 The talk would be divided mainly in two different parts. This is not one. I will start talking a bit about the integrated quantum photonics technology that was already introduced by Philip. And then I will talk about some experiments that we have recently performed in Bristol. We basically use photonics quantum simulators to learn the counter-ynamics of other quantum states. Zelo to je grupa Vristo. Zelo je to pravda grupa, je od 100 nekaj, je zelo prijeljena profesorši John Ravity, Mark Thompson in Jeremy O'Brien. Paul Dirac je v Vristo, da je je zelo početil, nekaj ne zelo, da je to početil in v skule Fisikša in srednjič je zelo početil. In vši labi se vse zelo početil nanosensakom informaciju, ki je vse zelo početil. Zelo početil, da je zelo početil Fisikša je zelo početil in je zelo početil v mnohjih vrstevnih teknologijih in je zelo početil. V Vristo je vrstevnih teknologijih v zelo početilu vrstevnih teknologijih in je zelo početil. Protočen smo je veseli tako genetno za tko spremniti bojnih zelo početilov in včasno vbalini vsi všetnih teknologijih zelo početil, nr. bilo, da je zelo početil na mnohjí segi. Bojneva časna je v tom skalabilitarijo, ker se zelo podjedno za taj blb, če bo še držav, tako, tezovost, pa je tudi, kar se je zelo podjedno, ki se je zelo podjedno, tako, kar je, ki se je zelo podjedno, ki se je zelo podjedno, ki se je zelo podjedno, ki se je zelo podjedno. Vse je neko, da je barba, ki je to se v kažajjev. Četko se prišli, da je to bilo srečne zelo, ki je to je, da je to zelo. Srečne zelo se načal jazna, ki je to, da je to zelo. Četko se počeša, da je dobro. Četko se prišlo, da je dobro. Zelo je naprej, da se neneče v počeščji. A počeša, da je dobro. Četko se prišlo, da je dobro. A pa je v počeši, da je dobro. Zelo je prišlo. in nakelej vzela in da vzela in šešanje in objev. Zdaj ni vse tega štega vzačnega prijezavljena začnega svača. Prvest nekaj objev je kaviti prijez. Zdaj nekaj objev je kaviti prijezavljena. Zdaj nekaj objev je kaj vzela in šešanje nalega poradnja počasno. Kaj je učil objev? Con objev je kaj objev, in začili, da se mikro rings, kaj je tem začiniti, in je izgleduje fotovite nrčo ena. Zva se fotovite drugi začiniti in vlično v 30. So, če je s predpravitodi fotovite, danes smo konc눈i všeljne informecije vahlenje. Sledaj edna je postojebo septima, da naminga se fotovite nekaj. vzlušiče. Zelo, ki je zelo, to leži, ki je vzluši, in kaj pa vzluši, ki je vzluši. Do nekaj puno, tukaj tukaj bi prič nesel, da je obtikalizavite vzlušiče. Arst. Vzlušiče. Sadej na odgleda. Tukaj je zelo, bo to, pa tukaj je vzlušiče. To podeš se otvariti v zelo, da mina je opljena avaljevaj, da dovoljamo sredne vzveče, na ampido vzveče, da je ili nabunil nape. In sekundna, nisih povodnji očene pristaj dobrali in ini optionalni in optikalni vsoce. Terno sreib時ak splobuje bolo dadosan delaa in nisi obdračen delavanje in pričo zelo v rdesni... ta je meseve ganja ne stranja. in in filerij, ki je 10 minus 6, ki je še, ki je izgleda. Zelo je tukaj vzostaj v obtitali modu, in je vzostaj vzpevati dve vzpevati vzpevati, zelo je to, da se vzpevati, vzpevati, ki je vzpevati, kaj je vzpevati, kaj je vzpevati, vzpevati, kaj je vzpevati. Z-gates je rotacija v zetku z blokstvu, in jaz za vzetku z blokstvu. Zetku. Rotacija v zetku je zelo jez vzetka. Vzelič si, da, kaj je tudi, kateri je vzetkati vzetkov vzetka na vzetku, je zelo težko vzetko za vzetka. Vzelič si, da bomo mi površili. ki narediti vrši bboljeneh vodnju. Pozirila sami iz pavnjem, kot nekaj prezipnem boste začal se ponaj na Vontang, ki vzipnem vzipnem začal, tako vzipnem vzipnem začal in ide začal se nekaj prezipnem začal se na zelo v odas. Na konštah ni, ni nimi na nekaj. confessirala je dobro vično izprove o zelo vodnoj, poziraj nekaj prezipnem začal se na dnev in delem. tako je pozirala Zelo smo počično vrste in pravno všim značenih, in tega je zelo, da všeč je začelje vsakaj pomej, tačno počično vrste in pravno všim začelje, in da všeč je začelje, začelje, začelje, začelje všim, tačno vrste in pravno všim začelje, Here we brakin breeze, so we started in 2008 where we havede basically few min splitters on a photonic chip, and now we just finished the experiment when we have... Ah, sorry. The green lines is the passive components of this splitter, the yellow line is the active components of phase shifters, and the red line is the number of integrated single-photon sources. So at the moment we can perform experiments where we interact 16 single-photon sources on a single chip, had very large interferometers with 100 phase shifters and so on. in lahko je kaj pa je vzivnil in je zelo v pravdu. Ok, to je pravda, da je vse tehnologija, vse predstavijo, da bi se pravdu, da je naprej, ki je vzivnil, da je vzivnil, da je zelo vse tehnologija, da je zelo vzivnil, da je vzivnil, da je vzivnil, kako do��je kratica istinje. V druž greatly etnih kratica, ki vama načal, je dimon in karstina dimon, hem je načal sem bil sem. Č��li z vzostaj, z kratica in vkotene, načal sem bil počet. Pre to, da vzelo kratica, da vzelo kratika, in ki načal mislili, da postajne erenitega modela ko je zaredil v zelo, bil izvrata oilo,暗stani. Spolaj, načal sem bil, da postavnゲjd ničal, of the spin interactions. By the way, the model is just, I want to stress that the model is just our approximation, our description of the systems, which in general cannot be, will not be a complete description, but will represent our approximation, our knowledge about it, our description of the physics of the systems. So, the goal of a quantum metrolene is to find the set of parameters, the Hamiltonian parameters, which best describe the dynamical, the dynamical Hamiltonian evolution of the system via the associated Hamiltonian. So, the goal is to find the Hamiltonian within the set of Hamiltonian that could be generated from the system, find the best Hamiltonian to describe our quantum system. And of course the first issue is that if the system is a quantum system, then we have to implement complex quantum models in general, that might not be simulatable by classical computers. So, the question is, if we cannot simulate, if we cannot predict the behavior of complex quantum systems, how can we perform quantum metrolene learning on them? And the idea of this paper from Webe and others a couple of years ago is to develop algorithms where quantum simulators are used to perform predictions on the quantum model and use this prediction to learn the Hamiltonian of the quantum system. So, this is the algorithm itself. As you see, we have a quantum system that we want to study, we have quantum simulators that we use to make predictions. And we use a bias approach. So, the information about the Hamiltonian parameter is encoded in a probability distribution called private probability distribution. Here it was implicit in talking about a single parameter model. And the algorithm is the following. So, it's an iterative algorithm where we start... At each step we perform this operation, so we start choosing the experiments to perform in the quantum system given the probability distribution. So, it's an adaptive approach. So, we choose the experiment of what we do is we prepare the quantum system in a state psi, we evolve it for a time t, and we perform a measurement and get an output data in t. Next, what we do is basically repeat the same experiments on our quantum simulator. So, again, we prepare the quantum simulator in a state psi. So, we go to the Hamiltonian with the Hamiltonian parameter media. We perform measurements in it. And what we measure is the probability of obtaining the same outcome that was obtained from the quantum system. OK. So, let me stress that this quantity here is called the likelihood function. And it's... In general, it cannot be efficiently... It cannot be efficiently calculated on classical computers. Because it requires quantum simulation. OK. But on quantum simulators, it's possible to obtain this quantity efficiently in principle. And this likelihood function, again, is the probability of obtaining the outcome that was obtained from the quantum system if the Hamiltonian parameter omega was the true parameter of the quantum system. And it's central in bagucin approaches because it allows to update the probability distribution, the prior distribution, OK. And so, what we do is we iterate these operations so that at each time we update the probability distribution and the goal is to collapse the probability distribution to the correct Hamiltonian parameters of the system. Of course, there are a bit of details. So, in general, in Bayesian approaches, the difficulty is in estimating the normalization factor when using the bias rule. And this is... And the reason is because this is an integral over all possible Hamiltonian parameters, so we will have to estimate infinitely many likelihood functions. So, we need to run the quantum simulator infinitely time for performing one update. So, of course, this is not practical. And, likely, this is where machine learning middle basically come in help. So, we use a sequential Monte Carlo sequential Monte Carlo approximation which basically means just we approximate the probability distribution using finite sets of points in the parameter space. And, of course, if you use this approximation, the normalization function just becomes a finite discrete sum. And we need to be a bit careful to resemble the particles in the parameter space to always have a good description of our probability distribution. So, in our case, the quantum system was an electron spin in an ambient center which is basically a two-level systems between these hyperfund splitings. And the dynamics that we are interested in are basically the dynamics that happens when we excite this transition here. Ok. So, basically, there are the Rabi oscillations of the electron spin. So, the model we use to describe this evolution, of course, is the Rabi model, which is a single parameter model where the parameter that we want to learn is the Rabi 3, we call it omega 0 here. So, the experiments that we perform on the quantum systems are the following. We prepared this using this optical and magnetic pulses. We prepared the state of the electron spin in plus. We let it evolve with its Hamiltonian which is Hamiltonian that we want to learn for time t. And finally, we perform a measurement. So, we perform projective measurements again in plus on the initial state. Ok. So, this is the experiments on the quantum system. Then what we do, we would like to repeat the same experiments on our quantum simulator. We would like to have our quantum simulator to estimate this quantity here that is the lakari tube function. So, the chip that we use is this one. It basically is able to perform an arbitrary control of new unitary gates, where u is unitary and the state size is unitary. And so, the way it implements this circuit is basically the same idea that Philip was reporting before to have a super position of different unitary evolutions in quantum optics, and then leading the information of basically which one of the operations was performed. So, we can perform this scheme, we obtain this state here and it's simple to see that if we perform measurements on the control qubits, on the plus basis we obtain this quantity of measuring plus which depends on this color product where if we put psi as the initial state of the nv center and u as the unitary evolution of the nv center according to our model then simply by reverting this equality we can obtain the lakari tube function. So, this chip is able to reproduce the studies obtained on the nv center in particular to obtain the lakari tube function and that's all we need to perform our experiment. So, again, what we have is our serial and photonic quantum simulator and our quantum system that we want to study, the electron spinning nv center. So, we have these systems with very different physics, one is a photonic system, the other one is an electron spinning. And what we need to do is to interface these two systems so that we perform experiments here, we get the data ID, we perform experiments here, we get the lakari functions, we send them to the classical computer that interface them, which perform the Bayesian update the prior distribution of the Hamiltonian parameters and repeats this operation. These are the experimental results. So, you can see that we basically start from a uniform distribution so no knowledge at all about the true Hamiltonian of the quantum system and we collapse to the and we collapse to this value here which is equivalent to a Rabi frequency of 6.93 megahertz consistent with the value that you can obtain from a full field so that the most inefficient way of calculating Rabi oscillations. And so, this shows I mean, it seems to work. Let me stress that during the algorithm we can obtain both the estimate of the Hamiltonian parameters and also the error and the distribution gives us the estimate of the error that we have on the estimation. Which is it is very important these estimation middles and we will see later on why it is the case. So, the convergence the quality of the convergence if you want can be quantified in the quadratic losses which is just the mean squared error if you want in this case. And what you obtain after 50 iterations is the mean squared error of 10 to the minus 5 which which means that we really converge with a very high precision to the current values of the Rabi frequency of the M descent. So, literally, what's happening here is that we have this quantum simulator that is learning how to simulate our quantum system. Ok, so what performed in the algorithm is very interesting features. For example, this one what I report here is the covariance norm of the probability distribution during the algorithm, ok. So, what your service that what initially shrinks so the probability distribution shrinks exponentially fast which means that we are learning exponentially in an exponentially fast way the Hamiltonian parameters of the quantum system. At a certain point, it's sideways. In this case, there is a limitation in the amount of information that we can extract from the quantum system. And this limitation is given by the fact that the model that we use to learn from the quantum system is not complete. So, basically, the quantum model that we use doesn't reproduce all the physics that are in the quantum system. And of course, if the model is not complete there is a limitation in the amount of information that we can obtain out of it. And this limitation is detectable using quantum maternal learning. Is a saturation here. So, now that we know that we are able to detect the limitation of quantum models we can also exploit it to somewhat generalize quantum maternal learning to something that instead of learning just the Hamiltonian knows the model itself of the system of the quantum system. So, what we do is the following. So, we started with the model one in a very simple rabbi model. And we somewhat introduced new parameters in our models. Here we just introduced some squeezing. So, now it becomes a two parameters models where one of the parameters is the rabbi frequency and the other one is the squeezing parameter. Again we perform quantum maternal learning using this new model. And what we observe is the following. So, first of all we see that the covariance norm using this new distribution goes below the limits of the first system. And then a precise statement on which model is the best one can be obtained using bias so-called bias factor which is a standard measure in model selecting approaches which basically is just the ratio between the averages likelihoods of the two models. In this case obtained 560 which is a strong evidence that the second model is better than the first model in representing the data obtained from the quantum system. So, let me stress also that in using bias factor also contains somewhat like an outcome race also, the outcome race in the sense that is somewhat prefers systems with lower parameters so that the simplest model to describe our system is preferable using bias factors. So, in this case also it shows that the new the new operators that we have in our model are not just used to perform another fitting but are actually important to describe the actual physics of the system. So, what we are doing is basically so now we know that the model 2 is better than the model 1 in describing the system and we can update our model to describe the system from model 1 to model 2. So, we can see that we are somewhat generalizing quantum material learning to something that learns the model of the system. So, basically it means if you want that it's an argument that learns the physics of the system in another middle grade. Ok, so let me just stress and concluding that the same methods, the same bias methods can also be can also be used to enhance the performance of quantum algorithm in this particular case we study the bias and quantum estimation. So, bias and approach to quantum estimation. So, quantum estimation is of course the problem of estimating eigenstates eigenvalues of certain eigenstates of antonium. So, we have the eigenstates of unitary evolution and we want to estimate its eigenvalue. This is an algorithm which is fundamental for quantum computation. It is used for example in short algorithm in the quantum simulation of molecular energies. And we have implemented this new bias and quantum estimation approach. I'm not going to the details but they are basically the same as for the quantum maternal learning. And what we serve is first that using this new bias and approach to quantum estimation you have to speed up in estimating the phase. And secondly I think it's the main result that the noise robustness of the bias and approach is way better than the standard way of performance of quantum estimation. So, in particular this is the key algorithm, iterative algorithm the green point. And you can see that as soon as we turn on a little bit of noise in our device it completely fades at learning the at obtaining the the chord phase of the of the the chord the eigen phase. When we study if you use a bias and phase estimation you obtain very high very high precision in terms of the minus 6 gradients that are huge and in this regime where the standard approach to quantum estimation completely fades. And this is actually quite important because this problem of key that is approached to do quantum estimation was in noisy systems was well known and this is the reason why it was thought that quantum estimation could not be performed to do to do to task like quantum simulation on prefer total on quantum computers just because as soon as we have some noise it becomes unreliable but what we show here is that using these new approaches combining machine learning approaches with the phase estimation you can get an important improvement in noise resilience and the possibility of implementing quantum phase estimation for practical task on prefer total on quantum computer. Ok, so in conclusion I hope I convinced you that machine learning techniques apply to quantum systems can enhance quantum technology and find novel application so in example of this novel application I think this is the quantum internal learning we implement the quantum internal learning where we have used a silicon photonic chip so a quantum simulator on a silicon photonic chip that automatically learns the Hamiltonian of another quantum system is an electron sphere and also I didn't say before but this kind of approaches can be performed so the quantum simulator can be both analog and digital so there is no limitation to which one of the two approaches you can use I also think that you don't need a quantum error correction from this kind of algorithm because in general if you want to study quantum system this quantum system won't be error corrected so the only important thing that you want to to help is that your quantum simulators the model that we implement in a quantum simulator has to be consistent with the model that we have in a quantum system so even if you have the model in a quantum simulator has noise it is just important that it has the same noise that the quantum system contains but the more I shown that the quantum maternal learning could be a nice path to to generalize this type of algorithm to algorithms that learns quantum models instead of just quantum ametronians and this would be I think the algorithm that learns quantum physics of system ok, this I would like to conclude I would like to thank of course the people that have worked and are working on this project so the team in Bristol and from Microsoft and Chris Grenade from the University of Sydney and of course thank you for the attention