Inside quantum optimization research

So how can quantum benefit optimization? >> Optimization is is everywhere. >> It's like you're viewing the problem from a different angle. >> If you have this exponential explosion of your search space together with a complicated structure, then this is very hard to navigate. >> And if you throw the quantum computer on it, you can find those uh solutions that cannot be found with a classical one. Welcome to season 2 of the Coherence Times, where we [music] bring coherence to the entangled world of quantum computing. I'm your host, Ryan Mandlebound. Every other [music] week, I'm bringing you stories about how scientists, developers, and businesses are making quantum computing [music] a reality. We'll explore new research and development, highlight the latest advances in the field, and see how users are trying to [music] extend quantum to realworld problems. >> [music] >> I think a big undercurrent of business computing is how we can optimize things. We like to get the most stuff for the lowest cost. So I hear a lot of questions about how quantum computing can help solve optimization problems like the traveling salesman problem or the knapsack problem. But the answer is that things are complicated. There's a lot of interesting research suggesting that quantum might produce algorithms that can outperform some of today's classical optimization algorithms. So to tease that out, I'll be sitting down with two experts who can help us understand where optimization stands to get a quantum boost. [music] First, I have Stfan Verer, who's a principal research scientist and senior manager of applied quantum optimization research at IBM. Also joining me is Stephanie Reed Miller, a doctoral research from the ZUSA Institute Berlin, [music] which is an interdisciplinary research institute for applied mathematics and data inensive high performance computing. Both of today's guests also participate in a working group spanning institutions around the world that's working to build and test these optimization [music] algorithms. I encourage you to learn more about that group's work by visiting their new quantum optimization benchmarking library website linked in this episode's description. Maybe we get started with you Stefan. Um what makes optimization such an important problem for us to tackle? optimization is is everywhere. Um if you if you think about optimization, what what it is, it's it's finding the best decisions that um optimize a certain goal or towards a certain goal while taking into account certain constraints. And that's quite quite generic. Let's let's think about complete examples. We have uh in finance optimization where we want to optimize some investments given some risk or budget constraints. Um in logistics or supply chain optimization, manufacturing, we want to optimize um production schedules or order plans to meet uh demands while having like capacity, production capacity under control or cost under control. And um there are plenty more examples in in like uh a lot of different disciplines. And uh often we have the situation that a small um improvement that say by by a few percent can have a big impact because there's a huge leverage. Think about finance. If you manage a lot of um money and you make a 1 or 2% improvement in your expected return, that can uh have a a significant impact. So like a good top line would might be I have some currency, money, energy, something that uh I have to spend in order to do something. And I also have some amount of work that I want to do. Maybe I want to uh buy the most peaches of anybody or from all the different price of peaches or something. You know, there's a million different things I could either buy or use the energy to do. And so then optimization essentially asks what is the best way that I can do that? what is the most number, the best value, bang for my buck basically. >> And if you if we take the example that you have with the with the peaches, that also gives you another another important point. Um, often there's uncertainty involved because how many peaches you might get at the end of the season that depends on the weather. But that's something you don't have under control, but you have to make some some estimates to come up with a good model that describes what you want to optimize. And then that's what you solve and what you what you try to um approach with the with the algorithms that we are developing. >> Cool. And then Stephanie, what are some of the ways that we've been tackling optimization problems today with a classical computer? >> There are basically like two directions you can take. Um one is if you really want to have an exact solution, you really need the optimum and you need a proof that it's the optimum. Um this is one direction or you take uh the other one wi-i which is called huristics. In that case you're fine if you have a good solution and you don't have a proof how good it is and no guarantee how good it is but you know that usually from this method there is a good solution you can use and this is often used uh for applications where you have big problems that are hard to solve. Now of course we have in this exact and heruristics um uh also some new emerging things like um quantum or GPU and uh learning. >> So I mean basically for the sort of problem space it could be like you have an ocean of waves and there's an optimization problem where you want to find the tallest wave and you know that there's a tallest wave in the ocean but then then so you have a method that might be able to find that but then of course you also have it that's just you're just interested in surfing some big waves. So all you need is to know where the biggest waves where a place where there's some really big waves that you can be happy with. And how would you sort of what do the problems look like? What are the sort of algorithms look like and how do they differ between those two problem cases? >> I mean a typical exact method would be if you have a so-called linear program or a mixed integer program. This is basically just a technique how to formalize a problem and then you there are specialized solver who will give you um the correct solution. But for heristic you could for example just explore different areas. For example with your waves you can um travel to different regions and look where you think oh they are usually big waves. So I look in the areas where they usually are and if they are not I I look in another direction where I know they they are usually there. So um this is like a typical approach. And then um maybe I'll ask you Stefan like what makes classical like why is this hard enough that we have to go looking for other methods with GPUs and quantum >> many of these of these problems have a like a combinatorial element to it. Um say you have to decide whether you buy a certain product or not whether you turn on a certain power plant or not. Um so these are the simplest one where you have like this yes no decisions to to be made and the more you have of those the more possible combinations of those you have as well and in general that that number like the size of the search space scales exponentially. Now that by itself does not necessarily make the problem difficult but then some problems have a very complicated structure and uh um if you have this exponential explosion of your search space together with a complicated structure then this is very hard to navigate because like in the in the worst case you really have to go through all possible combinations and since there are so many of those you you can't and that's that's one thing that drives complexity of uh of a problem. >> So Stefan, what makes quantum like a logical place to look to solve this complexity? >> We we have um theoretical uh results that show that for all we know today, they exist problems that a quantum computer can solve exponentially faster than uh a classical computer. Now these problems um are relatively abstract and they are usually like uh quite carefully constructed. So they're they're pretty artificial problems but they like the theory shows that they exist such problems where quantum can help with classical and um now since quantum works completely different it gives us new tools gives us new operations that we can apply gives us new ways to build algorithms. Um and together with this with this knowledge that they can be better in optimization, this makes it very exciting to now take this and search for for new algorithms that work not only for this abstract or artificial problems but really for the problems you care about. It's quite difficult for a concrete problem to say uh a priori whether quantum will work or not. However, it's essentially the same classically as well. So for many interesting practically relevant problems um like like the the finance or logistics problems I mentioned earlier we we cannot say usually a priori that a um classical algorithm works well. We have to rely on these uristics that Stephanie mentioned where we essentially have to we have to try them on the problem and see how well they they work. So this is how classical optimization um uh essentially works for for practically re relevant problems and the same is true for for quantum. So we know there exist problems where it's better. We know it can do things classical can't. But for a concrete problem, we actually just have to try and see what works best. >> I see. I hate to go to the sort of like we have the hammer but not the nail problem, but I think it's almost like we have this toolbox of like really amazing tools that have been tried and tested in places that are mathematically and theoretically interesting, but now we need to actually find those problems where those tools fit and they work. Um but the funny thing is that like with classical and quantum we have essentially like very similar toolboxes where we actually still are not at the point we have these amazing quantum tools that we know work really well for these sort of theoretical problems and then we have these you know classical tools that we already know don't work as well as we wished for the problems that we're already using them for. So the question is like do these cool quantum tools work better than these sort of not great classical tools we're already using? Exactly. Like we we uh back to your analogy um we do know that uh some nails exist where you need that hammer. Um and we we know that some other nails exist where the tools we have classically don't work. And so now we want to we want to build these quantum tools on top of of what we already know to to solve the problems that uh that are left over from from classical optimization that are still hard. whether it's is still a margin for a quantum advantage, still a margin for further improvements. >> And then Stephanie, can you tell me what's exciting about this? Like what got you into the field that you'd be interested in studying like something specific like this? >> Yeah, I mean I'm coming from the classical mathematics. So um it was like one day my supervisor came in and was uh talking to me about um how he works together with Stefan and how excited it is and he said you like multi-objective optimization they are now doing multi-objective optimization with quantum now you're also doing quantum and this was of course at first a little bit scary for me um but uh then it got I was so excited about it and I joined the group and it was uh yeah really excited to to to to see how this new hardware I knew nothing about before can um solve problem with a different view like it's like you're viewing the problem from a different angle >> what about like when you first saw like the quantum computing mathematics was it like surprising how did it actually feel to start seeing these these quantum algorithms >> it was uh surprising because I I had really no idea before and then I um and I saw and I think there are a lot of aspects I still don't really understand but um the way I I see it now is that yeah you just have to view at everything from a different angle maybe find um the the the type of algorithms that really use this new hardware and this is cannot just be the old hardware um but faster but it's a completely different way and this is so exciting for me >> uh and Stefan how about you I mean you've been in this for a while what what sort of first got you into I mean my background is also originally in classical optimization. I worked on optimizing uh our supply chains and and and logistic problems and things like that. And um then like it's now 10 years ago uh IBM built this first quantum computer. So we had this first small quantum computer in the cloud and it was was available and we could play with that. And um back back then I already looked into it a bit. But uh I was uh still working on our um our classical optimization problems. But then one day I also had the opportunity to to join some discussions with a local group that worked on the hardware and um was then asked to to to to join the discussion on suppose we have these devices what are we doing with them? So it's kind of the the same questions we we kept asking ourselves from the classical side. Now we're we're raised again from a different perspective and um that was that was very interesting and it it um yeah led me looking into quantum computing. I I read into that and uh then uh we started to build the the team in Zurich um looking into applications of quantum uh quantum computing more generally not only optimization but of course that was my background so that's where where I always was was involved that was uh now 8 years ago or so we looked at the same problems but now with a new tool and that was kind of what sparked my curiosity like uh we we were struggling to solve these problems now what can we do with these new approaches But does this new new type of math in a way or at least new to me um what what where can this help to solve the problems we were struggling with already for a uh yeah for a long time. >> Can we pick an example of like an algorithm that we're using today maybe an early algorithm like you know the QAOA for example um and talk about why it or how the mathematics looks different from a classical optimization algorithm. the the way we we represent uh a problem and the way we then algorithm works is is fundamentally different. So in a way we use different types of representations and um a algorithm that illustrates that quite quite well I think is the quantum approximate optimization algorithm QAOA. This is an algorithm that is derived from a um from from a a physical principle that's adabatic analing. Um and what what you do there is essentially you start with a very simple problem that you can easily write down where you can immediately write down the optimal solution. And what you then do is you you take a quantum state, you prepare that state such that it represents that simple solution and then you very slowly transition your problem and you [snorts] make sure that your system always stays in the optimal solution of that of that uh changed problem. So you very slowly change change the problem of interest and you do this until you reach the problem you actually want to solve. And this ideabetic principle um or ideabatic theorem that that tells you that if you do that slowly enough then you always stay in the optimal solution and you end up in the optimal solution of of your target problem and um I think this this kind of approach is something that is not really um possible uh classically in the same way. So it's really a different uh it's a different way to represent the problem and then and then um work with this uh solution space and uh the QAOA is now a very rush approximation of this idea instead of doing that very slowly which can actually be exponentially slow um it does this with a very um just a few uh big steps if you want you optimize the steps a bit but um it's just a few steps and the idea is that you can implement that on today's quantum computers um which have some noise so you can't do arbitrarily complex calculations and it could be shown for certain algorithms that this achieves certain performance guarantees and so it's a very widely used and studied uristic um to try uh solving optimization problems on today's quantum computers and uh it's um I think it's it's quite interesting because it's it's one of the example that we really can try today already and learn how well things work. Um where are bottlenecks? Where do we need to improve? What kind of problems might be better accessible to to uh these type of algorithms? What problems are further away? How does this thinking about quantum sort of change your view on classical algorithms and sort of change your understanding and how you actually go about creating algorithms for an optimization problem? I think like the main uh yeah difference for me was um that if you solve or use an algorithm to solve something in classical algorithms you usually usually get one solution um out of it and for the for example for the QA in the end we got a sample from a distribution so we get not only one solution out of it so a whole set of solutions um that are potentially good, probably good. And uh usually you would like still go for one of those solutions, but we noticed that we can just use this whole set of new solutions if we need several. >> Let's talk about multi-objective optimization now. So can you tell me about what that is and how it differs from class, you know, from a typical one variable optimization problem? >> Yes. So um for a classical optimization like a single objective optimization problem you just have one goal like in one direction you go to optimize um and for multi-objective optimization you have several directions you want to search in the same at the same time and if you go for several directions at the same time there is not usually not one optimum but there are several um optimal solutions um and you need a new concept to compare those solutions. It's called parto optimality. And this means basically a solution is PTO optimal if you cannot improve it in one direction without worthing worsening another direction. And the goal is to find all those parto optimal solutions. Um maybe you need an example to better understand this. For example, if you I mean my objective optimization is everywhere on your daily life. For example, if you want to uh buy a train ticket, you can go for the one that is the cheapest or you can go for the train ticket that um where you have to change trains um as as few times as possible or you can go for the ones where you um arrive the fastest as your at your goal. Um and maybe if you then have to decide you go for none of these options but something in between that is very good in time but also does not cost that much and to find all those solutions that are all kind of optimal in their own way. This is multi-objective optimization. >> I see. And so there's essentially if you imagine these can be like on a graph there's like a line that connects these various solutions, right? and you're looking for sort of that specific boundary between the two so you can get that optimal in both directions with your different trade-offs. >> Yeah. For um for if you have two um uh two objectives, this would be the case that you have like a like a relation between those two that you can imagine like a a graph like a 2D graph. But um if you have several objectives, the solution space becomes um like a multi-dimensional object. you actually came up you has worked on a quantum algorithm that helps to tackle this problem right I'd love to talk a bit about that and how it works and Stephanie you can tell me about about it because I know you were on this paper >> yes um so uh the goal there also is to solve a combinatorial multi-objective optimization problem and we take it from two sides from a classical and from the quantum side um from the classical side we use something that is called gallerization which is a very like an easy uh way to take a multi-objective um problems even for like wayward world applications and so on. The idea is that you take the multiobjective optimization problem and you transform it into a set of single objective problems. Um, and that you do by combining the objectives. Um, and then you do it several times to have different combinations of the thing of the objectives. Um, this is called weighted sum approach. Maybe you heard of it. Um yeah, we did this from the classical side and then from the quantum side we used the QA algorithm you were already talking about. Um and then we combined this and I think the the really nice thing is is if if you would do the same thing without the quantum computer just with a usual classical computer you would get a subset of the um solution set but not all of them. There are some that have a specific property you cannot get when you do this classically. And if you throw the quantum computer on it, you can find those uh solutions that cannot be found with the classical one. You get more of the solutions that maybe even all possible solutions. And I think this is like a pretty nice uh result. >> So then how would that um as like a user of this algorithm, how would that sort of um kind of be a material benefit? What what what would I gain from having more of that solution set? Yeah, usually those uh solutions you are that are more difficult to find um sometimes have a very good tradeoff between the different objectives. Um usually if you're a decision maker for um I don't know a big industry or something, you would never go for a solution that is very extreme in the in one direction but then very bad in the other. you would want to have like a good trade-off and those solutions we cannot find if we do the same algorithm classically are often those that are very interesting for real world. Um Stefan, can you tell me about like how this sort of collaboration came about? Like how did you kind of you know work with Stephanie to realize this algorithm and what's kind of exciting about it? So a few years ago, I think 2023, we launched a uh quantum optimization working group. And this working group is um has been uh founded um by bringing together classical optimization experts, quantum algorithm experts, uh subject matter experts from different application domains like um energy, finance, logistics. And um the idea was to to to bring this diverse set of of expertise together to really discuss where can quantum computing help in optimization. And uh our goal was to approach this from different sides like more from the um complexity theory algorithm side from the um applications and benchmarking perspective and then also like if we have certain things how can we run this actually on hardware? How can we demonstrate things? In this working group, we meet uh once a year in person and have a like a deep dive brainstorming workshop where we where we come up with ideas and then uh discuss them in in in more depth to kick off new projects. And uh one question that um came up there is how how we can make use of a certain property that uh we expect quantum optimization algorithms have where they kind of differ from classical ones. And that property um Stefan hinted already at it is that we expect some of these quantum optimization algorithms to not only generate good solutions but diverse sets of good solutions. So they might not necessarily give you the best possible solution. Um they in in in certain cases classical algorithms might be better but they give you a diverse set of good solutions very very quickly. and this diversity. So we were wondering where can we make use of this property? Where can we make use of a algorithmic building block that generates um solutions that might be given the objective function we look at um equally good or of similar quality but that look completely differently if you then look at what decisions are actually being made. So if if we take that that finance example, you want to invest in certain assets to achieve a certain um uh expected return while uh not exceeding certain risk constraints. There might be plenty of different investments that achieve more or less the same result. uh you can invest in different industries and different companies and and and whatnot and there might be different things that that kind of from the objective perspective look the same but from what you actually do what the what are decisions you actually take are quite different and uh this is exactly what we are interested in in multi-objective optimization we want to learn what are the different um the different trade-offs and um so this is the the the perspective from from where we came and then in these discussions um multi-objective optimization was brought up as a possible uh application that could benefit from this and then we we took it from there. we had certain certain ideas how to possibly realize that and um then we came up with the algorithm that Stephanie um uh described and and uh tested this simulation then really on the on the on the quantum hardware and we could show that it um actually works works pretty well it could find um the full set of trade-offs for the problems we studied. So the full paro front um the ones the solutions that classical algorithms are better at finding but also the solutions that are uh more difficult to find for classical algorithms. And um that was that was pretty exciting to see that really quantum can work. And what we have found is actually that at the moment since we studied that at a at a um regime that we can still simulate classically that was with 42 cubits. We found that the classical simulation of our quantum algorithm was the best algorithm we we we had to solve the problem of interest. And that was pretty exciting because now um what this means is that or this gives a very strong indication that as we scale up this problem when the classical simulation breaks down the quantum computer is is then really the best or might turn out as the best way to solve this type of problem. And that was a very strong indication that was very very cool to see. And um uh that's kind of how this how this uh collaboration happened, why we looked into this, and then we um we wrote this paper about it. >> I want to harp on this for a second because this is something that we didn't really get to before, which is that like quantum I think when quantum was first emerging, people were like, I don't know if it's going to be that good for optimization. Like it could be. We'll see. Um and you know, people were asking questions like, is quantum going to solve the traveling salesman problem? And everybody was like, no, no, not at all. That's not how I maybe it'll make it faster, but it's not like we're going to exponentially speed up these already exponentially hard NP hard hardest problems. Um, but this is like exactly the kind of result that this is looking for, right? Like the fact that you find a quantum algorithm that the classical simulation of the quantum algorithm is the best solution or the best algorithm you have means that when we have a big quantum computer it's like a not guarantee but a very very strong you know very good promise that the quantum version when the quantum computer is big enough is going to be the best version if the classical version of the quantum version is the best version already. Um, and I think I I wanted I wanted to repeat that because it's actually very cool. Like this is we now have like pretty clear good feeling evidence that quantum might be the way to go for some of these really hard optimization problems like this multi-objective optimization problem which is extremely important clearly to anybody who's purchased a train ticket before. Right. >> [laughter] >> Um I I think you you mentioned a couple of very important points and uh to be able to demonstrate a quantum advantage, you first have to find a problem where there is a margin for a quantum advantage. And the uh famous traveling salesman problem usually is none of those. This is a problem even if it's uh in general NP hard and if it's very large often can be solved almost optimally with classical tools and um so it's not a good example for potential quantum advantage just because we can solve it so well classically to give you two examples um there's a so-called world tsp uh which is a tsp problem where the goal is to travel around almost 2 million cities like starting in one and then visiting every city and coming back to the original one in the in the with the shortest distance and um that can be solved almost optimally. So since that's tackled people now study the galaxy tsp which I think has about two billion stars. So that's that that's the kind of problems we we can solve if there's structure and this is what I mentioned earlier and what is very important here the TSP has a lot of structure and um usually if we look at the the TSP problems that arising from from real problems those um satisfy we say the triangular inequality meaning if you go from CDA to CDB directly that's always shorter or or at least never longer than going from A to B via C. Like if if you if you take another stop in the middle, you can't be faster than if you go directly. This is a a very strong structure that classical TSP solvers can leverage. If I give you a graph that doesn't satisfy that, then TSP can can uh become very difficult. But practically relevant problems usually have this kind of structure for tsp and uh so quantum I'm sure quantum will be able to solve tsp um at some point but classical too. So that's why it's not a good example for for a quantum advantage since classical is already so good at it. Stephanie, can we talk about the working group model and like how it actually helps you come up with new research and like push the field forward? >> Yeah, I think they like uh the main thing is this uh yearly in-person meeting for me at least. I think this very inspiring because everyone comes together not just for one uh hour talk but uh for today's and everyone is giving some ideas and we work to really work together on it like in workshops and in smaller groups and so on which is not always the case if something is called a workshop but there we really work together and I think it's so interesting when all those different people from different fields um give their ideas um yeah then you yourself get also more ideas Um and then can you tell me about like uh sort of how you got involved and uh what your sort of part what like the participation looks like and what you do after these sessions are over. Yeah, as I said, there are those yearly meetings, but then we also have um in smaller groups and we work on a specific project um bi-weekly meetings uh and there we just always keep up with the results and get and and share the task between us and everyone is then uh coming together and share what they had um developed in those two weeks. Uh yeah and this made a lot of progress. So now I want to talk about one of my favorite things that's come out of the uh the quantum optimization working group which is let's talk about the quantum advantage uh the quantum optimization decathlon which is um the uh this sort of effort to actually try and benchmark and find these quantum problems that are providing value for the world right that you know because so much as we sort of were saying earlier is about these huristics right it's hard with huristics to use it because it works that's how heristics work you know the best heruristic is usually the heristic that's working best for you. Um, but you actually get to have you need to have people trying all these problems out, these quantum heristic problems and all these other different problems to come up with what these best quantum algorithms are, right? Um, so that's I'm guessing what this quantum decathlon is. Maybe Stefan, you can start by telling me about the uh uh the quantum decathlon and why it's exciting. So from the very beginning of this optimization working group we had benchmarking as one of the important topics and as you said the uristics um are more like trial and error. Uh they they are often uh strongly motivated by by theory or based on experience or they are exact algorithms or approximations that are applied outside of the regime where the theory holds. So different ways to come up with uristics but then in the end you don't have any app prior guarantee you have to run them and see how well they works and that makes it very very um difficult to then say for your problem what's the best algorithm or the best uristic to to apply and it also makes it very difficult if I come with my quantum algorithm and I say um my quantum algorithm is best because I tested it and I tested two other uristics and uh then of course uh since the number of uristics is so large I cannot test all of them I don't even know all of them and then you can also fine-tune them and there are many things you can you can do and so um what we our goal was for this benchmarking effort um that we that we had in the working group to really come up with a set of problems that that like um a broad group of people agrees on are good candidates um publish them and then work with the community to test the different uristics such that um everybody can contribute results from their algorithm or the algorithms they're interested in and uh that that of course helps to to um have a robust baseline for any advantage claims. If this problem is public and the metrics are well defined and um uh everybody can test their algorithms against it and and share the results then if I come and I say hey my algorithm works best compared to all the ones that are in that benchmarking library then this is a very strong statement and that was the the the goal behind this quantum optimization benchmarking library. It's also called the interactable decaflon because we started with 10 problems and these 10 problems have been selected to be difficult classically. Um so there's some uh some some some reason that uh there's at least the margin for quantum advantage. We don't know whether there will be quantum advantage but at least they are believed to be difficult for classical ones. So there's room for improvement and um uh yeah these these problems are on a on a public repository. They're available as open source and we collect all the solutions that people uh contribute by by running their algorithms. And by all I mean um quantum and classical. So I said this is if you want to demonstrate quantum advantage or if you want to claim quantum advantage you need to make sure you are better than the classical alternatives and better can mean different things. It can mean faster. It can mean giving a better solution in terms of the objective value. It can mean cheaper. Um, and depending on your context, depending on what you want to achieve, you might put more or less emphasis on on some of these object or these these these metrics. Stephanie, how do you approach this sort of challenge like this when you see this list of problems and sort of these classical and quantum solutions like uh how do you actually go about this sort of act of creating algorithm of benchmarking and participating in this whole effort? Yeah, I think um that I would look the other way around not seeing the benchmark and seeing oh what can I do with this problem but basically when I have created for some problem an algorithm I really need such a benchmark to to test my my new algorithm on it and this saves actually a lot of workload if I already have a collection of problems that I should test and a collection from other people um algorithm MS their results um and the whole thing just speed ups research in general I guess. >> Is there problems that you're excited about? >> I am myself I'm mostly excited about multi-objective optimization which sadly is not part of the decapon but I but I think yes but maybe in the future it will be >> not yet >> not yet. [laughter] >> Yes. >> Well I feel like multi-objective optimization is like a privileged child here because we're like already know that it's going to be an exciting one. So why benchmark? We already did this classical quantum thing. It's already the best. >> Yeah, maybe like this. [snorts] >> So, I do want to just say that this is like to the listeners like this is a good summary actually of what's going on in quantum optimization is it's actually like really quickly advancing right now. There's like a lot of interest obviously because of the business interest. There's a lot of algorithms coming up. Like we have ideas of algorithms that might work but other algorithms might actually be the ones that we're most excited about. And so it's like uh the whole field is actually pressing forward in in so many different waves that it's actually like it's you know we're trying our best to keep track of certain things but other things are going to emerge kind of while it's all happening which I think is just makes it a very exciting time to be in the field right Stephanie. >> Yes. [laughter] >> I agree. >> Cool. Um, I like to slip in something silly usually towards the end, but I did want to say that this may be giving away where we are recording this, but the World Cup was recently and um, at the end of the Argentina Spain game, uh, Leandro uh, Pedes uh, grabbed the throat of of one of the Spanish players in an act of bad sportsmanship. Uh but uh all I could think about was not at all the game but in fact the I was just like parados paro front which we have been talking about before. Uh, and I'm not just saying that. It was literally like as I was watching the game, I thought it which is very silly. And I don't know if there's a use case for uh the multi-objective optimization in soccer, but I'm sure there'll be some value in it somewhere. >> Probably. As I said, multi-objective optimization is everywhere. >> And and you find sports tournament uh scheduling actually even as one of the problems in our benchmarking library. >> I'm so glad I brought it up. >> [laughter] >> Let's finish off with um one of my favorite questions uh which is just especially in a field like optimization. Um it's probably one of the most easily graspable and broadest applicable things when it comes to the real world, right? Um so maybe um we'll take one at a time. Stefan, what is one of the most exciting problems that you're excited to see quantum uh tackle in the field of >> in general? the fact that we can now since since few years already but now really increasing and that we can run these algorithms on real hardware and really try this at scale. This is very very exciting like like trying these new algorithms and and uh operating in a regime where you really cannot do that classically anymore where you need a quantum computer to make progress on this um development of huristics. This is um this is pretty pretty cool to me. And the concrete problem class um to me that to be honest doesn't matter too much because if you translate that to the math it's it's it's more like um what what kind of equations describe the constraints etc and how can we implement those on a quantum computer. Recently we found a way to decompose them with a fier transform. So we kind of decompose complex quantum circuits that represent um optimization problems that we usually cannot approach. We can decompose them using a fiery transform into a simpler set of circuits and uh then then run those on the real hardware and get get results for it. So by switching the representation we extend the the the reach of our hardware. So this is uh this is not linked to a concrete application but this is what I'm I'm thinking a lot about these days and what I'm quite excited about. I'm going to cut in here before I ask you Stephanie because this is something that we write about a lot now is that uh part of the running an algorithm is not just having a good algorithm but having a way to actually represent the data and I think some of the most important algorithms that we have basically we're not I mean the algorithm part was exciting but the exciting part was that somebody found a new way to take the data set and re-represent it so that it can be an existing algorithm to take advantage of it. uh hashing is like a really good example of this and like fastforier transform is a really good example of this like some of the most important algorithms we have. It was really all about finding a new way to represent the data. I wrote a blog about this once and uh maybe I'll put it in the comments if I can find it. Um and then uh Stephanie I'll then turn it over to you. What is what's really exciting right now for you? Yeah, I think uh I really want to dive more into um seeing what's special about quantum computers. that we already talked about earlier about this solution diversity and you maybe already know from our conser conversation that I'm have a passion for multi-objective optimization but they are like similar problem classes uh that have the same problems and structure uh for example robust optimization which is also very important for um real world problems. >> Thanks so much for joining me guys. This is really fun. Uh this is a topic that I feel like we will probably be continuing to talk about for the rest of time. So uh I wouldn't be surprised if uh one or both of you join us on the podcast again in the future. So thanks for your time for now, but I'll see you again. That's it for this episode of the Coherence Times. If you [clears throat] enjoyed our conversation, please be sure to subscribe wherever you get your podcasts or comment in the comment section and share it with somebody who's curious about quantum. You can find us on Spotify, Apple Podcasts, and YouTube via the IBM Research channel. And now for more deep dives, resources, and episodes, please visit us at ibm.com/thinkodcasts. I'm Ryan Mlebomb. Thanks for tuning in. And remember, the quantum future isn't just coming. We're building it right now. [music]