 Okay, so there are two monitors, I don't know where to stay. I start here. Okay. So again, welcome everybody. It's a pleasure to be here, and to give this is introduction on quantum computing and application in natural sciences. So, here is the outline of this presentation. First, I will give you a short overview on quantum computing and application so oops. Thank you. So, a few notions about quantum computing, begin with. Then also I will introduce the concept of near term quantum computing. And also an overview on the application modules that we have in this kit. So panels was here for the entire week. And maybe already discussed with you about kids kids and how we want to interface kids kids with classical drivers like one year and other codes. And then, in the second half, we talk about some developments towards quantum advantage. Obviously, we are not yet there, but we are building up all the tools, starting from the hardware, but also software and algorithms in order to reach quantum in the domain of natural sciences. And then here I selected topics on electronic structure calculations, but I will focus on scaling up functionalities so how do we bring this so early stages in quantum computing two systems that can be of interest in chemistry material size and so forth. And then at the end, if I have time, I will also introduce the topic of quantum dynamics. And the reason for that is because we believe that quantum advantage could be something demonstrated for for quantum dynamics before electronic structure calculations. Okay, so gates. I will start with this very technical slide about the gate operations that you perform you know then quantum computing. You operate on a cubit register and that the kind of operations that you can perform in digital based quantum computers are given here. In near term quantum computing, you have access to gates that we call you three gates that are rotations on the block sphere of the single cubits. Unfortunately, these gates cannot be error corrected. So when we will move to fall tolerant so error corrected quantum computing, then we will have to replace these U3 gates that you will see during my talk with a universal gate sets so made off and this is written here or not. Made of tea gates. Sorry. Okay. Thank you. So let's go to the next one but now this doesn't work. Thank you. Okay, so how does it work. So we start preparing an initial state that it can be a simple product. So in the order of the qubit states qubit zero to qubit and so you have n plus one qubits each qubit can take a superposition of these two states zero and one. And if you introduce a basis, for instance, for two qubits, you will have a state defined by this factor here. So the circuit right so the circuit will perform the operations that I mentioned before. So these are one qubit gate operations that work on a qubit register. And then you have these other gates here that are two qubit gates that induces entanglement between this line and this line so without entanglement. So the quantum circuit could be simulated easily classically, but at the moment you introduce entanglement, then the size of your space becomes n to the power of two. But n is again the number of qubits, meaning that with 50 qubits you reach a size that cannot be handled anymore by a classical computer because to do the 50 you cannot place it in the memory of any computer. So if you could, then you go to 51 qubits. And again, you cannot anymore because every time you add a qubit you double the size of the space. Whatever you try to do classically every time you reach a result than the day after. I mean, I just add one qubit and then is over again. And what you build in the circuit is a linear combination of all possible states. So two to the end states of your system. And the algorithm is indeed about creating a circuit that is expressive enough that contains the solution of your problem. And then in a VQE that I will introduce later on vibrational quantum Eigen solver then you will optimize the parameters of this single qubit gates that will give you the coefficients in this distribution. And then by optimizing this object you will get the solution of your problem. Here I also introduced the concept of repeating blocks. So the circuits very often is given by repeating blocks, more blocks you add more expressivity you add to your circuit because all of these blocks here have an independent parameterization. So they are the same in shape but with different parameters. If you want to cover the full Hilbert space, you need exponentially many gates right parameters, but obviously in quantum computing we aim to get an approximate solution with a polynomial number of gates. For example, the solver key type theorem that tells you that if you are allowed to give a tolerance in so an epsilon in the precision that you want to reach, then there is a polynomial number of gate operations that could get you to that precision. Okay, so so far everything is pretty simple then at the end that you need to measure in order to get out results, right, and then you will measure a state. And that is the result of this measurement will be given to a classical bit of information. And how you do that you do it by measurement process so you need to collapse the state that you generate in the QB register into a bit string what we call a bit string which is one element of your expansion that you have here below. Right. And each of these outcome will show up with a probability that is the square of the amplitude in front of that state. So this means that when you measure an observable, you will not get a single value. So the expectation value but you will get a distribution of values, right, because you collect from this distribution here with the weights that are PI is the amplitude. So more measurements you do, and smaller will become the standard deviations of your distribution meaning that if you want an accurate results with near term quantum computing you have to repeat the measurements many times, so that this distribution at the end in the limit of infinite measurements will collapse on a delta function. So the errors that we will do with near term quantum computers or not fault tolerance or meaning that the gates are not corrected the errors that you do on the gate operations. So within this framework we do errors in setting up these rotations on the single qubits on the block sphere of the single qubits. So you have to set so an angle, no longer angle of theta and phi, right, you do it with an error and this obviously will will cause. Yeah, an error on the final result. So this is the decoerence of the qubits, the qubits deco here with a characteristic time that is called T one that is in the order of few hundreds of microseconds. And therefore you need to to complete the execution of the circuits before the qubit starts to deco here. This is another source of error. So these are two errors so how to set the block spheres, the angles on the block spheres, the decoerence and then we have also errors at done at the measurement and errors coming from the statistics of this distribution here so the fact that what we call statistical noise because you need more and more measurements in order to achieve a good accuracy of your results so this is really quantum computing in a nutshell. Now let's have a look at what is the difference between near term and fault tolerant quantum computing. So in fault tolerant quantum computing, which means that you have an additional layer that allows you to correct for the errors that you do in the single qubit operations. In order to encode these error correction codes, you will need something like 1000 physical qubits for each logical error corrected qubit. This means that is not something that we can do today because we have a few hundreds of qubits at the moment. And here you need 1000 to error correct a single logical qubit is something for the next decade. It would take five to 10 years to reach that now. Then for to do that we need the new hardware developments, because smaller you do the single, you can make the single qubit error, then the less physical qubit you will need to generate a single logical qubit. Then I mentioned already before you don't you cannot correct you three gates, then you need to decompose this into a universal gate set as I mentioned before Clifford plus the gates. That's also induce introduces more gates and a longer circuit depth. But on the other end, if you have a fault tolerant quantum computing, then you have a well known quantum algorithms that can provide a quantum advantage. And this is the work of the mathematicians right so the mathematicians proved that the day we will have full tolerant quantum computing, then you can solve many quantum mechanical problems with speed up. So that can be exponential or polynomial speed up. And also classical problems in statistical physics can be solved more efficiently with a quantum computers, there are theorems like mean the shore algorithm that can factorize numbers with exponential speed up. And we have a Grover search that allows you to find, I mean, data in unstructured databases with a polynomial speed up. Okay, so but this as I mentioned is more for the future my talk will be mainly about the near term quantum computing. So using physical qubits instead of logical qubits. So the problem is that we need to cope with the gate errors, the qubit deco hearings and statistical errors that I've introduced a moment ago but we have error mitigation schemes that helps to mitigate these kind of problems. We therefore have a limited number of qubits and the circuit depth because these errors accumulate in a way, and therefore more qubits you have and deeper is your circuit, larger would be will be the impact of the of these errors. But also in this case we have a very active research on quantum algorithms to demonstrate quantum advantage. Mechanics is definitely one of the topics where we aim to get quantum advantage with near term quantum computing, and here I'm talking about quantum chemistry many body physics and also high energy physics think about let this gauge theory. For instance, but as I mentioned also classical problems may one day become so. And then you have the near term quantum computing. This is less clear what kind of advantage you will have for classical optimization problems with near term quantum computing, and then you have a quantum machine learning. That's another class of say algorithms that using neural networks and support vector machines can provide quantum advantage in the near future. So, again to summarize our goal is to achieve quantum advantage with near term quantum computer computers. We need a noise resilient quantum algorithms and this is why we need continue searching for better methods and better algorithms. We need the noise mitigation schemes to reduce the effect of the noise. We have to develop scaling up functionalities in order to be able to tackle problems of interest in say in in this community, for instance, integration with HPC is becoming more and more important because I will show you later that we developed schemes that integrates quantum and classical. So there will be one part of the problem solved with the classical computer and another part of the problem solved with the quantum computer so the exponential hard part of the problem, exponentially hard part of the problem will be taken by the quantum computer and the rest will be will be solved with a classical computer. So if you think about embedding in electronic stature calculations, you can have one part of the system that is handled by a quantum computer because you have strong correlated effect. And the rest of your electrons may be treated well with density functional theory. Right. And this is the reason why we are here with panels because we would like to integrate key skit that is our software package for quantum algorithms with classical drivers like Vanier quantum espresso, in order to enable this cross talk between HPC and quantum computing. Okay, and this is to go via the cloud because the quantum computer we cannot bring it here. The quantum computer needs conditions that can only be so set in a lab in a lab. And therefore, we cannot take it where we need it so we need a cloud service that allow us to access the quantum computer. So, let's briefly introduce the technology that we are using at IBM. I don't want to spend much time here because in the interest of time I will like I would prefer to move to the applications. So we use superconducting qubits of the transform type right that have potential energy surface that is given here. You see that the potential energy surface is not harmonic and therefore the different levels energy levels are not equally spaced and this is crucial. Because then you can use the ground state and the first excited states has the level zero and one of your qubit and actually we are already working also with some other excited states in order to be able to encode more information in a single qubit. So this is what will function as a qubit. And then you need to entangle the qubits together. And for this operation we use a microwave resonator that in this case, instead, have an harmonic potential with equally spaced levels and those devices are used for readout for the entanglement of the qubits and also as a noise filter. Now you have qubits and you have the entanglers between the qubits then you can put all these together and then you get your quantum device. It looks simple but there are many technicalities obviously that I don't discuss here. If you want we can have a say a discussion later on in the problem with these devices is that so the energy spacing here between the ground state and the first excited states isn't the order of five gigahertz that corresponds to 240 millikel. So if you want to avoid the thermal excitations or the excitations of your qubits you need to cool down the device to very low temperature and this is why we cannot take it here because at the moment these devices are operating at roughly 20 millikel. Right, again, in order to avoid this kind of spontaneous induced the thermal induced the transitions. And this is how system one looks like the first quotation mark commercial quantum computer from IBM so you will have your fridge that cools down the device at 20 millikel this and then you have all the electronics that is used to control the pulse sequences. And then here the classical bits are sent to classical computer for the interpretation of the results. So these are the devices that we had available in 2021. So we started with five and we reached 127 in 20 in not yeah 127 in 21 and this year, we will this is the roadmap for the next few years, we will reach 440 430 qubits. And later on we we plan to to cross the 1000 qubit barrier in 2023. And there you get already something large enough to encode the first logical qubit, so the error corrected technology, and then using this transductor that are microwave to optical transductor you can entangle different chips together and transfer quantum information from one to the other so entanglement for instance, and in this way start building piles of quantum chips. Okay, so my contribution into this is the development together with the team in Zurich of the Qiskit software application modules at the moment we have functionalities in natural sciences, including obviously material design and electronics such as calculations but we also have modules in machine learning optimization. Okay, so about Qiskit panels was here for the first part of this workshop. You know maybe already quite a bit about it so it's an open source effort by IBM so everybody can access download this code and test it. We have a graphical interface you want for beginners where you have a qubit register and you can drag and drop gates and measure your results you can simulate the circuit or you can execute it directly. You can do it on computer right because some of the machines are available to the public. So let's say the previous generation of hardware is made available to the entire community for free. Only the newest machines, the premium machines are as a commercial. So you will need to pay to access them. And for learning purposes I think this platform is really very useful for the more more advanced people like obviously here you can use Python scripts also to prepare your algorithm set your circuits and execute your circuits in simulations or directly on hardware. For developers we have this GitHub repository where you can contribute your, your code. Okay, so we also introduced recently this concept of friction less. Use of quantum computer, meaning that even if you are not an expert on quantum computing quantum information you can use with just a few lines a quantum algorithms and collect some results. You can use these lines of codes, for instance, to get the energy profile of this association of lithium hydrate. Right. That's, it's really, we try to make a Qiskit a tool for everybody so that also a quantum chemist that is not interested to look into what are these new technologies, they can simply call this few functionalities and a few lines get already an experiment done on a quantum computer. Okay. So let's move now towards the applications, and then we start with applications in quantum mechanics. And I would like to start with this quote by Richard Feynman that was essentially saying that since the nature at the fundamental level is quantum mechanic. Why not using quantum technology or try to use quantum technology to solve this problem instead of classical technologies, right. And obviously quantum chemistry and physics are therefore the natural target for quantum computers. So the computer can also efficiently solve some classes of problems and already mentioned before, we have the proof that with the shore algorithm you can have an exponential speed up in factory numbers. And also Grover search that gives a quadratic speed up in searching unstructured data. So that's, again, more probably for full tolerant quantum computing than near term quantum computing. But also there is a lot to be done in these domains on the solution of classical problems, optimization problems, statistical mechanics problems with quantum computers. So these are some near term application modules that we made available on Qiskit. You can have modules to solve electronic structure calculations in the ground and excited states, plus also bibronic structures. We have this scaling up functionalities that I will discuss also more in the details later on. We have a quantum machine learning that can already be used for instance in and the study of molecular design. So, in this case, we will work with features instead of atomic structures so we extract features and then we use a quantum machine learning to to extract knowledge from these features so this is also something very promising. We have a modules for molecular design that maybe I will have time later on to talk about we have already the possibility to perform ab initio molecular dynamics or classical forces computing with ab initio methods. Let this gauge theory, we have a collaboration with certain on let this gauge theory that is going on since more than two years now. Classical problems we have a module to solve and to solve to look at protein folding on a lattice. Again, this is a classical problem, you have to be careful where the quantum advantage can be in that in this kind in class of problems, most probably you will not get more than a quadratic advantage. I mean, it's interesting to see how you can map this kind of problems into quantum register. Then we have quantum dynamics that obviously is something very interesting for us because it's a quantum mechanical problem that is very hard to do it classically. And then we have quantum machine learning for energy physics. Okay, so I will focus only on a couple of this, how much time was the level zero minutes right. Sorry. Okay. So in electronic structure. Again, here I don't have to say anything about electronic structure theory you know that if you want the exact solution the classical cost will be exponential in the number of orbitals and instead the quantum algorithm. So for example with scale like and to the four and immediately you see the potential advantage of this approach. This is a quote from a tier stroyer was saying that if you have 125 orbiters and you want to store all possible configurations. You need more memory in your classical computer than there are atoms in the universe. Obviously we are not interested to store the way function right because if you know how to generate it then we don't need to store it but if you would like to do that, it will be definitely impossible already with 125. Orbitals right and the quantum computer can do it easily instead. So, how do we solve problems in quantum chemistry I will not go into the details where we formulate the Hamiltonian in the second quantization approach so meaning that the fermionic statistics is encoded in the rising and lowering operators. We pre compute the coefficients of the Hamiltonian in the basis in the given basis with a classical computer and this is again why we are here because this has to be done by a classical driver and banier and all the codes linked to it. Could be a way of getting this. These coefficients. Obviously the quantum computer working with qubits. They don't fulfill the fermion statistics so you need a transformation from the fermion statistics to the statistics of your spins so your qubits and for that we use the journal being their transformation there are many other transformations that are more efficient and the journal being about the journal being is the easiest to to write down so it's the one that took here, and then you will have to introduce this transformation in into the Hamiltonian and for instance for these two terms here you will get this complicated formula here this is something that you don't want to do by hand and therefore here we have kids kids that once given this Hamiltonian you will transform it directly in a few seconds into the same Hamiltonian so it's ISO spectral to the previous one, but it will be now formulated in the language of the power matrices. So that's is done for you, and you don't have to bother about all these processes here again is part of the friction less concept that I've introduced before. So so far for the Hamiltonian then the wave function will be encoded into the quantum circuit. Sorry the resolution here is not great so probably you cannot read the details but it is good enough. But just to give you a flavor you start with the artery focus later determinants in the occupation. Numbers formalism so you have the first three occupied and the other two unoccupied and then this would be an excited later determinants where you take the orbital, the electron in orbital three you put it in for and this is the double excitations. So you will build your expansion. The function of there and and and this coefficients you can encode them into the rotations of your single qubit operations. Then you will have to optimize these parameters in order to minimize the expectation value for your state with the Hamiltonian of the system. So to do that we use the variational quantum eigen solver we start again with the Hamiltonian now given as some of Pauli strings in the language of Pauli operators. So you will be encoded as I showed you before in the quantum circuit. And then what we do in the measurement process that I introduced in the second slide, we compute the expectation values of the single component of your Hamiltonian we sum up everything and we have an expectation value for our energy that is parametrized on the teachers with teachers are again the angles on the block sphere of our cubits. And we get from this operation from reading this we have the distribution we use many shots in order to reduce the standard deviations of our distribution. And this will correspond to the energy that we give to a classical computer to do a step in optimization. We modify the parameters theta we send back the parameters theta to the quantum computer evaluates a new way function with a new set of parameters, you will estimate the expectation value of your Hamiltonian, it will send back this classical computer. This is again one first example of the interplay between classical and quantum. These are hybrid algorithms so they need quantum and classical component here the classical component is just doing the optimization of the parameters. And then you get your results if you apply this algorithm to for instance here the dissociation of and to that in the large distances as a strongly correlated character, then you see that one of the most commonly used classical functions of your many electron wave function fails completely. This is CCSD in the projective formalism. So it's well known to fail for this kind of molecules will give you this barrier. When you try to bring the two nitrogen atoms together that is completely unphysical the correct results should be the black curve there. The unitary copper cluster the quantum unitary copper cluster algorithm instead is able to capture correctly that the right dissociation profile right so with this I don't want to claim that there is any quantum advantage so far just want to say that there is something good in this algorithms and they will be able to use them also for larger systems, then we can get potentially a lot of benefit. So far on the hardware we can do only smaller systems because of the errors that I mentioned before so this is already three years old results so now we can do better. These are example for the H2 and lithium hydride where we use an error mitigation scheme in order to improve the quality of our results and try to mitigate the errors that we do at the single qubits. So you see that we are not within chemical accuracy but at least we capture the correct profile on hardware. One thing very important if you want to have quantum advantage you cannot get it by simulated your quantum algorithms you need to run it on the quantum computer. Okay, so that's very important point. We can demonstrate using simulations the power of our algorithms, but if you really want to get out the quantum speed up but you need to execute the quantum algorithm on a quantum computer. Whatever quantum computer is I can be superconducting qubits. It can be ions spins it can be whatever atoms. There are now many ways to build quantum computers. Okay. So the possibility once you have the ground state using the equation of motion approach to get excited states you just need to measure many more things with the ground state wave function that you have optimized. Then you can measure these other quantities here where these are the excitation operators. You can get this matrix element you put them in this pseudo eigenvalue problem, and you solve it classically and will give you the excitation energies and, and the coefficients for the wave function expansion. And here you see actually you don't see the reference lines but you can believe me that the quality in simulations for the excitation spectrum of the hydrogen molecule lithium hydride and water isn't it very good. So you cannot distinguish the exact from from the calculated value. So this is also something very promising because maybe you're familiar with excited states is very hard to get good excited states for larger systems using whatever method, right. And that was when you, when you have a new molecule, there's always a debate what are the excited states because if you use the DFT you get some values if you use custody to you get another value if you use. I mean everybody comes with different values because we don't have an exact solution right so it's very and if quantum computer can help. These entangling this, this kind of things I think it will be really beneficial for the community. So excited states, these are the, this is the ground state and the first for excited states of lithium hydride along the dissociation path. We are not within chemical accuracy, but you see that here you can see the reference which are the dashed line and dots are our experiments and they fit pretty well. There is some hope that soon we can say something about excited states as well. Scaling up functionalities, maybe after that I stop because I think I'm already. Okay, but okay we start. Okay, so this is the idea very old idea because you can have embedding, for instance, of post art refoc method in density function here and art refoc so it's nothing new. It's just that now we replace the active space part of the calculation so we don't use a post art refoc method but we use a quantum algorithm. It works more or less like this or the effect the core potential obviously you can forget about then you have the balance electrons that you treat for instance with density functional theory and only the electrons of interest to the catalytic one complicated one the strongly correlated one so you you you compute them with the quantum algorithm. And now we are, we have this implementation, so density, quantum use the CSD or any type of quantum expansion of your way function embedded in art refoc or density functional theory using different packages by SCF Cp2k. This is the collaboration with your the University of Zurich quantum express and Vanie, I should add here, CPMD and NWM EX. And we would like to continue here and Vanie could be really a way to get interface to many of these classical codes. And also Vanie is crucial for us, because if you want to localize the orbitals and the region of interest that you need a localization tool, right, because the drawback of an active space embedding scheme is that if you're, if your orbitals are distributed overall the entire system, then you would need essentially to include all of them into the office space. So if you want really to, to, to get some advantage by using this method you need to localize the orbitals where they are needed. And the Vanie functions is a good way to do that right back and rotate my orbital so that they are maximally localized in space, and then using an active space approach, embedding approach, then I can leverage this kind of localizations. Yes, great. So here are some applications so this is the last molecule we could do a full CI to get the reference is oxy rain. And here is the stretch along the CC bond. And obviously here you don't see the details doesn't matter. Obviously performs great. Otherwise, I will not show it. And these are the orbitals, the all the orbitals that you will need to, to use to generate your way functions, the one in black are taken by the DFT, and the one in red are the artist is the active space that is given to the quantum processor. And depending on the size of your active space, you can approach as much as you want the reference. Good. Yeah, very briefly machine learning I mentioned many times is also nice tool that we have. The first in this case is, is that you try to bypass the solution of the Schrodinger equation by teaching a neural network about the molecules of that you're interested in. So instead of using the entire configuration space of your molecules you just use a subset to train a network by solving the Schrodinger equation. In the remaining set of molecules you bypass that and you use the neural network, for instance, and the nice thing is that you can feed directly away function to a quantum neural network. And this you cannot do it classical classical you extract features. So in just these features to the network or the classifier or whatever to your algorithm in the case of a quantum computer you can use directly the way function to train the network. And you can even partition the molecule into pieces. This is done already classically, and then solve your neural network for each of the pieces separately combine the results and try the quantity of interest. In machine learning we also see we have also similar pipelines we have interface kids kid with Rd kit. That is one of these game informatics packages, you give molecules as smiles, so you give strings of atoms and information about the 3D structure of your molecule. You extract features, you compress them with a principal component analysis and then you feed them to quantum computer and here I would just like to get your attention on on some of these results. So these results were done in collaboration with a group as the artist center in the UK that are specialized in this kind of algorithms. So we use some data sets don't ask me about the details of these data sets but our data sets used routinely by them to train machine learning, in this case, a super vector machines to classify molecules. So you will teach your neural network or whatever so your quantum, your classical machine learning algorithm to recognize properties of molecules. And then you screen an entire database to and try to classify the good and the bad, in a way, right. And if you use the classical approaches here in blue. This is the score. So how good is the performance of your algorithm. And you see that classically is always inferior than the quantum so the quantum can already for this very small test cases outperform by much but significantly the classification of the best known classical approaches and these there is really no bias because these calculations were done by experts in the field of drug discovery using classical. So, again, there is some, I mean, potential for quantum advantage also in this kind of approaches already now with me on quantum computing. So I just browse very quickly to another important topic that is quantum dynamics in first and in grid based or second decision framework, we have totalization of the time evolution operator, or this variational type. Solver of the dynamics using McLaughlin variational principles. We have integrated both framework first quantization second quantization using this type of solvers for the dynamics. The limitation of the classical algorithms that they will scale. Exponentially with the size of the system. So remember that the vibronic structures are computed in the configuration space of a molecule so it's three n dimensional. So, and the classical algorithms case as n to the m where n is the number of grid points and m is the number of dimensions so this is a killer for classical algorithms. And the quantum algorithm scales m log n. So that's you see that there is a huge potential in solving these classes of problems with a quantum computer. And also in second quantization the classical will scale exponential to the number of modes. Instead, the quantum will be poly n in the number of modes that you have in the system. A lot of potential we have done implementations of the spin boson model, and we can have so good understanding about the effect of the noise. In this case, but also we have now implemented quantum dynamics in a grid based setup was not easy because of many technicalities but now we are working and is stable. I'm very happy to show this because I was working with classical methods on this kind of dynamics for many, many years. And now I can do it again also with the quantum computer so that was really very nice for me this is a test case is the dynamics without any external potential this is an harmonic potential so you don't see the potential here. This is a very tough one is the scattering of a wave packet against an echo barrier, where you have part of your wave packet that is tunneling across the barrier and parties reflected so to do it classically I can tell you is a nightmare. Right, but now we have a stable algorithm that can do it in in say using polynomial number of resources. In fact, we need to introduce some tricks but they're really working fine. Okay. We have also known about the dynamics but they don't have time and thank you for your attention. Okay, so thank you very much for the great talk now we have quite some time for questions and comments so please raise your hand if you have a quick one. So, is the, you do the measurement by the amplitude and the phases are irrelevant. This has to do with the first part of how you read the thing is the phase of the way functions you're relevant. No, the global phase no, no. So we, we simply project the state on the different realizations right so that are the big strings. No, no, no. Yeah, so you have a few participants connected online so we'll read the question. There's a question that I don't want to take. Okay, so, Kemal at a lot is asking for which problem calculation, do you think the first practical quantum advantage will be achieved where you would choose quantum computers over classical. That's a very, very complicated question. I mean we are working a lot on quantum chemistry but quantum chemistry, you need in quantum chemistry you need really high accuracy, right, this famous chemical accuracy one kilo per mole or something like this, few milli heart rate, and we have noisy devices. So for us is very hard to reduce the noise below this chemical accuracy, but still energy is not the only thing that you want to measure in the system, right. So you can measure excited states gaps, and there, obviously you will have some, say, constellation of errors, most probably you can measure spin gaps, you can measure. You can also use these approaches for solving the dynamics of the hubbar model. So I think that there is a lot of potential in solving quantum problems with a quantum computer. This is nothing new but what is probably new is that we hope to be able to show something using near term quantum computers. So this quantum advantage, then, then quantum machine learning is also very promising, because there, the answer is zero and one, for instance, if you have a classifier. And therefore it's also more resilient to noise, right, because even if I mean you do some errors in measuring your circuit that since your answer is only zero one maybe. And the problems that I mean the applications that I show is they are pointing in this direction that I mean these algorithms are very resilient to noise. And therefore, you can really leverage the advantage of the quantum secret that gives more expressivity for your cost functions. And what else instead for classical problems optimization problems is not really my business to look into that. There are, as I mentioned, some algorithms that will provide the quantum advantage but the depth that you need is such that you cannot implement them with near term quantum computing you have to wait for full time. This is further away. Any questions here. Thanks for a really, really nice talk. One of the ways in our field that we justify what we do is we say that it's less expensive to do a density functional theory calculation and to go and measure the material in the experiment. Besides you show the dissociation curve of lithium hydride measured by experiment and the excited state so you know you can do the experiment. Can you comment on the relative ease and cost of building a quantum computer 20 milli Kelvin versus actually going and measuring the quantum system directly. Okay. There were studies about that a quantum computer, despite the fact that you're this kind of quantum computers you have to call them to me at 20 milli Kelvin. They don't consume much power because they're based on superconducting technology so there is no dissipation right and bringing down to 20 milli Kelvin doesn't cost much. I'm not surprised for me but these calculations were done by other people independent from my. Yeah, you three but then you can do it at relatively modest cost so it will not use a lot of power. So they did comparison. So for full time and quantum computing the power that you would need to solve a problem classically with the quantum computer and there are order of magnitude more efficient the quantum. Yeah. Yeah. The time to solution or I'm measuring the quantum system direction. Yeah. Experimentally, I mean on a quantum computer for me the experiment is the quantum computer calculation, right. It's not the experiment using. Yeah. Sorry, just a quick comment this all these things are done automatically for you so you don't have any experimental complex here you just ask to measure Hamiltonian and he's he takes care of doing everything for you. So if you're referring to this kind of complexity of doing an experiment. No, I mean his question was about. Yeah, no, no, sure. So you can measure it. But then the same question applies why we are doing classical calculations are if you can measure. Absolutely, I mean this is way more easy. I mean, if you believe on on your equations and you can trust them, then the numbers that will extract from these calculations would say match the reality. We don't want to enter into philosophy right, but this is exactly the same. So this is instead of running this on an HPC you will run it on a quantum computer it will give you a nice. If you did a good job in setting up the right theory the right algorithm and the right way you execute your algorithm on the then you will get a good result in a time that is much less obviously then by setting up an experiment and experiments are beautiful. They always corresponded to the truth but the conditions are not always the one that you would like to know I mean if you want to study a molecule that is in your body in a lab, you have to make many, many steps in order to isolate it and I mean your environment will be completely different. In calculations we try to simulate the molecules in in a realistic environment so it's true that the experiments are beautiful and we should always look at them as reference but they also have true backs right. I mean once once you make a quantum computer you can use it to solve infinite problems and experiment you have to set up always a new one for you. Experiments are always there and it's good that we are investing a lot in doing always better and better experiments but for me calculations are important because our experiments are important and this I mean think about the same question 50 years ago when they were building the first transistors right is worth investing in these experiments and try to do this varies. The experiment right yes it was worth investing in this because now we have high performance computers right. And here is the same now that looks very complicated technologies but the hope is that we will bring them to the point that there will be routinely build easily and that everybody can have access and do the calculations. Okay, so we have a question from Giovanni. Thanks a lot. Really very nice talk. I have a question also related to say the speed and maybe the specific example with my third. And I understand we don't have quantum. It's faster than a classical computer probably but can you give orders of magnitude like for instance in this specific example for lithium hydride with respect to the classical algorithm let's say how long it takes and maybe also what are currently the bottlenecks and what is the roadmap for I mean, and then there's also question, there is would be a latency before transferring data between classical and quantum or do we have to do a lot of measurements so be how fast can we do these measurements how many you really need you have orders of magnitude maybe. Yeah, these are all very important questions. Thanks a lot. So, if you, I don't tell you how much time it takes to go. Obviously, it's huge, right, but there is no limitations in squeezing this time down to something reasonable already last year we got 100 times faster approach to that. Because the classical computers and the quantum computers are not sitting next to each other. Right. So then you have to go via the cloud and transfer data or the things that you are mentioning but now we are trying to with the runtime approach to bring the classical on top of the right so that very close essentially, even with share memory between the two right in that case, obviously can reduce all these latencies to the minimum. Okay. To do what to do. So be negligible compared to the time that you need to read out the state. Yeah, this will go below that. We do for each expectation value we do at the moment 10,000 measurements, the coherence time of of our devices in the order of 100 microseconds. So then you have to multiply 100 microseconds by 1000 10,000 and then you know how long it takes to get. Yeah, then you need time for reinitialization of your state every time I mean yeah there are some. Other questions. Very nice. My question is about the correlation length, for example in chemistry right we have an active space and you're a correlate space is quite small. I can think about materials like your correlation name is much larger or needed near critical point for example. Can you can you comment about that. For that you will have to wait. Because if we can localize the system nicely. Then we can use a few orbitals to this. I mean, if you have a very delocalized state of interest and can be described with a few delocalized orbitals you can still use the same approach, right. But if the system is larger the states are very packed you have a band that then in that case you would need many qubits in order to describe these kind of situations. There's no way out I mean an embedding scheme would not be good, but then you can use first quantization approaches instead of second quantization approaches. Welcome, or plane waves right we use a different basis set than orbital atomic based. Other questions. Maybe I have a one less. So when you show the Grover algorithm at some point it was like, and I'm asking this because I saw you mentioned my destroyer. So once I was tending a talk by him and he said that yes, you know this, this search in an argument in a database it will be very very efficient the problem is the IO that you need to read the entire. Yeah, so sure. Yeah, so I was wondering, I mean, even when there is a clear speed up with the IO kill, you know, in the case of quantum mechanics know. Okay, because quantum mechanics, if you use this occupation number representation then each state is a bit string you prepare your bit string and your sense of it's really bit of information that you have to input to your quantum computer. In the case of Grover algorithm, obviously, the way you input the data is, is critical. Right. If you, if you want to find a name in the phone book and you have to enter all the names one by one obviously at the time you go through the name that you're looking at them because you were inputting all the data and you have it already. Right, so you do even not have to search for it. So, and this is, this can be a problem when you need to input or quantum register many many data so we have ways to. To load the distribution efficiently into quantum computer, right. That can be done you can load functions, then load for instance partition functions stuff that you can can do it. You have to discretize space and like this but there are algorithms to do that but if you have to input, say, letters and these letters you have to digitalize them so your alphabet and like this, then really. You need many many qubits. Thanks. Any other questions. If there's anyone online. No. So then if not we can thank again you are not for the great talk.