2025 QUANTUM PROGRAM ❯ Day 11 ❯ The State of Quantum Optimization in Practical Applications

0:00 So we are moving on to the technical session for today with Dr. Pascal Hoffman from the front of Institute for Industrial Mathematics. Those of you who are new to this program this year uh front institute is one of the largest industrial research organizations in the entire world and has been the leaders in a lot of inventions. You might have heard about airbags. Fronoper was the one who invented them. white LEDs again coming from the front of our institute MP3 the data type for a lot of your audio files and we have today Dr. Pascal Hoffman joining in from front of our ITWM to talk about the state of quantum optimization and with a more focus on practical applications a little about

0:45 Dr. Rascal. He holds a PhD in mathematics and is currently the research coordinator for quantum computing activities at Prono for ITWM in Kel in Germany. His research is focused on quantum computing and optimization with applications ranging from finance to energy. In particular, he has provided substantial results on quantum algorithms or application oriented optimization problem. All in all, he's an amazing lecturer. He was also a participant and and one of the key lectures in last year's program. If some of you are joining in again this year and and remember last year's program, front offer was also one of our contributing project partners and that project ultimately translated into a QSL project. Many of the fellows worked with

1:31 the front offer team and are currently publishing the papers. So it's it's really very exciting and I'm honored to invite Dr. Pascal again. I'm sure you would have a lot of fun in the next 30 minutes or so. So with that over to you Pasco. Thank you very much. That was a really really nice introduction. I'm I'm flat up that I'm a wonderful person. So you you are too. So thank you really much and very much to to that for the invitation here. I'm I'm really proud and also really delighted to provide like a small lecture here. I'm from the FRO Institute for Industrial Mathematics which is part of the FROA society. So we are indeed one of the leading applied research organizations in the world with over 76 institutes, 30,000 employees and over three billion of business volume.

2:16 We do a lot of patents and we have a lot of successful spins of even over 500 since the 2000s with also institutes in the international area ranging from the US to Singapore. And our mission is to provide researchbased decision making for the industry. That is we transition fundamental hot of hot news research towards the industry to provide like readytouse solutions for our industrial partners. Our name comes from Yuan Frown Hoofer who was both a researcher, an inventor and entrepreneur. And that is exactly the intersection we as frown over see our mission. One part of the frown of society is the

3:02 frown of institute for industrial mathematics and our m mission is to provide industry solutions via our mathematical expertise. That is we everywhere every time everywhere where mathematics is involved we are there to provide you with a solution based on our mathematics. So and that hopefully for a good future and this intro includes the automotive sector, finance, the energy sector, uh also material science, engineering, optimization, transport, logistics, also next generation computing, healthcare, um transportation and obviously quantum computing. And for quantum computing,

3:47 I'm the research coordinator of our activities there. And we have two I I think missions. First of all, we want to make quantum industry ready. That means we want to accelerate quantum computing so it can provide utility for the industry. But on the other hand, we want to raise awareness for quantum computing at the industry to see okay there's a new player around that could benefit mass there where you could benefit massively from in your day-to-day business at one point. And we focus on several parts. We have for example two main use cases. This is finance and material science. And we use both optimization and AI to enhance quantum computing and vice versa enhanced quantum computing in optimization and

4:33 AI. And we do that not just solely with quantum computing but also with the integration of classical for example high performance computing hardware. Yes. So today's topic after this short introduction is obviously optimization problems. For those of you that are not fully familiar with optimization problems, I give you a short recap. So a general optimization problem consists of an optim of course function we want optimize in this case for example min minimize and this can be a linear a quadratic or even like a totally non-explicit nonlinear function. And we have some side constraints for example we have equality constraints and inequality constraints. And these functions could be likewise linear or

5:19 nonlinear. And we have some decision variables that could be continuous, integer or even both. That we have like a mixed integer problem here. And these optimization problems occur everywhere. I mean you could just go to Google Maps and find the shortest path to your grocery store. Then you have solved an optimization problem. I bring two interesting optimization problems with you. One is a rather famous one, the traveling salesperson problem where you want to find an optimal like with respect to the distance route visiting for example all given cities exactly once and then you return your to your starting point. For example, a small example we have all state capital cities

6:04 in the US excluding Alaska and Hawaii because it's a bit difficult to get if not to not cross any borders. And of course these so if you check for all of these possibilities this is like 48 * 47 * 46 so these are is quite a lot but nevertheless with our current optimization solvers like Gorobi and your usual laptop you can solve this problem in 5 minutes similarly I have bring brought another application from the energy industry this is a so-called unit commitment problem we want to find an optimal planning of our power plants that produce our electricity with which we want to satisfy obviously our energy

6:50 demand. But of course we want to minimize the production costs of our energy and we want to set yeah satisfy the the properties of our thermal units. That is that for example a nuclear power plant cannot be easily switched off and on but you have to run it for example a certain amount of time and each power plant has obviously a certain capacity of energy it can produce and then you get for example a schedule over 24 hours where you say okay I produce at hour five this amount of coal and electricity and I produce with gas this amount of electricity and so on. So, and with a little bit of experiment on our side, we have conducted that even with 2,500

7:36 units and different load capacities, you can solve this problem with commercial optimization solvers in under 5 minutes. So, it's even though and this is the important factor now both problems are seen as NP hard problems. That's one of the toughest problems you will face in optimization. meaning that those problem those problems cannot be solved in polomial time but the the the problem or solution time scales exponentially but still these can be solved rather quickly. So just because an optimization problem is np hard it is not necessarily hard to solve in practice if your size is not that large. So and it's mostly

8:23 said that quantum computing and quantum optimization can provide a solution somewhere where we have faced NP hard optimization problems. But this is not entirely true from my point of view because the bar as you can see is set really high to to even provide quantum utility or for most quantum advantage to these problems. So quantum computing has of course the potential but the classical side is really strong here. So what do we do now? Well there are obviously there are some some quantum algorithms that perform really well. Um the most famous one is probably quantum

9:08 analing. Um this uses adiabatic evolution. That means we transition from a well-known quantum system where we know the lowest energy state and the lowest energy state is the one that represents our optimal solution and we transition this slowly over to our problem formulation that is also encoded as a quantum system and with the slow transformation we remain in the crown state. We use this one and we also use quantum tunneling. That means we can from one energy state we can tunnel through such a peak without going over it. But that so we we yeah we spare a lot of time and also we can from a local minima get to the global optimal easily.

9:55 Then we have the variational quantum solver. This is a quantum circuit consisting of so-called parameterized gates. That means we have gates in our circuit that have a certain parameter and then the goal is that we run the circuit, measure it and then optimize using a classical solver these parameters until we found the optimal solution. The quantum approximate optimization algorithm is a combination of the previous two because it's a specialized variational quantum solver that mimics the quantum and leaning approach but instead of this continuous adabetic evolution we discretize this. And lastly, and this is a bit of a more exotic exotic approach, is the Crow adaptive search that uses the famous

10:41 Crowver search algorithm, which is originally intended to find an item in a list by marking it and amplify its probability in the quantum circuit. But here we now mark all items that have an objective function which is lower than defined threshold. And once we have found such a solution, we update our threshold and go even lower. Yes. So to to capture this fully. So this is how the VQE looks like and this is like the QAA where we have two specialized parts of our quantum algorithm the problem unitary and the mixer unitary and we alternatively apply these in the quantum circuit and of also update our class our parameters using a classical solver. And

11:28 here's a small example of proa adaptive search. So, how well does do these quantum optimization methods perform? Well, starting from the from the back with the Crover adaptive search, well, this one performs rather poorly at current quantum hardware because it provides a really lengthy quantum circuit. So, we have a deep circuit and it's hard to execute this on current hardware. So this is rather an exotic one for the moment but could be interesting once once we have reached fall tolerant quantum hardware. The VQE and Quawa the most promising ones because they can be executed on any hardware and also right now but also leave room for fall

12:14 tolerant quantum computing where we can build more elaborate quantum circuits. And lastly, quantum analing, which is a specialized quantum approach and only works on specialized quantum hardware for example as the D-Wave quantum computer where we have seen and this is where we have seen some major updates in the past time in the past year that for example Dwave proposes quantum supremacy that they say okay we have solved a problem in our DWF quantum and that a classical computer takes ages for and they also provide two interesting use cases. case for example to optimize training for truck discovery with Japan Tobacco or they also collaborating with Volkswagen to navigate to pro provide a

13:00 new navigation system for their vehicles in their production cities but this is what Dwave is proposing and well it's hard to prove that they are correct we did our own experiments and we took like a little bit different course And if you just check here in this red table that for our unit commitment problem which is with rather small instances, we see that our classical solver can dis solve this in milliseconds where our quantum uh computer takes a bit more of approach but provides barely the optimal solution and gets like really poor quality once our instances get even larger. So this

13:46 is somewhat of a problem and also we we op optimized our our algorithm to at least get with the get down with the result quality but that obviously topples up our running time as you can see in the graphic below. So one could of course argue our algorithm might not be optimal. Dweb has a better knowledge of the quantum computer. So I think that the that the current state is somewhere between there between having like no utility at all but also not the supremacy that they are targeting at. But also I would say to to come back to the NP hard problems just because the NP problem is NP hard is not sufficient to provide a quantum advantage here.

14:32 Indeed, I will now quickly showcase three problems where it's more suitable that we find a utility because those problems are even harder to solve classically and also on top of it these problems feature features that usually occur in real world problems. The first one is multiobjective optimization problems where we have multiple often conflicting objective functions. And these often occur for example in portfolio optimization where you want to optimize your return but also you want to minimize your risk. And here we have it that there is no clear optimal. If you have two objectives here that you both want to minimize, it's not clear if this solution is better for you than this solution. And therefore we came up

15:18 with a different notion of optimality in this field. And this is the so-called parto optimality. And this states that an image is optimal if there's no other image that is better in every objective function and strictly better in at least one. And with this information you can say okay this solution down here is not parto optimal because this solution is better in both objective functions. On the other hand, this solution here, there are obviously solutions that are better in the first objective function, meaning all those here. But none of these have a better objective function value in the second objective function. If you want to more know more about this, there's a nice book by Matias Agot, Multipier Optimization, that

16:04 provides a good start to this. And basically dear colleagues of mine have found that there is indeed quantum utility because they have a a rather simple quantum algorithm here and they have a pre-trained QA they are using and providing random samples from this and they show that this can indeed provide a better or even equivalent good solution than classical solvers. So this is a really nice result here. Another way is to look at it is robust and stochastic optimization where we on the one hand have like an uncertain parameters for example the wind energy production in the unit commitment problem and we have a set of scenarios and we want to find a solution that is robust against changes

16:51 and thus works well in every scenario and for example we can define this robustness by looking at okay I want to max like optimize the worst case performance over all scenarios for my solution. On the other hand, stochastic optimization provides has has random variables given and we want to find an optimal solution to objective function. But since we have random variables, we restrict ourselves to find something like the expected value of our function. And for the first one, we ourselves have provided a nice approach where we say okay, we take the samples we obtaining with our DWF quantum computer for deterministic problem and then check which of those solutions we obtain is the best one against our different

17:38 scenarios and this provided quite well results already. And at last we have the multi-stage, multi-level and other complex problems. For example, multi-stage problems consists of two or more sub problems that have to be solved consecutively. So you have one decision made and then you feed this decision in your next problem and you have to optimize again. Multi-level problems even indeed harder because then the problem has one or more sub problems in it that need to optimize once you every time you evaluate your solution. So a prime example for the letter one is a transportation problem where you for example have a city and you want to provide a new public transport for X for example a bus then you has to first you have to set the bus stops then you have

18:25 to assign those bus lines and you have to provide schedule for each of these and as you might know if you for example want to have an optimal with respect cost trans public transport then of course an change in the in the bus lines can also trigger a change in the bus stops because there is room for optimization. So this is a really complex and multi-level problem and I was recently on a conference and there they showed that with quantum computing you cannot you you don't have to look at this problem sequentially but you can solve as a whole proving there that you also have the prospect of quantum utility and with that I'm at the end of my talk thank you very much uh for having me here thank you very much for

19:11 listening and if you have any questions just shoot at me Thank you so much, Pascal. We've got some questions coming through on Discord and then I can pass those on to you from the students. I guess while we wait for some of them to be typed up because I can see people typing, is there I guess the three the kind of three takeaways you'd want the students to have after the end of this session? Um well first I would say the the main takeaway of my of my talk is okay we have NP hard problems that are seen as hard from a theoretic point of view but in practice in our practice everyday

19:58 life these are not as hard as you think because we have 60 70 years of optimization techniques and it's hard to to overtake this with the newly and not perfect quantum computing here and there but there are problems and this is the second takeaway that are extremely hard and we don't have these commercial solvers like that that exist for these kind of problems like multi-objective problems so there is indeed more probable prospect that quantum computing will succeed and the third one is we always have to check not for the algorithm or the hardware itself but the quantum algorithm plus quantum hardware

20:45 is the benchmark against classical systems. Thank you. So we do have a question that has come in. So this is from James in New York City. Which problems exactly do you suspect quantums quantum computers will excel at? Um I would suspect that especially stochastic optimization problems that you for example that often occur for example in portfolio optimization portfolio like like portfolio theory and so on will succeed because this is a sto soastic system a quantum computer and a quantum system itself is a stoastic system. So there is a close relationship

21:30 here and also since it's finance there is obviously a lot of efforts and a lot of money and a lot of gain for you there and that is why big companies like JP Morgan Chase have elaborate quantum departments that work effortlessly on these kind of topics. Thank you very much. Peter from Nigeria is asking what are the yard sticks we need to use to ascertain D-Wave's proposed quantum advantage. Well, first of all, you need probably your own D-Wave device because they and also maybe 10 to 15 years of expertise in working with that device because I've worked with them together at some point

22:16 and they know their machines really well. So you have to and also when you have access to their devices, this is like publicly available or at least behind some some some pay uh border. But if they do their experiments, they have a perfectly trained and perfectly calibrated system that you probably won't have with your access. So this is one part and of course they are shown the quantum supremacy in that what they label as a practical problem but this problem is really close to their architecture. So this is also main advantage. I think these are the main topics or the main main reasons for this. They have a perfectly calibrated

23:02 system. they know what they're doing there and on the other hand the problem they are looking at is perfectly fitted to this architecture. Thank you. All right. So we've got one more question that is would it be better let me just rephrase this. Would it be better for user optimized hybrid algorithms or is it more efficient for an entirely independent algorithm that is native to a specific hardware? Well, I'm a big fan of of hybridization. I think that even if you look at only like one optimization problem that there are parts of it that can be worked well

23:49 on on the quantum system and other parts can be really worked well on a classical system. So hybridization is especially in the current area of NISK devices we are still at is the way to go and as you can see QA and VQE are both hybrid algorithms in my mind since we need need a classical solver. Thank you. Siri from Texas is asking, "How can quantum be used in real world businesses? For example, how would an established company integrate quantum into their business?" Um well I've visited some of E-Wave keynotes for example where they as as I

24:36 showed you in the in one of my slides they have really worked with with companies in their data and and at least they they they tell you so that they have provide quantum solution to like their practical day-to-day problems. So that of course leaves you with two options if you want to do that. First of all, either you buy a quantum computer for your for your company. Of course, this can be possible for large companies, but for smaller and medium business entity entities, this makes no sense. But there you have to rely on cloud access. And I would say that the latter one is the the thing that works well, especially since many supercomputing centers are working

25:21 effortlessly to integrate quantum computers in their supercomputing centers. That means we have a quantum and HPC orchestrator there and I think this is where we will benefit from in the future and where companies will benefit the most of it. Thank you. Arthur from New York City is asking for portfolio optimization with a single objective function will there be a quantum advantage over Groby? I highly doubt it, especially since the original portfolio optimization problem, if you go by Henry Marovitz, is a continuous optimization problem. And with continuous optimization problem, we would have to discretize our continuous

26:07 variables as of now to the quantum computer or we have to use different specialized encodings. For example, we have an angle encoding instead of a simple cubit encoding here. So and of course this single objective problem is indeed easy to solve. So I wouldn't expect their quantum advantage. I would expect a quantum advantage either if you have multiple objectives or you have for example some different uncertainties in your parameters or you have some extra constraints you need to respect. Thank you. And I think we have time for one final question. So this is there's no location but this is from Arte. Are there any particular hardware

26:53 platforms D-Wave, INQ, IBM, etc. better suited for optimization use cases right now? Well, Dwave is well suited because the quantum anal basically solves your quadratic unconstrained binary optimization problem and it's specifically designed to do so. But of course that's comes this comes with a caveat. This is a special purpose quantum computer. So you can only do this task. So everything has to be designed or changed s such that it works for this task. And from like a research perspective I cannot mingle with the quantum algorithm because the quantum analing process is fixed. Um on the other hand I would say that there are

27:40 three interesting quantum hardware for universal quantum computers that are suitable. This is superconducting cubits because they from all the cubits that are out there the most matured one with IBM bolsting now our thousand cubits. The ion trap cubits have the advantage because in our quantum optimization problems we need a more variable connection between where we can do entanglement between the cubits and with the superconducting cubits we are restricted to the architecture. So this can be an advantage there. And at last we have the neutral atom ones where we have these ritback atoms. And what they do in these in this analog quantum

28:26 computer with the ritback atoms is solving a maximum independent set problem. And this is basically also an optimization problem. So there's also a really close connection there. So these are my three favorites currently. If you want to currently solve your your optimization problem, I would restrict myself to Dwave. If you need a specialized algorithm, you go to the superconducting cubits. Thank you very much. Would you have time for just one more question? I know we're slightly over time. That's that's okay for me. I have time. So Ron in Chicago is asking if anyone at Franhoffer is looking into quantum optimiz optimization for the healthcare industry. Um

29:13 as I currently know not really. So I know from colleagues that are working on other ways of quantum computing for the health industry that is either in the detection of new drugs or in quantum sensing where they're working on using magnet resonance therapy or thermometer to to for example get an image of your brain that I'm aware of but especially for this I'm not aware of but we are currently checking this in our institute because we a really strong optimization work group that for example has an elaborate algorithm for the use case in in the healthcare industry especially for example with cancer therapy where

30:00 you uh use radioactive material that you shoot at the cancer cells and there you have a multiobjective problem where you obviously want to maximize the effect on the cancer cells but minimize the harm on your your healthy tissue on your organs, for example, on your liver, on your brain, if there's any cancer cells nearby. And obviously, it would be rather interesting because there's a highly complex problem where we work together with physicists with with people from medicine and so on. Um, where you also have certain uncertainties and it would be interesting to check whether quantum computing can be can be used to improve our algorithm there.

30:46 Thank you. I would we we don't see that so much, do we? We see more the the applications in finance or or other but not so much in healthcare for those specific problems. But that's but that's our mission. Our mission is mathematics for a good future. Thank you so much. We've come to time. So thank you for your time today Pascal. That was amazing. Fantastic session. Thanks a lot Pascal. And with that we come to an end for today's sessions. Thank you everyone and have a great day ahead.