If you’re a developer who wants to write code for a quantum computer, how do you know which quantum architecture and by extension which company’s quantum computer is best suited for the problem you’re trying to solve? Likewise, if you’re interested in connecting quantum computers together across a quantum network, how do you pick the right hardware and network design?
Aliro Quantum, thinks the answer to both these questions is to use an abstraction layer.
On this episode of Dynamic Developer, I talk with Dr. Prineha Narang, Assistant Professor at the John A. Paulson School of Engineering and Applied Sciences at Harvard University and CTO and co-founder Aliro Quantum about how the company is trying to make quantum more accessible with cloud technology.
Alrio’s Q.COMPUTE platform is designed to help software developers pick the best quantum computer for their projects without having to understand all the different types of quantum computing hardware. And the company’s Q.NETWORK product can help network engineers design functional and efficient quantum networks.
The following is an transcript of our conversation edited for readability.
Bill Detwiler: So before we get to Aliro and we talk about quantum computing and quantum networks, I’d love to hear a little bit about your journey into this world of quantum computing and quantum networks. You did a lot of your early work, I think, around light and around 2D materials and looking at how they interact. Talk about how you go from doing that, things around, like plasmonics to quantum computing and quantum networks. How do they relate to each other?
Dr. Prineha Narang: Absolutely. Okay. So I’m glad you asked about my personal background. I got my PhD at Caltech. And when I was there, I really started to think about how do light and matter interact and how do we describe that from a computational perspective. And it turns out that as we were thinking about, “Are there existing messages? Do we try new methods? How do we think about these quantum interactions?” I got really, really, really into GPU accelerated computing. Okay. And I’d always been one of those nerds who was like, “Okay, pulling these out of PlayStations.” And this got me to a point where I said, “Wow. There’s real scientific power associated with these new computing architectures.”
Fast forward a few years, it turns out that almost every big supercomputer that we run calculations on today, whether it’s for 2D materials, whether it’s for nanophotonic interactions, whether it’s for interesting new topological materials, all of that is on actually GPU accelerated supercomputers. So, that just ended up being really good timing. As I was doing that, the fields of quantum computing was just about getting to that point where people said, “Hey, one of the first applications of quantum computers could be in thinking about describing these quantum interactions, thinking about whether they’re molecules, whether they’re materials.” There’s this phrase reviews to chemistry and quantum chemistry is a killer app of quantum computing. So that phrase was just coming on the market. And I said, “Okay. Well, I’ve always thought about interesting new ways of computing stuff. So maybe this is going to be the new normal and I should start teaching myself what to do here.”
So, that’s when I first came to MIT. And now, of course, I’m a faculty at Harvard. I started talking to faculty here, and they said, “Yeah, let’s think about these various architectures.” And this is before IBM made their quantum computer available via this Q Network. Just this idea of being able to access a quantum computer from home, I feel like a hipster saying this. I was doing quantum computing before that. And of course, that really completely changed the game, because it went from me going and talking to colleagues who have hardware, them telling me about, “I use a trapped-ion,” or “I do photonic quantum computation,” or “I’m a superconducting person.” Those lunch conversations really turned into actually these technology pieces that will be commercialized and we should really be thinking about what problems can be run on them. So for me, it was a very natural transition from thinking about using the largest awesome as possible classical resources to using quantum resources for some of the same problems. So, long-winded answer to how I got here.
Bill Detwiler: I mean, it sounds like it was born out of a lot of that work you were doing there in the theoretical space because you wanted to be able to test things and do experiments using… You had to use the computers to do those, and you needed faster and faster and larger computers to be able to do them at a level that was precise enough to replicate maybe what you couldn’t do in the real world, right? Is that kind of what…
Dr. Prineha Narang: Exactly. Exactly. And that has been the promise of quantum chemistry, quantum trials is that you can actually predict the behavior before you measure it and before you go out there and do it. So I often describe it as doing experiments in a computer before somebody goes out there and tries to synthesize the material. Because if you think about the possibilities for number of molecules and materials, different dopants, their behavior, there’s far too many. You can pick your favorite example, while there are more combinations than there are atoms in the known universe or whatever mathematical analogy makes sense for you to realize that it’s an enormous problem. We’re never going to span that entire parameter space brute force by people going out there and doing it experimentally in their labs. But of course, the power of computation really is that you don’t need to do that anymore. You got it right on.
Bill Detwiler: So you can do it all at once. I mean, that was part of the beauty kind of, I guess, what we’ve heard about quantum computing is, especially with these optimization problems, you can run every solution at the same time, which dramatically reduces some of the time that it takes, as opposed to running these, like for encryption algorithms, running them over and over and over or running every solution one after the other, you can actually run them all at once. I know you’ve done a lot of stuff with materials science and that is one of the things you were talking about. So you’re looking at how you can create new materials that can be applied to consumer electronics or power generation, things like that, right?
Dr. Prineha Narang: Right. Exactly. And as you’re thinking about predicting those combinations, the qubit optimizing, what you have for these various materials, something you realize is that everything that is made of something is inherently a quantum problem. And there is a conjecture out there. We haven’t actually shown this, but most people think it’s true that the best way to describe quantum interactions is to actually capture them on a quantum computer. And the fact that we’re dealing with correlated states, which is a fancy way of saying something that’s happening here is actually talking to something that’s happening here and you can’t easily decouple those. So those types of many-body states are really, really hard, and in fact, in most cases, mathematically impossible to exactly compute on even the largest classical computers. And some of those problems, though not all, become almost trivial to do on the right size of a quantum computer. And of course, that naturally brings me to this point of what right size of a quantum computer is. So maybe that’s something that we’ll discuss a little more.
Bill Detwiler: Yeah. So let’s jump to what you’re doing with Aliro. And you’ve got two products, projects. Two things you’ve got, you’ve got Q.COMPUTE and Q.NETWORK. Since we’ve been talking about quantum computing, let’s do the Q.COMPUTE first. Tell me about what that is, what it does, how it works.
Dr. Prineha Narang: Absolutely. So Aliro is a startup that spun out of my group. They were very, very motivated students who worked with me, who said, “Hey, we’re trying to compute stuff on IBM’s device. And we’re also trying to do things on other quantum computers out there.” And something they realized very, very organically is that you don’t want to develop everything for one architecture, one type of computer, and then had to figure out how you’re going to put it over to everything else. I guess it’s something we take for granted in classical computers, right? That I can always write once and run anywhere. And that just wasn’t true and remains incredibly hard for quantum computers. So that’s probably the biggest problem.
Aliro Quantum Q.COMPUTE
Bill Detwiler: I was going to ask you about that. So is that the case currently without solutions like Q.COMPUTE, right? So if you wanted to use something from what IBM is using, or D-Wave, or whoever it is that you’re trying to work on, it’s almost like you have to learn a different language. And that isn’t something we’ve had to do for a very long time with traditional computing. So it’s incredibly inefficient also to completely rewrite your code every time you want to run the same problem.
Dr. Prineha Narang: Right. And it raises the barrier for people who are entering the field. So part of our motivation at Aliro in introducing this product is that every software engineer out there, every future quantum software engineer out there shouldn’t have to learn everything about five different types of hardware. And even if there are hardware solutions out there, they’re very similar. So if you think about superconducting systems, you might say, “Well, I wrote it for one superconducting system.” Well, it turns out that the way they implement their gates might not be the same as another provider of even a superconducting quantum computer.
And the situation totally changes if you start looking at different qubit realization. If you go to trapped-ions, so if you’re talking about something like Honeywell or IonQ, there are other companies that are now coming on the market versus somebody who is doing cold atom realizations or somebody who’s doing photonic. Those actual implementations of qubits are fundamentally different from how people are doing it on the superconducting side. So it’s not only learning a new language, you actually have to figure out how to map your entire problem over. And it may or may not be actually possible to directly map that problem over. That is an enormous barrier for people out there to overcome if they want to get into quantum computing. So that’s exactly the problem that we want to solve and are trying to solve at Aliro.
Bill Detwiler: So you need that abstraction layer, right? You need that layer to interface between what the developers, the programmers, the research, or whatever they’re trying to do, and actually translate in that back into the language to set of instructions that the machine can use.
Dr. Prineha Narang: Exactly.
Bill Detwiler: And is that what Q.COMPUTE does?
Dr. Prineha Narang: That’s what Q.COMPUTE does. Another thing, when we think about abstractions a question that comes up is, are you losing performance? So is that the trade-off? It turns out that’s not the case. Our product actually allows you to not only do optimizations at the circuit level and at the decomposition level, but also at the pulse level. So many of these hardware providers have given access. And this is literally at the pulse level. This is as close to the hardware as you can get. It turns out that because the hardware is at the moment limited, you can do some Q tricks at the pulse level. You can make some optimizations that allow you to increase the coherence time. And that actually allows you to directly compute larger problems, have deeper circuits more to qubit gates, which is something that people really want for these more complex problems. So, that’s the…
Bill Detwiler: Oh, sorry. What were you going to say?
Dr. Prineha Narang: I was just going to say, that’s something why we were excited about Q.COMPUTE and why people have reached out to us and say, “Hey, would you be willing to add our hardware to your….” And people are really excited to collaborate with us on it, on the hardware side that is.
Bill Detwiler: Cool. So talk to me about the different languages that it supports right now, because I know one of the ones listed is the some of the open source stuff, like QASM.
Dr. Prineha Narang: QASM. Yeah.
Bill Detwiler: And maybe Quil, I guess, as well too.
Dr. Prineha Narang: Yeah. Yep. Yep.
Bill Detwiler: How can people who want to take advantage of Q.COMPUTE from Aliro do that? What’s the first step?
Dr. Prineha Narang: So the first step is for them to upload something that looks like a circuit, right? So something that is in whether they’re thinking about gates that are native to superconducting or to trapped-ions. So say if they’re thinking in terms of Mølmer–Sørensen gates, which is a native gate set for trapped-ion systems. If they have something that looks like a circuit, they can upload it, and that’s really the first step. And something that the product does is walks you through is which hardware realization might be better for the type of circuit you’re looking at, or to give you some guidance around, “Hey, maybe you can break the circuit down into three components because it seems like the circuit you’re trying to run is incredibly long. It involves too many two qubit gates. So it’ll try and decompose that down to fewer and fewer, recognizing, “Well, you could actually reformulate this particular part into this gate set rather than this other thing, right?”
And the advantage of that is that to a user, perhaps like yourself, you can write down the most inefficient circuit and yet be able to run it. And you don’t have to personally think about, “Oh, maybe I could do this in a slightly different way or try it on a simulator before going to the product.” Because the other thing the product does, it gives you a list of simulators, both a noiseless and noisy simulators that you might be able to run on immediately, say if you were trying to figure out what it would do on a superconducting versus a trapped-ion system. So that’s really part of what the product is doing, is before you say go out there and try and buy time on Honeywell’s device, which is going to the cost you some-
Bill Detwiler: Not cheap, I’m sure.
Dr. Prineha Narang: Yeah. Or you go out there and say, “Aha, it seems like my very big complex problem requires me to have access only on the premium devices at IBM.” It’ll try and give you some of those optimizations. And also tell you if you run it on noisy simulator, “Hey, it seems like the circuit is… Ultimately, the errors are going to add up such that you’re going to get a result that you’re not happy with. You may want to reformulate this problem in this other way.” So that’s what…
Bill Detwiler: It’s a little bit of a guide, right? It helps you understand how best to optimize whatever the circuit is that you’re trying to create and run.
Dr. Prineha Narang: And for more expert users, it does the full transpilation step. It does everything that… You could send a job to an actual quantum computer if you felt like you were ready to do that right now. And I think that by having these different levels that people can interact with the product at rather than only expert users or only beginner users, we actually, I think, are helping the fields embrace quantum computing more fully.
Bill Detwiler: I mean, I think most people are at very beginning stages of realize or understanding how this might be applicable to their specific business or their specific research problem.
Dr. Prineha Narang: Exactly.
Bill Detwiler: What do you think the industry needs to do beyond, I guess, what you’re doing to help beyond the hardware, beyond making it cheaper, faster, more accessible, but I guess to help people understand how best you can apply quantum computing to problems that you have, right?
Dr. Prineha Narang: Right. Exactly.
SEE: Quantum computing analytics: Put this on your IT roadmap (TechRepublic)
Bill Detwiler: So we’ve talked about optimization problems. We talk about encryption a lot. We were talking about materials experimentation doing on a computer, theoretical experimentation there. What are some other ways that you see quantum computers being used in the future maybe more at scale?
Dr. Prineha Narang: Yeah. So we expect that there will be a set of problems that you would want to solve, part of it on a classical system and part of it on a quantum system, and identifying what those problems are, identifying what part of it can actually be done very efficiently classically, and what’s the crux of it that you want to do quantumly is something that I think that the industry is really moving towards. What I’m saying implicitly is that a lot of attention goes towards the hardware needs to get better, but actually a lot of effort needs to go towards what algorithms can be run in the near term. I’ll give you a concrete example of this.
IBM released this amazing roadmaps, very similar to what the roadmap that Google and folks have had internally, though they haven’t made it public yet. And there are other roadmaps of trapped-ion systems. And then you ask people, “Okay. So what exactly will we be running when we get to that 127 qubit device or 427 qubit device?” That is still a long ways from fault tolerance, that’s still a long ways from something that it does everything magically, but it is much, much larger than anything you could meaningfully simulate on a classical system. So how would we know that the algorithm is actually doing what you expected to? What is a good benchmark? What is good verification? And those are all problems that I think people are working towards solving on the algorithm side.
And built into that is this idea that maybe we want to do a little more co-design. So you’re thinking about the problem, at the same time as knowing where the hardware is, and thinking about, “How could I make some modifications on the problem side, whether it’s an optimization problem, whether it’s a problem in molecules pharma out there?” And you can say, “Okay. I have access to somewhere between 100 and 200 qubits. How do I best take advantage of that? What does that co-design? What’s that joint algorithmic development that I can do?” And that’s something that the industry is really moving towards. And we are-
Bill Detwiler: Is that concept of co-design a different way of thinking than the way we’ve traditionally used computers to solve problems? Or is it not? I mean, is it just extending how people are already designing programs, applications, problems for traditional computers to the quantum? Or is it really a new way of thinking?
Dr. Prineha Narang: It’s a little bit of both. I always think about the early days of CUDA and how you had to think about allocating memory very specifically. You had to think about how you were threading various GPUs. So it wasn’t obvious, but once you did that, it would apply to a whole host of problems out there. So you didn’t have to do it for every problem. I think what’s different here for quantum computers is that there’s going to be a lot more tinkering than you would have to do in any classical large-scale computation, both today and also say even a decade ago. But co-design has some feeling of the problem is not completely independent of the hardware you’re running it on.
This becomes especially true when you ask the question… While some algorithms, and we know this now a little bit experientially, so we don’t know this to be rigorously true from our colleagues and thrive on computer science, but we know that some problems run more efficiently on one hardware and not on another. And that needs to be fed back to the user somehow, right? They shouldn’t and won’t be able to rediscover all of that as they go along on their very, very tight timeline. Everyone’s working towards some milestone and they want to access to quantum computer to solve that problem. So the more we can transfer all of this knowledge to them, I think the better off the community will be and the faster the adoption of quantum computers will be.
Aliro Quantum Q.NETWORK
Bill Detwiler: Well, let’s switch gears and talk about the other product that Aliro has, which is Q.NETWORK. Now, this is something that I think is even maybe more, or how I should say, less well understood than maybe quantum computing, which is quantum networking. So talk to me about what you’re doing in that field.
Dr. Prineha Narang: Absolutely. So quantum networks are really, really, really exciting. And the way to think about it is that anytime you wanted to connect two quantum computers or two quantum devices in general, you would essentially be creating a very small scale quantum network. Okay. Now, of course, connecting two quantum computers that are next to each other has some implications. It means that you might be able to create a larger quantum computer. And the way you would think about that is, “Well, if I have two quantum computers and I connect them, it doesn’t obviously mean that I suddenly have 2X, the same quantum computer. I need to think about how I’m going to discortize the problem over that.”
A large-scale quantum network, however, would imply that I have a way of transferring a quantum state from point A to point B. And this is where things become a little bit difficult. When it’s local, it’s all fine. All I really need is a good way of getting fiber in, fiber out, maybe a step that then allows me to take the quantum state from a superconducting to photonic state and back to a superconducting state. Okay. And I’ll tell you why we need to do it that way here in a second. When thinking about a large scale quantum network, the challenge is very different, and there’s a whole host of reasons to do this. Of course, security implications is the fact that you have truly an unhackable internet, but also ideas like you could do blind quantum computing. And the reason you do that is maybe you had a really particularly valuable circuit.
Say this morning, in October, you came up at something and you were like, “This is what is going to change the world.” You don’t want your hardware provider to be able to see what you’re computing. You want to be able to do that the same way that you would run a calculation in any other cloud-based platform. And the only way to do that is to do that over a quantum network. So why a quantum network is so hard? A few different things. So in quantum mechanics, there is the most fortunate and unfortunate, no cloning theorem, which is that I can’t take a quantum state and essentially copy it, which is… That lies at the heart of all classical networking, is that at some point I realized I had too much loss in my fiber and I can copy that state over. Redundancy is my friend. Life is good.
In terms of quantum states, you really need to think about these things called quantum repeaters, which I know sounds completely out of some science fiction novel, but they are something that would allow you to then connect to say Boston and New York completely securely without there being any opportunity for hacks that we are not familiar with from various breaches. And no single fiber is awesome enough to carry that from here from Boston to New York. Okay. So that’s why I picked that example. Maybe if you were doing Boston to Cambridge, you’d be fine. But Boston to New York, you would not be fine. So you need a few repeaters. And as you introduce those repeaters, you’d realize, “Well, wow, there aren’t really existing repeaters out there that I can go and buy.” So there’s a huge hardware effort at the moment that various groups are pursuing, which is around how to build a quantum repeater. And my own research group thinks about how we can actually build next generation quantum repeaters as well. But how does that relate back to the Aliro product?
Okay. So I’m describing this network and I’m telling you, “I’m going to place a repeater here. I’m going to do this. There are various components that people making repeaters out in from different types of hardware realizations, different fiber out there.” And you’re thinking, “How does somebody who’s going to build this network know what components to put together, what typology to pick, what data rates they’re going to get, what performance are they going to get?” So that’s exactly what our quantum network product does here. It allows you to simulate. And of course, simulating classical networks was something that was essential to their success.
But the other thing that was very, very important for classical networks was actually doing direct emulation. And that’s where you’re essentially able to not only extrapolate something associated with a performance, you’re were able to set up a dedicated small version of the full network. And it really allows you to emulate the process before you go out there and actually say, “Aha, I’m going to put my repeater here. I’m going to use this type of fiber. I’m going to use this single photon source.” So that’s what our product here is doing. And it’s recognizing that there are multiple efforts underway now in the U.S., and this is extremely important that there’ll be these testbed efforts, right?
So these are small scale networks that people are building, connecting labs, connecting national labs across hundreds of miles to essentially try to show what a quantum network at scale would look like, even though they’re small testbeds. And we think that now is the time to introduce simulation and emulation of eventual network. Because if a big telecom company is to come in and actually pick this up, if we want some of the bigger players to actually embrace this as a technology, they want to know those numbers before they start actually putting their flag there and saying, “Okay, this is what we’re building. This is how we’re going to build it.” So those hardware choices need to be made, and those will be determined by our simulation and emulation product. So I’m incredibly excited about it.
And as this implicit in thinking about quantum networks, there are security implications is something that is a national priority. It’s something that has bipartisan support, that this is an area where the U.S. should be investing. We’re a little bit lagging behind actually. There are big efforts and demonstrations that have come out of the EU, out of China and elsewhere. So this is something that we hope being one of the few startups in this area that we can contribute to the efforts. Yeah.
SEE: How to build a quantum workforce (TechRepublic)
Bill Detwiler: So if I hear you correctly, what you’re able to do with Q.NETWORK is help the telecoms or help companies, help whoever is interested in building one of these networks create a virtual model of that within the software simulation of that, and then figure out how to create one more efficiently or at the most efficient way than they can before they actually start digging up the ground, laying fiber cables running. So this is a way to test that before you pour billions of dollars into construction.
Dr. Prineha Narang: Exactly. And this is also recognizing that there are more hardware choices. Okay. This resembles very much the early days of classical networking as well, where everyone had a solution. It was a lot more custom than we have now. So the repeaters that are out there, there are various realizations. And people who are saying these are mater-based, and then you’ll do some form of transduction to the photonic domain. There’s some people are saying it’s going to be all photonic, there’s no reason to go back and forth. There are some implications of that. There are fundamental hardware choices to be made. And this is where we think that very, very detailed simulation and emulation products will give any company that wants to be the first to… Actually, any telecom company that wants to be the first to build this quantum network, a huge leg up, because if they’re trying to develop this simulation, emulation in-house, that itself will take them a few years. And this isn’t something that lots of people are able to do anyway. I think this is enabling for various existing companies now.
When will quantum networks be a reality?
Bill Detwiler: How far away do you think we are from actually being able to deploy a meaningful quantum network? I mean, I can remember learning about back when I was doing my MCSE certification stuff, learning about network attenuation, learning about how to build a network. That give my age away here. That was 20 years ago, right? So it-
Dr. Prineha Narang: I wouldn’t have guessed. I would have said it’s a few months ago.
Bill Detwiler: But how far are we now from getting to period where the equipment is not commonplace, but is actually sort of tangible? There’s a commercial viable commercial market for this kind of networking equipment, where people are actually looking at laying cable in the ground and we’re installing. Current networking engineers, future networking engineers, are learning about how to polish the ends of your fiber cable, not blind yourself when you connect it, those kinds of practical steps to create this network. How close are we or far away are we from that?
Dr. Prineha Narang: Yeah, that’s an excellent question. And this is where I’ll give the candid, honest answer. I think testbed networks are in our very near future. So ones that are purpose-built for some application, something that needs to be secure, something that needs to happen, whether it’s for a national lab for the military, that type of stuff I think is already people are trying to make that happen. And they’re asking questions that our simulation and emulation products can immediately addressed. I think that a point where an AT&amp;T would be interested in this is a few years out, and part of that relies on the outcome of these testbed networks. So I think that it’s crucial that our testbed efforts be incredibly successful and that people show why they made certain hardware choices. And if there were certain hardware choices that were wrong, that actually feed back into our models, into our emulation.
So I frequently tell people simulation is kind of if you were a pilot and you were trying to figure out how you would have a fancy flight simulation, that would be great, but you also want your pilots to be trained, and maybe you want to do that in an emulation environment and less of a simulation environment. And you want all of that data to then feed back into what you’re actually going to build and do in real life. And that initial part of the process where we’re iterating, where we’re generating data that will be valuable for eventual commercial quantum networks is happening imminently. It’s happening now. So that’s the answer there. But of course, it’ll be a little while before the quantum internet is delivered to my home and allows me to talk to you securely.
Bill Detwiler: What is one or two things that you think people who are current working in networking now, whether they’re engineers, whether they’re administrators, whether they’re at a higher level working at say the large equipment manufacturers, or even the telecoms, I mean, what are the things that they should be watching out for in the near future when it comes to quantum networking?
Dr. Prineha Narang: That’s an excellent question. I think my first suggestion to all of those people would be take a class in quantum information, get familiar with either the problems. It could be a quantum information class. It could be a quantum technology class, quantum engineering class, depending on what it’s called. There are online versions that maybe in the COVID quarantine, you could spend a few hours on. And the reason for that is it’ll expose you to the types of hardware and various quantum technologies that will eventually be leveraged in one of these networks. So even though there are choices in the hardware that are being made, there’s still a lot of fluidity there, those will crystallize. And I think just having that exposure at this early stage will be pretty important for people.
I think for people who are in roles that are leadership roles, CTOs out there, I’ll say keep an eye on the various demonstrations that are coming out of both these testbeds in the U.S. and the testbeds overseas, because we’ve seen this in other areas of high-tech, where it’s very far out one day and it’s there and you may not have the workforce. You might not have the internal know-how when it’s at your doorstep. And at that point, you risk being too late.
So I think there is a spectrum of answers depending on who’s thinking about it. But yeah, for students out there, I encourage you to look at… There are more pedagogical papers out there about what is the quantum network, what’s the quantum internet, what will the quantum internet do for you. I’m writing something. I’m happy to share that with your viewers, happy to share it with you. Just read about it. And I think having that level of knowledge right now, as you see the announcements come in in the media, I think, we’ll all be follow what’s happening and keep up with the good developments.
Bill Detwiler: Well, where can listeners and viewers go to learn more about the work that you’re doing and what’s happening at Aliro?
Dr. Prineha Narang: Well, the Aliro website is perhaps the best spot for everyone to hear about what’s happening. Our products, if you’re interested in trying them out, if you’re thinking, “Hey, my company’s been looking for one of these products,” please go look at the website. It will give you instructions on who to contact within Aliro. They’ll get you set up with an account. Everyone is super helpful. If you’re interested in my research, my research group website, narang.seas.harvard.edu, please go check it out. If you Google me, it’ll show up. Again, I respond to emails from students all across the world. I love receiving emails from students, so write me and happy to share more about our work.
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