WEBVTT 00:24:25.000 --> 00:24:39.000 anymore for a large lattices or very deep circuits. So you ended up with this bound plateau that you cannot move anywhere. So what can I do? What is the what is the solution to this? 00:24:39.000 --> 00:24:51.000 How can we go beyond this configuration? So, the main issue is there are commercially available gates that I have to use to be able to run anything on my quantum computer. 00:24:51.000 --> 00:25:07.000 What if I don't? What if I just create my own gates according to my own taste? Because if, for example, I want to go here on this plus sphere, I have to take this 2 step operation to be able to get there. It's already. 00:25:07.000 --> 00:25:19.000 to see two 60 nanoseconds wasted of time. How? What if I can just go from here to here directly, but there's no direct way to go there, because there's no gate available. 00:25:19.000 --> 00:25:34.000 How can I use AI to train my quantum computer to directly go there without using available gates? So it turns out I can use the pulses that they used to create these gates. So in order to create this gate. 00:25:34.000 --> 00:25:47.000 If, for example, in Ibm, they have a Josephson junction, they tune the electricity signals going into Josephson junction to be able to get a certain fidelity gate set that available to you. 00:25:47.000 --> 00:26:05.000 What if I directly use these pulses inside the quantum hardware and tune my gate evolution for a for a single for a certain direction, pulse duration, and directly get what I'm looking for instead of applying this multiple gates. 00:26:05.000 --> 00:26:18.000 Billion times, and hopefully, maybe if I tune this in a really good manner, it's basically giving me an ability to simulate everything much more coherent than a short time frame. 00:26:18.000 --> 00:26:32.000 So let me, let me try to go through how this works. So in a superconducting quantum computer, Josephson junction is simulated by something called transmonal Hamiltonian. This is basically an unharmonic quantum oscillator. 00:26:32.000 --> 00:26:48.000 So that's why I said there's a cumul inside your superconductive quantum computer as well. Underlying hardware is actually working as an unharmonic oscillator, where you have the 01 shift between transition between 01 state. 00:26:48.000 --> 00:27:04.000 There's a unharmonicity to be able to split second and third or any higher degrees, higher order modes in your system so that you don't leak into that because it's really hard to. 00:27:04.000 --> 00:27:23.000 measure those states in a superconducting hardware, as far as I know. So you want them to be separated enough so that you end up with the lowest zero one state. And then, of course, you have the qubit architecture. Which qubits, which physical qubits are actually talking to each other inside your quantum computer. 00:27:23.000 --> 00:27:30.000 So these parameters are pretty much fixed by the IDM, for example. 00:27:30.000 --> 00:27:42.000 Listed the typical values for these in IBM quantum computers. You can access them from Ibn's website. 00:27:42.000 --> 00:27:49.000 So I need another term to be able to control these pulses and everything inside my quantum arc. 00:27:49.000 --> 00:28:05.000 So this comes with the control Hamiltonian. Essentially, I have a pulse term here, basically giving me a certain range pulses depending on your laser. You can tune it. But typically, these are between -22 to plus 20. 00:28:05.000 --> 00:28:21.000 Michael Hertz. And there's the phase rate between between qubits and Q mod that they are interacting here. So using this, basically, I can tune my pulse rate and then the phase between these pulses for each pulses. 00:28:21.000 --> 00:28:35.000 to be able to get a new gate that is designed particularly by me. I don't care what gates available in my quantum computer by tuning these parameters how many ever I want. 00:28:35.000 --> 00:28:41.000 I can create a new gate that basically solves my problem, hopefully for me. 00:28:41.000 --> 00:29:00.000 So why this is really important? Because if essentially there might be that shorter coherence that is not shorter coherence time, but shorter time execution time, so that I don't hit coherence limits during the quantum computation, and it has been shown that this method is free from local minima. If you have a. 00:29:00.000 --> 00:29:10.000 certain evolution time achieved, and so that it likes from barometers, which I will show you a little bit later. 00:29:10.000 --> 00:29:23.000 So let me tell you about Schrodinger model, and how do we simulate Schrodinger model using these techniques? How can we prepare the ground state, for example, of the Schriner model? 00:29:23.000 --> 00:29:41.000 using these pulses. So shooting model is basically one plus one dimensional if you want gauge theory that is coupled with neurot fermions. You can see the Lagrangian here, and I have an extra chiral rotation here just to make things a little bit more spicy. 00:29:41.000 --> 00:29:53.000 I can use staggered fermion discretization and draw the linear transformation to be able to map this to a Hamiltonian formalism that I can use it to embed on a quantum hardware. 00:29:53.000 --> 00:30:10.000 So the 1st equation here is very simple. It's basically a Hopington Eisenhoppington term. It's very simple. Just in this addition of this kind of rotation. Even the second term is like really similar to a master, for example. 00:30:10.000 --> 00:30:19.000 But the third term, since I'm implementing this Gauss law, I'm integrating out my gauge field to be able to simulate this, it becomes a bit messy. 00:30:19.000 --> 00:30:33.000 So this last term creates this non-local Hamiltonian effect, which becomes really challenging to be able to simulate in a classical computer because of this long range interaction in my lattice. 00:30:33.000 --> 00:30:43.000 That's why we choose to… choose to work with the Schrodinger model because it's really challenging, especially when you have this current limitation kind of throughput. So. 00:30:43.000 --> 00:30:58.000 If I just take this model, take this Hamiltonian, convert this to a Trotter step, a single charter step in for qubit, just in four qubits, foresight Hamiltonian looks like this. 00:30:58.000 --> 00:31:14.000 It takes 11 microseconds to run on a quantum computer. If I don't do any smart things, and I'm actually cheating here, as you can see, my qubits are jumping over here where I need to introduce actually some swap operations here. I'm even avoiding this. 00:31:14.000 --> 00:31:29.000 I'm even avoiding those swap operation, just raw, assuming everything can talk to each other. I have 11 microseconds. That means I can only run monitor steps in my quantity computer, which means nothing. What can I do with this? 00:31:29.000 --> 00:31:46.000 So how can we improve this this limitation? So what we did is we let's assume that my quantum computers same structure, just 4 qubits. I have a linear quantum computer that everything is talking to each other in that adjacent format. 00:31:46.000 --> 00:31:52.000 And I'm creating my Hamiltonian with using just pulses, right? 00:31:52.000 --> 00:32:04.000 Basically, again, just like in VQE, I'm optimizing to get the ground state expectation value of the Hamilton. So I'm dynamizing the Hamiltonian with the quantum computer. 00:32:04.000 --> 00:32:21.000 If we optimize this, what we got is basically I can execute the entire circuit with 180 nanoseconds, which is 61 times faster than single throttle step. And I cannot guarantee you that single throttle step will be enough. 00:32:21.000 --> 00:32:39.000 to prepare the ground state of my Amazon. Probably I'll need to repeat this multiple times to be able to get the graph state. But with quantum optimal control, I can achieve much, much faster, 61 times faster than single trottercept, and this is basically showing you my. 00:32:39.000 --> 00:32:51.000 The pulse profile inside my quantum computer, and I think if I'm not mistaken, for each qubit, I have 100 different pulses at single phase for the entire qubit. 00:32:51.000 --> 00:32:57.000 I can't even overkill this, I can add more phases, I can add more pulses, etc. 00:32:57.000 --> 00:33:15.000 So how about my evolution structure look like? Because I told you that this can leak into higher energy states inside my simulation. Then I lose the information. Then I have to find a way to retrieve this information if I leech into, for example, second. 00:33:15.000 --> 00:33:31.000 the excited signal, third state. If I look at my past evolution, I don't see anything leaking. I think I didn't add it in here, but there's a little bit of leakage to second site in. 00:33:31.000 --> 00:33:46.000 Some of the states in the middle, but at the end, it all dies out, and I can compare to my state to an exact organization. Of course, I can get exactly matching results with the exact diagonalization and prepared state in terms of. 00:33:46.000 --> 00:34:05.000 I can state of my haplot. Okay. So this is this was for only a quantum computer that is just adjacently perfectly sit together next to each other. The problem is my Hamiltonian is not like that. My Hamiltonian is all to all correlated. 00:34:05.000 --> 00:34:12.000 or in a different Hamiltonian, maybe my Hamiltonian has a purely boundary condition. 00:34:12.000 --> 00:34:31.000 How can I integrate? Is there anything that I can improve in the architecture that will reflect my Hamiltonian structure? Would it actually affect the result? Can I make it faster by manipulating actually the hardware itself? 00:34:31.000 --> 00:34:47.000 What we did is, basically, this is experimentally not possible. But what we try to do is, what if my quantum circuit quantum hardware is also all connected? Does it improve anything? And it turns out that I can go 109 times faster. 00:34:47.000 --> 00:35:04.000 than single torture step. Again, just single throttle step. So it's really faster than if you implement the physical information that we have from the Hamiltonian, we realize that it's much more efficient to simulate the quantum computer. So imagine that embedding. 00:35:04.000 --> 00:35:16.000 entire, um… predile boundary conditions, you can have a quantum hardware with the periodic boundary condition already embedded in there, that they're circular circuit structures. 00:35:16.000 --> 00:35:24.000 we can use that information. Is it this structure to be able to achieve much more efficient computation with this. 00:35:24.000 --> 00:35:37.000 Okay, so I have this infrastructure. How about in a real hardware? Can I put this in a real hardware and get anything comparable to what I just showed you before? 00:35:37.000 --> 00:35:55.000 It turns out the answer is no. If you go through a publicly available not research-specific quantum hardware, you will see that anything around one microsecond even goes up to two microseconds, and this is the mean value with the uncertainty of the red one. 00:35:55.000 --> 00:36:12.000 So, I cannot achieve anything. So what is the reason for that? It turns out there is a reason why this particular quantum hardware is public, because the coupling strength between each qubit are only 2 megahertz, and the state of the arts. 00:36:12.000 --> 00:36:20.000 I think Eagle processor, they are calling it. It's around 20 megahertz each coupling between between qubits. So. 00:36:20.000 --> 00:36:26.000 It makes a huge difference to have a higher value of. 00:36:26.000 --> 00:36:43.000 of coupling between each physical qubit. We thought, Okay, if that is the main concern, what if I can increase this this coupling strength to, I don't know, 30, 40, 50. Maybe I will get infinite efficiency. 00:36:43.000 --> 00:37:13.000 Well, there's no free lunch, unfortunately. We try to increase the coupling strength and see what is the effect of this coupling strength on the simulation efficiency. So this is showing you the best, uh… Minimum estimated time that you need to have it on the pulse, and as you can see, when I decrease the coupling strength, it increases quite drastically, exponentially, actually, and also my uncertainty on the ground state also increases. 00:37:14.000 --> 00:37:30.000 If I increase this coupling strength, I start to hit a plateau at around 20 MHz, which is currently what we have in the quantum hardware. So there's no free lunch. There's no limitation, which is cold, actually. 00:37:30.000 --> 00:37:46.000 the quantum speed limit. If I'm not quoting wrong, I hope. So there's a certain limitation that you can evolve an adiabetic state from state A to state B. There's a certain speed that you can achieve. 00:37:46.000 --> 00:37:56.000 And you cannot go beyond that. And we actually basically seen that effectively by playing the coupling strength as well. 00:37:56.000 --> 00:38:12.000 So if this works, that's great. That means we basically cheated our life from the coordinate time. We solve the coordinates problem. What about the barren photos? Because I still need to optimize the circuit. 00:38:12.000 --> 00:38:32.000 How does it work? If I cannot use VQE, I cannot use quantum optimal control. So is it a problem step? So what we looked into is we basically sampled from a really uniform distribution of the parameters of the pulses and phases that are tagged, and we calculate the variance for each. 00:38:32.000 --> 00:38:49.000 sample. And what we get is basically, as you can see, the variance increases with the number of qubits, and the pulse duration. So when I increase the pulse duration, I give much more contribution to each pulses, so they are. 00:38:49.000 --> 00:38:58.000 the probability of having this Barropata. Where was I? 00:38:58.000 --> 00:39:16.000 So… so I have more time for this single possible evolved inside the function. So I have. I can increase my variance with the number of sites. That means that if I increase the number of qubits, I'm going away from the empatheter. 00:39:16.000 --> 00:39:29.000 And I can if I deep into diamond Plateau, I can basically increase the concentration to get out of it as well. So there's much more control on the issue over here as well. 00:39:29.000 --> 00:39:47.000 So, that's all I wanted to talk about. Let me conclude. Let me summarize what I've talked and tell you a little bit about what I'm planning to go beyond this. So I've talked about different methods, different quantum hardware. How can you use different quantum hardware to. 00:39:47.000 --> 00:40:04.000 Basically simulate fundamental physics, because we have different pieces in the standard model that we possibly want to simulate, but they might not be suitable to simulate just by qubits. Maybe we want to embed… extend this to use Q-modes. 00:40:04.000 --> 00:40:25.000 By using eye trapped quantum computers, this might be possible, or there are, um… cavity interacting with superconducting qubits that gives you the ability to have this humor qubit interaction as well. I'm not an expert on this any shape or form. It's just by what I read. So there are different technologies. 00:40:25.000 --> 00:40:44.000 that we can use to be able to get this cyber model simulated on a quantum computer much more efficiently, hopefully without much truncation. Of course, there has to be truncation because of the experimental limitations, but hopefully it's in a much more nicer way. 00:40:44.000 --> 00:40:59.000 And I talked about quantum optimal controls because of the hardware limitation, coherence time limitation in the hardware. You can use the constant optimal control to basically engineer a specific computational structure. 00:40:59.000 --> 00:41:13.000 for ourselves, for our specific use of QCD simulation or whatever our Hamiltonian needs. So we can tune the hardware specifically for our needs. 00:41:13.000 --> 00:41:29.000 So what I want to go from there is basically my goal is hopefully one day to simulate the PDFs and fragmentation functions more accurately. So I want to understand how can I use this hacker systems to do some scattering. How can I do use them to. 00:41:29.000 --> 00:41:47.000 Similarly, PDF or… quantum leak model, for example, if I implement quantum gauge fields as a quantum links instead of just integrating over them, I can represent gauge fields as Q modes and link them with the with the qubits, for example, fermions. 00:41:47.000 --> 00:42:05.000 This hybrid system, so it's much more efficient. We got truncation. I want to understand how this hybrid systems will basically eventually evolve into QCD. And I'm looking into different methods beyond tensor networks and quantum computers, for example. 00:42:05.000 --> 00:42:20.000 neural quantum states to be able to understand how can we actually achieve bridge between today's limited classical methodologies to tomorrow's hopefully more able quantum computers. 00:42:20.000 --> 00:42:31.000 Thank you very much for listening. I hope I can try to speak. 00:42:31.000 --> 00:42:38.000 Very interesting talk. Questions from the room? 00:42:38.000 --> 00:42:49.000 So I might have missed something. So when you're talking about the speed of when you design these like custom gates. 00:42:49.000 --> 00:42:59.000 It seems surprising that it's like orders of magnitude improvement, not because of individual gates presumably formed a short composite. 00:42:59.000 --> 00:43:13.000 So you have a few discrete gates. Are you too many gates to be able to achieve the same result? So we looked into how can we so the problem is, how can we prepare the ground state? Right? 00:43:13.000 --> 00:43:24.000 So it's not that you still decomposing the gates and you… you just… made kind of composite gates, it's that you go and… You're doing the entire evolution. 00:43:24.000 --> 00:43:40.000 Yes. Instead of… okay, so I need too many gates to be able to achieve what I'm trying to achieve so that it takes a long time to be able to do. So if I can shrink that even a little bit, I have a little bit more time to do time evolution. I have a little more time to do. 00:43:40.000 --> 00:43:59.000 or measurements of different observables, for example. So I'm just trying to shrink that time as much as possible. Now I have a PhD student actually working on how to do this, not just for ground state preparation or excited state preparation. How can we do this? Use the same methodology called maximum control. 00:43:59.000 --> 00:44:11.000 to compress the timing motion, for example. How can we shrink that time evolution so that we can do the characterization with much more actionable? 00:44:11.000 --> 00:44:23.000 Yeah. just to say towards the end, when you came to sort of talking about taking your custom gates and making them real. 00:44:23.000 --> 00:44:44.000 Uh, how exactly… Do you go about this? Is this some sort of, like, low-level API available, which gives you more direct control over the pulses? They're worth. What? So now, according to U.S. Government, it's a national security interest, so that's why it's actually really important for us to develop our own quantum computers here. 00:44:44.000 --> 00:44:59.000 So there was something called Qiskit dynamics interface, so that you can use the pulses and design your own pulses into inside quantum computer and actually submit this job into into hardware. 00:44:59.000 --> 00:45:05.000 They canceled this after we published. You were so lucky. 00:45:05.000 --> 00:45:16.000 But yeah, I think it is really important that we have access to our own content so that we can explore these capabilities over here. 00:45:16.000 --> 00:45:25.000 What changes do you have to do with the hardware to achieve this compression of gates? 00:45:25.000 --> 00:45:39.000 I don't need to change anything. So there's if… I don't want to change the architecture itself. Sure, that's fine, because it's harder to change the architecture in the formula in there. 00:45:39.000 --> 00:45:53.000 Uh, as long as I have access to pulses that they use to create these circuit gates, they already use them to create the gates. If I have the access to use them directly. 00:45:53.000 --> 00:45:59.000 They just do their job for them for my purposes. 00:45:59.000 --> 00:46:14.000 So instead of having a keyboard, I have an electronic signals to write my, uh… I'm fine. 00:46:14.000 --> 00:46:24.000 Have you ever tried or are you planning to eventually benchmark these gates relation the things on the real quantum computers? 00:46:24.000 --> 00:46:29.000 For each one are you asking for? For hybrid one or two? 00:46:29.000 --> 00:46:38.000 Like, the real… Both of them. So, so for hybrid system for Qub, we are actually working with Sandia National Lab. So they are. 00:46:38.000 --> 00:46:52.000 They have experimentals who are experts on designing these trapped iron quantum systems, and they are currently working on how to make our simulations real applied to their quantum systems. 00:46:52.000 --> 00:47:05.000 Basically, they are using Quad optimal control to be able to achieve between we propose to achieve. So yeah, we are trying to… They already have a constant circuit slowly, right? They have, yes. They do have access to hardware and everything. 00:47:05.000 --> 00:47:17.000 We just want our gates in their machine. And can you apply it here in the Uk? You know, thank youcc here has program that's going to allow. 00:47:17.000 --> 00:47:25.000 implementing or doing any simulation benchmarking on real prospective users, basically. 00:47:25.000 --> 00:47:54.000 Basically, database here in the UK or elsewhere as well? Well, I did that for regular superconducting projects that I'm working on, but I believe, so… I believe in QCC for iron trap, for example, working with Quantinium. And I think Quantinium only allows for qubits instead of having access to qubits as far as I know. So I think the superconduct 10 is regretti. 00:47:54.000 --> 00:48:01.000 Um… That's really good. 00:48:01.000 --> 00:48:27.000 So I am traps. Yeah, for the… it's like an internal… Uh, internal hardware teams as well, which was, I guess, basically, there's, like, two modes of working with the NBCC. One is that there's this kind of platform where you access commercial offerings, but you probably don't get this low-level access. But there's also the internal research team, so you'd probably have much smaller devices, but. 00:48:27.000 --> 00:48:38.000 potentially a more meaningful collaboration on… But there is also with IBM, you mentioned IBM, you have that there is access also to Willow. 00:48:38.000 --> 00:48:53.000 the famous chick that's where it basically probably the most. But I think maybe you don't have to still level access. Yeah, we tried… well, when we were doing the paper, when we were writing, we were working with IBM, and we submitted there. 00:48:53.000 --> 00:49:00.000 But after… after we published, basically, they cut the access for the low level. 00:49:00.000 --> 00:49:18.000 Yeah, I don't know if it's possible through NQCC. Definitely possible, and the call for basically soon the deadline for research for academic research. Before, it was only open. 00:49:18.000 --> 00:49:41.000 I'm not currently open to academic researchers here in the UK. Yeah, I had the… can definitely send you the link will show you the link. I did apply for a PDF project that we are working, but I didn't know that you have access to non-level pulses through one QCC. 00:49:41.000 --> 00:50:00.000 That would be really interesting. I think there is a possibility. Yeah, another question. Did you also explore other modalities like for quantum computers, concept abuse in hardwares? For example, the other modalities. 00:50:00.000 --> 00:50:06.000 Um, having much more coherent sign, but much slower speed, gate speed. 00:50:06.000 --> 00:50:33.000 These kind of things. For example, um, cold neutral items can give… Very long, coherent time with the trade-off basically with the much lower gain speed. It's improving, but like if there is any kind of… I am very interested in it, but I've never worked on particularly natural atoms, but yeah, because we don't know which hardware going to be perfect. 00:50:33.000 --> 00:50:50.000 So I'm really interested in because, yeah, the bigger thing also is with these modalities, you have multiple atoms, you can… you can create icing chains and complex systems where you can basically have harmonic oscillators and so on, so it's. 00:50:50.000 --> 00:50:55.000 It's very interesting as well there. And we'll look into it. 00:50:55.000 --> 00:51:02.000 Any questions from Zoom? 00:51:02.000 --> 00:51:03.000 Oh. 00:51:03.000 --> 00:51:09.000 Hi, uh, I have a question. I was just wondering how… if you could expand a little bit on similarity scattering systems. 00:51:09.000 --> 00:51:13.000 Uh, using a quantum computer? 00:51:13.000 --> 00:51:30.000 Oh, that's that's something that I'm trying to learn at the moment. So I let me try to describe as much as I know. I'm I'm learning, so not expert at any means. 00:51:30.000 --> 00:51:46.000 So what do you need to do is, for example, you have the Hamiltonian, but you need to prepare the date package first to be able to put it on a on a quantum computer. And I think for the fermionic models, you need to do some sort of. 00:51:46.000 --> 00:52:05.000 will live off transformation to be able to do this embed this wave packet on a fermionic lattice, for example. It's much more easier if you have a scalar field theory, because then we can describe your wave package much easily, but with fermions, it's a bit more trickier. 00:52:05.000 --> 00:52:13.000 But then you can basically evolve this in time once you… Embed your way back. Sorry. 00:52:13.000 --> 00:52:19.000 Once you embed your brain packet, you can evolve the symptoms and observe how they collide and everything. 00:52:19.000 --> 00:52:23.000 But this is basically the extent of my knowledge. 00:52:23.000 --> 00:52:25.000 Wow. Thank you. 00:52:25.000 --> 00:52:33.000 Thank you. Any question from Zoom or Room? 00:52:33.000 --> 00:52:41.000 Not that I can ask. In terms of doing it, I mean, particularly, how do you see the hybrid approach scaling for a really realistic? 00:52:41.000 --> 00:53:01.000 uh, gay story, particularly non-alian QCD. Uh… That's a very hot box. So the the I think currently there's I don't remember the numbers. We have the numbers in the paper, but the problem is. 00:53:01.000 --> 00:53:16.000 You can put only so many ions inside an iron trap depending on your technology. So you need to sacrifice some of the ions to control the molds, and then you have the mold and everything. 00:53:16.000 --> 00:53:23.000 So there are different limitations on that being able to achieve. So I think. 00:53:23.000 --> 00:53:43.000 It needs to be evolved a lot. I don't have the exact numbers, but… I think currently, as far as I know, it's much more limited compared to a larger size also because right now we have, I mean, thousands of qubits. I don't think we can have. 00:53:43.000 --> 00:53:53.000 documented qubits and cube numbers. I mean, you can have in qubits, I believe, in fact, but not. 00:53:53.000 --> 00:53:57.000 at the same time, that many qubits of Q-note at the same. 00:53:57.000 --> 00:54:11.000 And I'm just following up, uh… Particularly the algorithm work which you did, how transferable it is from ironcraft versus the aggregate forms. 00:54:11.000 --> 00:54:26.000 gate structures that are very much transferable, depending on the technology. For example, if you want to use superconductive quantum computers, you cannot use the same gate set, of course, then you need to truncate your gate field or integrate over your gate. 00:54:26.000 --> 00:54:45.000 So that's… that's to the solutions that you can do. If you have, for example, this cavity interacting with the superconducting periods that gives you another environment. I don't know much about it, but that gives you another. 00:54:45.000 --> 00:55:03.000 Q1 to qubits at the same time, for example. So… they have a similar dataset to how we thought that you can map directly. You need to change some of the operations, but at the end of the day, you can get similar things. So… 00:55:03.000 --> 00:55:14.000 There's one more thing that I've heard about photonic quantum computers, but this is just what I heard. Apparently you can use the polarity of. 00:55:14.000 --> 00:55:27.000 of photon to make it look like a qubit and then what one is a Q model. I don't know how they interact, but maybe that's a possibility too, but. 00:55:27.000 --> 00:55:33.000 It doesn't track this. I don't know, I don't know. 00:55:33.000 --> 00:55:43.000 I'll be. I'm particularly happy to see our colleagues from NQCC here, and that sort of gives us a great comfort. 00:55:43.000 --> 00:55:58.000 engaging multiple times in physics and, uh… I'd like to find my computer and this seminar is an example. So let's thank our speakers again. 00:55:58.000 --> 00:56:17.000 And thank you very much. Please feel free to join us for lunch, and we'll have some follow up seminars as well in the PQD and QCC seminar series in the coming weeks, so keep you updated on this. Thank you very much.