applications to quantum computing. Grover's algorithm has a lot of practical uses. We definitely talked about applications. It was not like we're expecting to make money on this in the next year type of thing, or even next five years, but when you sell it to government to write a grant, or you sell it—presumably, the people in Microsoft and IBM, when they talk to their bosses of why they should support quantum computing, are telling these same stories, right, that someday, it's going to be really useful.

ZIERLER: Yeah.

GOTTESMAN: But this is also a bit of a later era. By the time I got to Microsoft, we were kind of ending that first bloom of activity in the field. I'm not sure I would say progress was slowing because the number of people had grown enough that there was other stuff, but the work that was being done—in the mid- to late 1990s, there was just like a major new result coming out every week. It was like an incredible ferment of stuff, stuff that even today seems important. By 2000, it had kind of slowed down. There was still important stuff coming out periodically but not at quite as high a rate. We had some better ideas, but we still didn't really know what a quantum computer could do, and what it couldn't do. There hadn't been a huge explosion in the number of quantum algorithms, so people were starting to recognize that that was a hard problem, but, at that point, it was more like, well, there still could be lots of things out there; it's just hard to find them. That's still true today, I would say.

ZIERLER: How did the paper with Alexei and John, Encoding a Qubit in an Oscillator, how did that come about?

GOTTESMAN: That's kind of a funny story.

ZIERLER: That's your first collaboration with John, right?

GOTTESMAN: Yeah, it might be. Probably. That paper—of course, Kitaev was at Microsoft as well.

ZIERLER: But he had been at Caltech for a small amount of time, and then came to Microsoft.

GOTTESMAN: That's right. He visited Caltech for like a year or two. Then he came to Microsoft for two years, I think. Then, I think, after that, he definitely went back to Caltech. I don't remember if he got permanently hired right away, or if it was another year or two. He knew John. He collaborated with John. Actually, the origin of that paper was me visiting Caltech. John and I were talking about some older papers about quantum error-correcting codes for continuous variables that we thought used an unsatisfactory error model. They used a model where—continuous variable systems, they can have like any value. A classical continuous variable system is like a real number, a position, right. It can be anything within a range of zero and one, or infinite range, as opposed to a bit, which just has two values, zero and one. It has infinitely many values. Then you can think about analogous quantum systems, which can now be superpositions of different positions, or all of these infinitely many values. The error model that they were thinking about in these previous papers was, OK, you have a number of these different continuous variables, or systems that have continuous variable degrees of freedom, and one of them gets messed up in some arbitrary way, but the other ones are perfect.

We thought that's very unrealistic. What you'd expect in a system that could take any value was that it kind of got shifted a little bit, and that would always happen because getting perfect precision, that's not realistic. We said, well, can you come up with an error-correcting code that can do that. This was our idea, what's now known GKP codes. Then my visit ended. I went back to Microsoft. For years, I actually told people I never talked to Alexei directly about this paper; that he visited Caltech, and talked to John, and that's where Alexei's contribution came in. Actually, it turned out, last year or something was the 20th anniversary, and I was speaking at some conference panel discussion, or something. I looked back at my old emails, and it turns out I did actually talk to Alexei about it a little bit. Primarily, it was me and John, and then Alexei and John. Even though both of us were together at Microsoft, we didn't do much direct collaboration on it.

ZIERLER: Looking back in retrospect, what was the impact of those ideas?

GOTTESMAN: For a long time, very little. It came out at the same time as a paper by Knill, Laflamme, and Millburn, like roughly the same time, which was a bit different. Light is an example of a continuous variable field. This was a proposal basically for how to build a quantum computer with light fields in a way that was a bit robust. It had error correction built in, but there was a different proposal at the same time by Knill, Laflamme, and Millburn. The problem with the GKP codes is that just creating these codes, they were very weird states of light, and we had no good ideas how to do that, and nobody else did either for a long time. While it was theoretically interesting, it didn't seem that practical in the short-term. You had to get past this first step to make the codes.

Once you did that then, kind of like doing gates and stuff like that in a fault-tolerant way, that was pretty straightforward, although there's one that's hard. That meant that nobody could do it experimentally back then. Whereas this Knill, Laflamme, Millburn was much more accessible experimentally; that people could do it right away on a small scale. In the long run, it's much harder to scale up. Error correction is something you have to put on top of it. It's not built in. While evolutions of that idea are still important, at the time, that was the only thing. Our paper was like, oh, that's interesting, but this is the real thing. It was only in the last five to ten years that people have actually been able to do it experimentally, our stuff, and then that's kind of fueled a resurgence of interest.

ZIERLER: It was far-reaching. It just took a while. It was latent for a while.

GOTTESMAN: Yeah. It's not like it was unknown. If people had not known about it, probably it would never have been revived. But people knew about it. They thought it was interesting but, like, too hard.

ZIERLER: Now, the next position at Berkeley, it was the Clay Institute that made it possible? How did that work?

GOTTESMAN: Yeah. Clay Math Institute was brand new. One of the first things they did is they wanted to have like a prize fellowship for postdocs. Normally, nowadays, they like to pick like people right out of grad school pretty much, or basically pretty young. I was old. Having done three years of postdocs, I was older than they would now consider, but because they were just starting, they wanted to get some people who were kind of further along so they would finish sooner, and so they could have a stream of people every year. They offered me this. They offered me this fellowship, and I didn't apply for it. It was just they came up with the idea somehow, but they didn't want me to do it at Microsoft because it was a company. I had to move to take it, and so I moved to Berkeley, which was, as I mentioned, another at that time hotspot of quantum computing.

ZIERLER: Who was there? Who was doing interesting work?

GOTTESMAN: There was Umesh Vazirani, who was one of the people that was doing quantum computing before Shor's algorithm. There was Birgitta Whaley, who was a latecomer, relatively speaking, like post-Shor's algorithm—post me, actually. [laugh] I think she had moved into the field later. She had a group of—first of all, Umesh had some amazing students, and there were some also pretty amazing postdocs there. Birgitta had some as well. A bunch of people whose names are now famous, some of them have left the field and come back into the field. There were a bunch of people there.

ZIERLER: Now, being back in California, although far away, were you following developments with the IQI at this point?

GOTTESMAN: Yeah. It's not that far away from San Francisco, right? I visited pretty regularly. By then, IQI had grown into a big thing, and there were a lot of people, and it was always interesting.

ZIERLER: The other paper with John at this time on squeezed states, did that come out before or after the one on qubits and oscillators?

GOTTESMAN: That was the same time. They were—

ZIERLER: Were they related at all? Were the topics related? Was it all one conversation that was split?

GOTTESMAN: Yeah. No, they were 100% related. We came up with these error-correcting codes, the GKP. Maybe a little more context. Quantum key distribution was proposed by Bennett and Brassard in BB84 protocol, but it took a long time before people had proofs that it was correct. The first proof came out kind of in the late 1990s by Dominic Mayers, but it was complicated. People didn't really understand it. Then there was another much simpler and cleaner proof. There's again some sequence of events. There was a kind of entanglement-based protocol proved by Lo and Chau. Then, Shor and Preskill had this proof that used quantum error-correcting codes to prove that quantum key distribution was secure. We came up with this new class of error-correcting codes, and of course John knew about it. I knew about it as well, this Shor-Preskill paper. We immediately saw that, oh, if you plug our new family of codes into this same argument, you get a new family of key distribution protocols that we can prove is secure. It was mostly like a natural consequence with the paper.

ZIERLER: Berkeley was an exciting time. There was a lot of good work that was happening there.

GOTTESMAN: Yeah, so, you mean in general?

ZIERLER: Right, just as a center of quantum information.

GOTTESMAN: Yeah, that's right. It was, I would say, comparable in size at the time to IQI. IQI might've been a bit bigger. The universities to go to for quantum computing back then were Caltech, MIT, and Berkeley.

ZIERLER: At Berkeley—it's more an administrative question than scientific—but would the home department have been mostly Physics, or would it have been Computer Science at that point?

GOTTESMAN: Not Physics at all, in fact.

ZIERLER: Interesting.

GOTTESMAN: Umesh Vazirani is a computer scientist. He's in the Computer Science Department. I was sitting in the Computer Science Department. Birgitta Whaley is in the Chemistry Department, I believe. She's originally kind of a physical chemist, but moved into quantum computing, and so her people work mostly in the Chemistry Department with her, I guess. There may have been some students that were coming from the Physics Department that work with her. I'm not sure.

ZIERLER: That's interesting. Were people talking about quantum chemistry, which has been cited as perhaps one of the most viable areas of commercial utility at that point?

GOTTESMAN: Yes and no. Simulations, one of the applications was clearly to chemistry, of simulating quantum systems. In that sense, we were aware. At that time, people weren't kind of going through and saying, well, what molecules should we try to simulate, and stuff like that.

ZIERLER: The Perimeter Institute, by the time you got there in 2002, it's only, what, a couple of years old at that point?

GOTTESMAN: It was one year old. Okay, it was kind of two years old but the first year, they didn't have any scientists yet. They were just kind of like ramping up.

ZIERLER: Lee Smolin told me the whole crazy origin story of [laugh] the Perimeter Institute. [laugh]

GOTTESMAN: There's a book on that.

ZIERLER: Right, that's right. Being so new, was quantum information baked into the founding story, or was your hire part of building something that might not have been there at the earliest discussions?

GOTTESMAN: I think it was there from the very early stage. Howard Burton, I think he saw it as a hot topic, and he thought it was a good thing for Perimeter to get into. Mike Mosca was already at the University of Waterloo in the Department of Combinatorics and Optimization, and he was doing quantum computing stuff, so he got involved. There was an effort to hire Raymond Laflamme, except that he wanted to do experiments, and a theoretical physics institute is not a great place for experiments.

ZIERLER: Right.

GOTTESMAN: They kind of created the IQC at Waterloo for him to kind of get him to come. They were there already. Then I was in kind of the next year applicants where along with Lucien Hardy doing quantum foundations.

ZIERLER: Yet again, the job market at that point, obviously, this is an academic position but the Perimeter Institute is not a degree-granting—it's not a traditional college. Part of the idea there is that that's simply not quantum information scholars, physicist computer scientists, whatever you want to call them? It was really still a tiny field at that point? There were not new programs that were looking to hire?

GOTTESMAN: Yeah. By then, the job market had opened up a teeny, tiny bit. There were still companies that were interested, although some of those companies—one of them was Bell Labs, was Lucent, and that didn't work out so well. I actually had an offer from them, and, if I'd taken it, I probably would've been looking for a job in a couple of years.

ZIERLER: Yeah, that's right. [laugh]

GOTTESMAN: Not probably; definitely. There were non-academic jobs. There were national labs. I had an offer also from NIST in Gaithersburg. I did have an academic offer as well from UC Davis. But the Perimeter seemed like the most attractive.

ZIERLER: Is that because it was just exciting, again, to be there at the beginning as these things were just coming to be developed?

GOTTESMAN: I guess there was an element of that. The design, the goal, was to make a kind of a research utopia where you didn't have to do anything but research. That was attractive as well. I was attracted by the goal of building a world-class institution, which is an aspiration that I could definitely get behind. I did come from this background where I was interested in quantum gravity, so I enjoyed talking to Lee Smolin and to the people that were there about other crazy stuff. It was a combination of a bunch of things, I think.

ZIERLER: How was the Perimeter Institute situating itself? It's not a degree-granting university. It's not industrial research. What space was it looking to occupy as this quantum information field was rapidly growing?

GOTTESMAN: First of all, in terms of academics, the closest analogy that's usually made for Perimeter is the Institute for Advanced Studies, IAS, in Princeton. It's a nonprofit research institute. There's not that many of those in the world, although there's more maybe nowadays than there were back then. In terms of quantum computing, this is a strategy that lots of places can use and have used, which is if you can identify a new area where the universities are kind of behind, you can jump to a quick lead by snatching up good people in that area. Now, I spent a lot of years trying to hire people at Perimeter, and it was not actually that easy to snatch up the good people. Between Perimeter and IQC, there's certainly a lot of people there.

ZIERLER: Being in that environment, did that influence the kinds of things you wanted to work on, the people that you were working with?

GOTTESMAN: Not that heavily. There's this thing that if you're at the same institution as somebody, you can talk to them anytime you want.

ZIERLER: Right.

GOTTESMAN: Therefore, you don't because there's no urgency about it. I had all these colleagues at IQC at Waterloo who I hardly ever saw. I saw them at seminars maybe. But then when I went to a conference, I would talk to them there. [laugh] So, at that point, I think I would say I was still kind of part of this global community, and my collaborators were elsewhere, almost exclusively.

ZIERLER: Daniel, what about on the mentorship side? Did you have opportunities to interact? Could you serve on graduate committees, work with postdocs, that kind of thing?

GOTTESMAN: Yeah. Perimeter had great opportunities to hire postdocs. We hired many, many over the years. I tended to let them do their own thing. That was kind of Perimeter's philosophy was that the postdocs should be their own researchers. They're not working for the faculty members. I collaborated with some of them sometimes, but mostly when we hired people, I didn't make any effort to make it something that I was going to collaborate with. Some of them were doing stuff that was related. Some of them were doing other, totally different stuff. Most of them were doing totally different stuff. At first anyway, the students were all at University of Waterloo, so I didn't have quite as good access to them. I met some of them. I talked to some of them. But I could serve on their committees, certainly, in a number of cases. But I didn't supervise any students, although many people at Perimeter didn't do that, even back then.

ZIERLER: Tell me about the work with John, and Wilson loop operators.

GOTTESMAN: That was another visit to Caltech. That one, I don't feel like I had a big role in. There were two papers, two related papers there again. One of them is this paper on Causal and localizable quantum operations, and the other one is the Wilson loop operators paper. Those are actually related although, nowadays, I might have difficulty explaining how and why. But, basically, the idea is we were trying to understand what could actually be measured in a physical way. You can write down measurements in a formal sense where you measure there's these possibilities for the outcomes. But it was a question, can you physically implement that? So, what we found in the first paper, the Causal and localizable, was that there's some measurements that you can write down but can't actually be implemented if the pieces are distributed in space. They can be implemented if you have the right entanglement resources to start with. But, even then, you may need some communication as well to implement those things. There's, again, different kind of resources. Can you implement them if you don't have any entanglement? What if you have entanglement but you can't communicate? What if you could communicate but only in one direction, from Alice to Bob but not from Bob to Alice? So, that's what that paper was looking at. Then, the specialization—Wilson loops in non-abelian gauge theories turn out to be one of these things that you can't actually measure, and so that's what the second paper was about.

ZIERLER: The single-author paper you did in 2003, Unclonable Encryption, what's the idea there? Does that get to some of the NSA's interests in quantum encryption?

GOTTESMAN: Yes. It's hard to know exactly what the NSA's interests are. But it certainly relates to cryptography. In that sense, it's of interest to the NSA. The idea there, there's this famous no-cloning theorem, which says that there's no process that will an arbitrary, unknown quantum state, and make two copies of it. That's something that's very different from classical information, which has this property that you can always copy it, and make as many copies as you like. My idea to apply this property to encrypted states. If Alice wants to send an encrypted message to Bob, one problem that they have is that Eve is the eavesdropper listening in. If they're sending just classical bits, she can just copy all of them down. While she won't understand them at the moment, she can spend as much time as she wants later to try to break that code.

But my idea was that, well, if Alice is sending qubits to Bob, then Eve can't do this. She could take them, but then Bob knows that she took them because he didn't get anything—or she can let them go through to Bob, but then she can't work on it later. If she wants to break it, she has to do it at the time. Anyway, that was the idea. I came up with a protocol that does that, and gave its relation to some other cryptographic protocols, and basically no one cared. That was like a completely unknown paper, even though I was relatively well-known. But it was one of my favorite papers. I liked it. It was very kind of cute. But, like, a couple of years ago or a year ago maybe, there's been, again, a resurgence of interest in this idea, of people revisiting this.

ZIERLER: We've emphasized, obviously, the impact of mathematics, Shor's algorithm, on quantum computing. When did you start thinking about the reverse, about the ways that quantum information science was providing new insights into mathematics?

GOTTESMAN: Good question. [pause] It's something that's grown over time. I think math has actually been a relatively late field to be impacted by quantum computing. But Kitaev's toric code is important in condensed matter. It's the simplest example, basically, of a topologically ordered system. Then there's been this slow accumulation of quantum information ideas dripping out into other areas. Certainly, I actually haven't written all that much about that. But I had this one paper with John, which is a comment, actually, on a Horowitz and Maldacena paper, Black Hole Final State, where we use quantum information ideas to critique this basically string theory. It's not really a string theory idea but it's from string theorists. As far as awareness that this would be a good or useful thing to do, I'm not sure when I came to that realization. Again, it's probably a kind of a slowly growing thing.

ZIERLER: Sure, sure. Here's a fun one: Quantum Refrigerator. What is that?

GOTTESMAN: You're just picking out the ones that have interesting titles, I can see! That paper, again, is something that I feel is like mostly other people's work. My collaborators, Michael Ben-Or and Avinatan Hassidim, had—this paper's about kind of the limits of fault-tolerant quantum computing, and what you actually need in order to make fault tolerance work. There was an old result by Dorit Aharonov and co-authors, one of whom was probably Michael Ben-Or, where they showed that for certain kinds of errors that if you had a quantum computer where you had no ability to reset qubits or bring in fresh, new qubits, then fault tolerance was impossible; that, eventually, the errors would overwhelm the system. It's kind of a thermodynamic thing; that entropy is coming into the system through the errors and, eventually, you don't just get maximum entropy. You can't do anything. Eventually is not very long. It's like logarithmic in the size and number of qubits you have. Michael Ben-Or and Avinatan Hassidim had studied this same problem but with different kinds of errors, and they found that there were kind of three classes of things that could happen, depending on the types of errors that you had. One of them was this original result where it just didn't work. Another one was where you could run a quantum computer for a limited amount of time, for like a polynomial amount of time in N. But after that, the errors would overwhelm things. The third class was one where you could run it for an exponential amount of time because you could use the errors themselves to reset your qubits. That's the part that gives it the name quantum refrigerator because you can use the errors as a kind of refrigerator to cool down your qubits so you can use them again for error correction. I heard about this in a talk that Michael gave at Perimeter, and I thought this was a really cool result, but they didn't have a paper on it. A couple of years later, I'm writing a book on quantum error correction, and I'd been writing it for a long time; not as long as John has been working on his famous book.

ZIERLER: [laugh]

GOTTESMAN: There's one area where he's been a very bad example for me. I was writing this book, and there's a section of the book where I talk about the limits on fault tolerance, and what properties you actually need, what you don't need. I thought I wanted to say something about this result but there was no paper about it. The reason for that, talking to Michael and Avinatan, was that this second case where you could run for a limited amount of time, and then errors would overwhelm it, they didn't have a proof that it actually behaves that way. I thought about it, and I came up with a proof, and then we wrote the paper.

ZIERLER: Now, during this time in the 2010s, going back to when John was thinking about black hole information, when you were a graduate student, and then later when Alexei was thinking about black hole information within the context of all of the advances in quantum information, were you part of that at all? Were you working on this topic at all yourself?

GOTTESMAN: No. My contribution to that area is this comment with John on the Black Hole Final State. The paper's called the Black Hole Final State, and we wrote a comment on that. That's been my sole actual contribution in that area.

ZIERLER: What does that mean, of the final state?

GOTTESMAN: There was a proposal by Horowitz and Maldacena where they said—remember I said black hole has this horizon. Information can't get out. The other property of the black hole is that at the middle of it, there's this singularity where the gravity gets infinitely strong, and presumably physics goes crazy. Quantum gravity is going to be a really important bit of that. That's the thing about the black holes is that, at that singularity, quantum gravity seems like it's important. But out at the horizon, well, that's a big deal. But, locally, you can't tell that you've crossed the horizon. If it's a really, really, really big black hole, it just seems like anywhere else. But it's the point of no return. Once you've crossed the horizon, you can't get out. You're always going to hit the singularity. If the information is going to get out, it seems like it has to do it from the horizon or before the horizon because, otherwise, it's too late. But, at the same time, quantum gravity shouldn't be important till you hit the singularity. That's another way of phrasing the problem. Horowitz and Maldacena, they had a very interesting proposal. They said, "Well, what if what happens at the singularity, which we expect is crazy, is actually even crazier than we think, and it's something that's non-unitary?" So, that's normally not allowed in quantum mechanics. It's non-reversible. It breaks the rules. But if it's the right kind of non-unitary thing—remember, we talked about quantum teleportation. Quantum teleportation splits it up into an entanglement piece that's the quantum piece, and a communication piece. The entanglement piece in the black hole comes in the form of the Hawking radiation, which has two parts. One of them is inside the black hole. One of them is outside the black hole. But what about the communication piece? You can't communicate out of a black hole.

This is where the non-unitarity comes in. If you get this appropriate projection at the singularity, then you don't need to send information out because you're kind of forcing it to be this one particular outcome. In quantum teleportation, you make a measurement. There's four possible outcomes. But if you know which one it is, then you can reconstruct the original state without having to communicate classically. That was their proposal, that the physics of the singularity just forces it to be one of these things somehow. The crazy stuff is going on at the singularity but the information is still coming out. That's kind of a cool proposal, and it obviously has a quantum information aspect to it. But John and I had heard talks by people using the idea of teleportation with a similar kind of projection, you can kind of imitate time travel because, while you can get out of a black hole, you could also have one part of the entangled state be back in time. Just the same way, if you don't need communication, you might as well, say, send it back in time. Then it starts to interact with each other, and you can get time travel paradoxes. Thinking about that, we kind of both immediately and sort of independently realized there was something wrong with this proposal, which is that in order for it to work, you had to make sure there were no interactions between the entangled state and the stuff that was falling into the black hole before they hit the singularity. That seemed very unlikely to us, and so that's what's in our comment.

ZIERLER: Sort of a retrospective question in this narrative, to go back to the exuberance again from the Caltech days of infinite possibility, as you were getting into 20 years in the field, what developments or lack of developments might have given you pause that the breakthroughs might be on a longer timescale than might've been apparent in the 1990s?

GOTTESMAN: First of all, experimental progress was and is always slower than I'm hoping and expecting. Even though I knew it would be a long timescale, it's not quite—it's longer, still longer than I expected. For many years in this field, people would always ask, and they probably still do, "When can we expect to see quantum computers as a real thing?" For a long time, I would say "20 to 30 years, on the basis that, by then, you'll have forgotten what I said." That was a way to represent that there was a lot of uncertainty, because it was clear that we didn't know. If you asked other people, they would say all sorts of different numbers. I kept telling that joke for like 20 years. Then I finally, in the past five or ten years, I had to stop. Well, I didn't have to stop, because now it could be less than that. It's possibly less than that. But maybe, actually, that's still an accurate estimate, I don't know. It depends what you consider a quantum computer, how big it has to be before you're satisfied.

ZIERLER: You're biased, of course, as a theorist, but do you appreciate how experimentalists might say, "Hang on a second, now, I think that the theorists need to catch up with us"? Is that defensible in any way?

GOTTESMAN: I'm not sure the experimentalists would say that. I think it's more likely they would say, "Those theorists are wasting their time on stuff that's not going to be practical for many, many years." Nowadays, that's not true anymore because there's a lot of theorists doing near-term NISQ stuff. But, for a long time, that's what we were definitely doing. No, but even then, I don't think they were saying that because first, when you go to the funding agents, you want to say, "Someday, this is going to be great, and here's what it can do," and that's where the theorists doing this far-future stuff come in. The other thing is that experimentalists, what they're doing is they're developing their systems. They're improving their control. They're getting more qubits. They're connecting them up. Whenever they do that, they want to write a paper, of course, saying that they did that. But it's not that interesting to just say, "Oh, and now we have better qubits. We can do this." They want to do something with those qubits, and so they like to pick out theoretical protocols, and demonstrate them.

The media tends to report this, "Oh, this is the first demonstration of this theoretical protocol." But that's not actually what's interesting. What's interesting, from a scientific perspective, is the new technical advances that made that possible. The fact that the protocol worked, that was never in doubt. If it didn't work, either quantum mechanics was wrong or the experiment doesn't work that well, and it's always the latter. The experiments are hard. If it doesn't work, that's not surprising. If quantum mechanics is broken, you need a lot of evidence before you conclude that. It's kind of a funny field in that, for many years, the experiments were not to find out new stuff; they're to demonstrate and develop new capabilities. Now, we're starting to reach the stage where you can also find out new stuff. It was always true that you're finding out some stuff about the physics of those specific devices, which can be important. But, now, it's starting to get to the stage where there's even more stuff that you can find out, like does this quantum algorithm actually work or not?

ZIERLER: Daniel, throughout this talk, we've had peppered references to string theory. I'm curious, as you're well aware, this dynamic in physics where there's a certain set of physicists who have lost patience to some degree with string degree; that it's gone off way into mathematics. It has not shown any promise in demonstrating nature. Obviously, right now, in quantum information theory, there's so much excitement, and nobody's talking like that, as far as I can tell. Is there a concern at some point in the future that that similar dynamic or tension might come up, and is that incumbent upon the theorists, or really are the experimentalists the ones who everybody should be looking to so that a lack of patience for a breakthrough is not really a reality?

GOTTESMAN: In quantum computing, there are definitely voices who are critical of it. From the beginning, there's been the voices critical of it. It's different critiques. A lot the critiques have been of the nature, this will never work, either because quantum mechanics is wrong or those stupid quantum computing people, they don't understand this, that, or the other thing. Only occasionally, the real reason that it might not work, which is that it is so hard. [laugh] Nowadays, you also get a lot of people saying there's so much quantum computing hype. Those are people in the field, out of the field, everywhere, and there is a lot of quantum computing hype. That's definitely true. Part of the problem of having all this industrial interest, it's a big source of money, but industry usually works on a much shorter timescale than the field of quantum computing has so far, and that research does in general. If it gets impatient, and says, "We've put in all this money. Why don't you have quantum computers that can do whatever you said?" some of that or most of that money could dry up. That's definitely a possibility. It hasn't happened in string theory. There's been a lot of doubters but the field's just continued to grow, and there's lots of people doing it. The better analogy of what could happen to quantum computing is something more like fusion, where it's clear that if you could do it, that would be really useful. But it's a hard problem, and people have worked on it and made progress over the years, but the progress has been so slow, lots of people just kind of gave up on it.

ZIERLER: If there was a do over, would you have found it preferable to have dampened expectations about a scalable quantum computer being the thing that we hold up to define the viability of the field? In other words, the string theorist Cumrun Vafa, for example, would be the first to tell you, listen, this is a toolbox for mathematics, and it advances physics research in and of itself. Even though there's frustration, there's lack of patience, there isn't this big prize at the end of the string theory rainbow that everybody is waiting for maybe a quantum theory of gravity, whatever, but quantum information has, in some degrees, put pressure on itself to produce something. Is that a fair analysis of where we are?

GOTTESMAN: Yes. But I would say that we have that same argument in quantum computing: that it's useful. It's useful in string theory. It's useful in condensed matter. It's useful in a growing variety of fields. It's useful in classical computer science. It's useful in math. There's a recent result that proved a kind of a fairly major math conjecture. I don't really have a sense of how important that conjecture was, but it's a definite thing. We definitely have those spinoffs. If somebody asks me, "What if nobody builds a quantum computer? Was it all wasted?" I always point that out. But it's definitely true that most of the noise comes from the applications.

ZIERLER: What are you most optimistic about as a physicist in terms of the big problems in physics, and the possibilities that quantum simulation will really provide breakthroughs in that realm?

GOTTESMAN: If you think of the capabilities of computer-aided design for—it's just like a standard tool now. If you're building anything classical—if you're building a bridge, if you're building a plane, if you're building a car, if you're building a computer—you design it on a computer first. You don't try to put it together. A quantum computer gives us that same capability but for molecules and for new materials that you can imagine building at the atomic level. That's just a very powerful tool that can be a catalyst to immense improvements. Some of them will just be kind of incremental in that bridges are safer because we can simulate them first. You don't have to over-engineer them. You don't need as much materials to make them safe. Some of them will be of that nature, and some of them will just be transformative. It's just like something we didn't think of before because we had no idea it was possible. But you found it by exploring it on a quantum computer.

ZIERLER: Then, really breaking news, bringing it right up to 2021, 2022, tell me about your decision to join University of Maryland.

GOTTESMAN: This was mostly a personal, family decision. I liked Perimeter Institute. I was happy there. But for my wife, this was kind of a better opportunity. She does both science and music. Waterloo's kind of a small city, so there's not quite as many opportunities there as here.

ZIERLER: Looking to the future, with expanded opportunities now to work with graduate students postdocs, undergraduates, to get back to this idea of where things might be headed in the future, for the younger generation for whom there might be uncertainty, even though it was you had uncertainty when you were a graduate student but you might not have known it at the time, is the uncertainty more obvious now, would you say, to a graduate student interested in quantum information?

GOTTESMAN: No. Right now, I think the job prospects for someone that graduates with a degree in quantum computing are quite good. There's a lot of people doing that but there's a lot of jobs as well. This new quantum computing industry has a huge hunger for people.

ZIERLER: This is boom times in quantum information right now we're in.

GOTTESMAN: Yeah. Now, I don't know how long that will last, of course, hopefully a long time but maybe not. I don't know. Probably, it depends on the individual graduate student, how aware they are of the ups and downs of industrial investments. But I guess I haven't really talked to them about that. The students that I'm talking to are like early students, so they're not really thinking about that sort of thing yet.

ZIERLER: Right. Finally, Daniel, for you, last question, what are the big topics? You've worked on so much in so many different aspects of quantum information. Are there big topics that really you see as the frontier, the areas where you want to spend your time, going forward?

GOTTESMAN: Well, yeah, I'm still interested in fault tolerance and understanding—I think a lot of these fault tolerant protocols are very ad hoc, and I'd like to kind of get a better understanding of how they work, and the similarities and the differences between them, and kind of some sort of unifying theory. As I mentioned at the beginning, I'm interested in applying quantum information ideas to telescopes. I think there's a lot of other opportunities beyond this interferometry thing, so that's, I think, an interesting thing.

ZIERLER: On that point, all the excitement, like the James Webb or the ELT program, what might we see in the universe as a result of quantum telescopes?

GOTTESMAN: That I don't really have a good sense of, partly because I don't yet have a good understanding of the scope of things that quantum information can help with. That needs more research. Specifically, the interferometers, that would be very high-resolution optical telescopes, so may be useful for things like imaging extrasolar planets or something, although that, it turns out, is kind of faint, so it's not a great candidate for this type of thing.

ZIERLER: Well, there's some hype: quantum information scientist discovers life on an exoplanet. [laugh]

GOTTESMAN: Yeah, that's not going to happen. But—

ZIERLER: Hey, maybe. Who knows? [laugh]

GOTTESMAN: I think, someday, I suspect that quantum information tools will be critical to telescopes. It's a good area for quantum information in the sense that if you have a delicate technology that really requires experts to build and maintain, that's kind of the regime that telescopes are working on at the pushing edge of technology. They're always willing—and quantum information's alien to them, so it's not ready for that yet. But the culture can adapt to new technologies like that. Even when they're kind of still experimental, they can start to integrate them.

ZIERLER: Being in NASA's backyard, and right by Space Telescope, is it possible that just being geographically nearby, that's an advantage at some point, or that's way too far afield?

GOTTESMAN: Yeah, I haven't really thought about that. It could be, I suppose. Like I said, I haven't really thought about it. But it's useful to talk to people that work on actual telescopes, and understand what the issues are, and what you would want to solve with quantum information.

ZIERLER: Daniel, this has been a fantastic conversation. I'm so glad we were able to do this. Thank you for spending the time.

[END]