Simulating complex quantum networks with time crystals

Simulating complex quantum networks with time crystals



she and possibly formation okay and in SPG assistance and after that she so she will issue one year ago and now she's as opposed to working additionally simply really moving to other competitions she's working and not only is last year is also studying in computing engine with engineering from the division and she's not so easy so you paid my what here what part of my work as Rebecca said that from Majorca and it's very special for me here is my Ireland so I'm going to talk about I chose this topic because I would bit more with what was going on here in this centre as Roberta said I'm focusing on computer architectures I'm working on a large scale but computer architectures and error correction so it's pretty far away from this so this is a side project we started exist muscle six months ago especially with Victor bastide's that is also into in Tokyo and he's in the private sector is working in entity and with other collaborators of Menai Tokyo University of Science University of Osaka so the side project is something as a separate part from what I'm used to so if you have main questions main form ends just please feel free to throw them to me I want to learn more about these type of things and it's just something we were having fun with so I wanted to show you that beside I could get some good input from you guys so now a small introduction to know where I come from does the naturalistic look informatics it's a center an interdisciplinary Center in computer science it's owned by the government the Japanese government and it is driving the center of Tokyo it is the Imperial Palace this is where the Emperor Li and this is the view from my office so I can see the Emperor house we have a lot of groups we have a lot of people working on data science machine learning complex theory a lot of computer science theory and we also have the global research centered center of quantum information and we are the only one working on formation and now we are focusing on small scale applications for small scale quantum computers quantum devices that can prove what they like for huntin supremacy so they instead of proving quantum supremacy as Google and IBM and sonar trying to do like proving that they have a quantum computer that was better than classical computers we want to prove we just to find one application that was in a small system that we can actually implement in the lab that is better that cannot be done with classical systems so this is the thing we are focusing on in one part and in the other part which is what I'm working we are focusing we are developing large-scale quantum computer architectures which are not possible to be implemented in the lab yet but we think they will in a not to part future make likely news but the theory has to be done very so we focus on error correction and languages population languages optimization so a number of qubits we're talking about less than 100 events large-scale is more because we have to allow for error correction so we need many physical qubits wound co-owners you can cubed so that's the order yeah well Google permit 100 cubits this year I think so China is also working with that Christmas numbers anyway so those are my collaborators for this work kinda moto one a modest insane she's my boss in the director of Power Research Center this is me in my chemistry years money and Bill Monroe is the director of the basic research labs identity and he is like a telecom company the biggest telecom company in Japan and they too have to be married so we've worked a lot together we join teams Victor Bastidas is a research specialist identity he's from Colombia so we are unified by our language we can speak easily tomas ally the PhD student and Tokyo University of Science and Kanaka for which I could not find a picture is she supervising and last but not least Benjamin is in France and he's not a scientist it was an associate the Institute for that ability science in Osaka and up this moving back to France is very happy about it and we another collaborator I want knowledge is fear because we are a very join team we have a lot of discussions after work to link our beer breaks so I didn't want so let's go let's start with this if you want to ask anything please III not have interruptions so I remember how where I am that going back to the end so it's feel free okay so crystal or space crystal or what we know as normal so the pistols that we are used to come as a result of breaking the translational the continuance herbicide their continuous translation symmetry of the free space and as a result we get a discrete translation periodicity so we get repeatable structures so for instance in you can find them in molecular crystals and so on and this symmetry can be further broken by for instance having atomic impurities if you have a molecular system between the lattice structure and this way we break for the symmetry and we make the the periodicity to be nurtured so that's a way of breaking symmetry because they should symmetry for a program for them and the question is could we find a parallel behavior in the dimensional of time so could we break the time translation symmetry and in order to do that we would first need some system that has some periodicity in the time dimension so before coming that before going there let's first talk about rocket theory Luca theory is the theory for video radially clear driven quantum systems so the the fundamentals of our world here is based in the study of the dynamics of general many-body quantum systems that are described through these time periodic Hamiltonians so we have a time-dependent Hamiltonian our system is governed by a time-dependent Hamiltonian but this Hamiltonian is periodic so the structure is the piece over time in the way in a way that after a movie book of periods the Hamiltonian goes that's very important because everything is based on that on that fact the way we have to post nine defendants is by driving a Hamiltonian we can write they continuously like the you signal like this type we like California slowly continues way or on the other side which is for me doing this work we apply consecutive opinion operational systems such that we apply a Hamiltonian is formed by many more small Hamiltonian that we apply consecutively so we apply H 1 H 2 H 3 and they go but wait one is to a few in such a way that our period is the sum of the times that we applied to each of these so the one person and then we go in each one is three once we have this type of systems we can apply drug in theory the this theory builds from the calculation of what's called an operator which is this operator here that is nothing more that the evolution operator within one period of time so from P equals 0 to t we let the system evolve and the operator that that creates that causes is evolution is our rocket operator and thanks to this the evolution of our system at stroboscopic times and life through Soviet times I mean only sampling the dynamics of our system at those times of multiples of T can be described by a time independent effective Hamiltonian so it's a trick to go from time-dependent Hamiltonian to an effective time independent Hamiltonian that is only valid for certain time and it's obtained from the rocket operator is the precursor of the dynamics that cause rocket operator and this is and it is very useful for implicit engineering because this hamiltonian contains effective interactions that are not present in the original system so for instance that's very useful for simulation like my team will have a spin chain that only has nearest neighbor interactions and for some reason we want to faraway sites or spins or whatever to interact they cannot touch each other because they don't have a direct interaction but with effective Hamiltonian you can effectively simulate don't grant interruptions because it generates attractive interactions that are not present in the physical system but it's illusionary because it only works at stroboscopic times so our theories based on those on this formalism and now we go back to thank crystals so Oh we'll check the know how to pronounce his name whistling was the first to propose the existence of this Panama and he thought there was a lot of debate because he was suggesting it to attain equilibrium systems and a lot of people say that no that was not possible and it was later proven that these systems would only exist in out of equilibrium so flocking systems very ethical implement systems is a is one a system where time crystal can be realized so what exactly is a crystal so thank Wriston is nothing more than a system whose dynamics but it's a super model response with respect the characteristic period of the drive is being driven and it's caused by the synchronisation of the particles of the many-body system and another important characteristic for it to be implicitly that it has to be robust it has to be robust and the responses for money response needs to be constant at evening time so it has to be if it is keep showing that response so one example is this one that was published in in nature three years ago and this is the most basic that the the type of thing crystal that most people use this was realised as pre mentally with I think it was trapped ions and it was a very important paper pen and what they do is they have these per seconds they apply H 1 H 2 H 3 H 1 infinity they have a one-dimensional spin huffing and what they do is they apply date so they initialize the system enos peanuts and they apply a global high rotation to spin it now then they put interactions in not rent interactions and they also put after that some local disorder some random data to be helped fill and then they go game applying again people's do the same because we most people so what happens at the state the initial state is recovered after two applications of the full sequence because you start with this with all spin-ups you go another sequence pin down another students spin up so you are technically breaking dynamically the translational symmetry because we are having dynamical response of two periods instead of one video so this is the most kind of trivial example of an eye crease turn and the nice think of pieces are thanks of the interactions of the resolver which apparently is a very important ingredient for integrity some rice you can add a small perturbation here he is described as epsilon to the rear pi rotation if I post that as long as it's moderate it's not very large your particles are gonna able to correct and the response is going to be constant and exactly so the time crystal things become became very flashy I'm very popular two years ago because they started proposing that we could encode quantum information in in such a way that would correct itself from the errors so everyone was very excited about that we can make one two memories lalala but no one proposed how this could be done no one would oppose or otherwise and water we just use this specific system to show our methodology in space our alpha container very limiting maybe there is yes sir yes nope rocket plate I would say that they well it's only only will be receiving a special operation but one of the people I have with me the cities and frequencies with my crystal so you this is a routine this data crystal because if it has the responses of a routine set of team but you got my 20 40 and a any arbitrary we were actually working with lithium not only not with pump which we we have some culture symmetries that that play an important role in in the way so yeah as I said is this the study of Tang crystals was very active for a while and many implementations were realized trapped ions like police beam impurities in indictment and other systems but it was always a little bit complete an intuitive picture of what was going on with thank recent we thought that it was missing and as I said before the proposed applications of quantum memories were still fake so we we're missing some like specific applications of practical one in a practical way so that's why we chose the system to apply an approach strategy we were working on before and these what what this approach do is to involve graph theory in in representing abundant system and we believe that by using these neighbor representation periodically system general than before so that's what everything is all about here so this is our approach so we start with a periodically driven system in this case it was a tutti discrete-time crystal this is the response the dynamics the fidelity of the initial scale over here and another response of the period to so we go back to the initial state every period to every two times the period because of what I mentioned before and that was quite robust against the small error on the global rotation what we do after that is calculated locate operator which is obtained from the Union hari evolution operator within one video from zero to T and by applying focus here theory with no sorry we can obtain the petty Hamiltonian by doing the matrix the log of the matrix of the target operator and by doing this we obtain the baby Hamiltonian in in form of a matrix because our Hamiltonian is the fine on a finer and discreet paper space we can represent it as a type type in the model and we can define basis that the basis set covering the whole Hilbert space and write a comment Oh in terms of liability model where our basis of population states are all the spins the spin States it's been configurations big epsilon is the is the energy of its configuration and K is a transition energy between configurations here a so we have to be an figuration to being and the number of spins we have in our changing I think at the moment we are working with an equal eight so we have eight sites so two to the eighth basis duration basis so what we do it once we had defective Hamiltonian business matrix is to generate a graph based on this percolation rule we decided to put so what this population do does is to get rid of the resonant transitions and only consider visualize the significant ones so whenever it is present in the rotation when epsilon is equal zero this is the type of graph we obtain it is a graph of diamonds so I it's a bit confusing because people normally doesn't understand I founded that something that is a little bit difficult they don't understand that note here our bases are configuration bases population states so we have to to the end note in our browser we start the basis of our hilbert space so you compare that if you ever speak I speak here these are different locations yeah yeah will be compared the the so in order to draw a link between two nodes yes we compare the energy of each of the nodes with window ever yes I start this this network news are they give money yeah so what we do with this is instead of she's always part because I think that about my daughter connections are not identical he's always in the waiting area of what otherwise was what it was so these are for any container of bathing position with interaction subject of and then if they were I mean what is the meaning in this what you say okay it's difficult to see the physical presentation of this because it's only a way to visualize the Fatiha which is not physical whatever these composite of several pieces because the second delivery system and now they the leaves that they get in this procedure cast any interpretation from the physical point of view on the system so what the way I see the way I understood it is you have you have your effective new Hamiltonian or whatever and you have an a spectrum associated so we consider that if the if the difference between two states in that spectrum to energies in that spectrum is less than a threshold then with rolling because we consider that the transition between these two states are possible yes so a link is a transition between two configurations so coming through so by doing this we were able to so we have name when the epsilon 0 we have no error we obtained dimers like all the configurations were there in climbers and the Diamonds were formed by the configurations of I and the rotated ice of Albion because there's not configuration so for instance let's say one computation here is all spin ups and it's linked negatively with a configuration with your spins up down and so on and so on with no the possible 2 to the N configurations or the hilbert space and we realized that this was happening with all the discrete 9 crystals we were calculating for epsilon equals 0 we were getting for the two T earthing crystal we were getting dimers if we were calculating the 3 T this we thank research we were getting triangles so connections between jury if we were doing for T V DC we were getting squares so we found that this was a nice way a very visualized way to see what we call the crystal in order by always getting the periodicity with the know that were being connected so no no that's good epsilon that speak up season and the other epsilon is the one that cool to see ever yeah so what we get is for epsilon equal zero for no ever we get a graph with two decoupled two dimensional space decoupled so then we thought what we do with that so we considered starving what could be seen as the melting from the tank visible with the increasing value of epsilon which is the ever in the rotation so we were calculating effective Hamiltonian for different values of ever getting the The Associated graph and see how this graph was changing as as we were changing the error and for n equal a any polite speech that the graph we get those are the two to the eighth tribulations of and their connections so when epsilon is 0 we get decoupled dimers but when we increasingly the ever we start getting clusters small clusters being hopeful and for the small values of epsilon we still get some time for the couple's but as we get bigger bigger bigger bigger everything connects into a very highly connected component so what this taught us is that it was very easy to track the robustness of the tiniest of in a visual way because as long as we still have a decouple dimer in the graph we still have time history knowing when the last diamond disappears are so maybe later the title is totally melted and we don't get the super harmonic response anymore so that was why we like to very good way to see to track the robustness of the system it was also a good way to see with this one-liner as long as the system is initialized in one of the computation that one of the library that was my second okay so it was not all the timers who revived the same amount of disorder so it's a good way to see which dimers our promoter was once and if because the Diamonds our computation you inject a use for the system you initialize the system in one of those configurations of the longer-lasting dimers your thank you sir so it was a way to know initialized and have your boss and yeah the word reason why we call her the nose is because we realized that there was some order in the way things were clustering together in the way the nose were trusting together so because we had a data scientist he realized that and we decided to find what what was the rule that was making him since flour so we soon realized that the rule was depending on the number of Kings or domain walls that were in the in the configurations of each node so by domain wall I think a job from spin up to speed now so we realize that the first to start crossing the know star clustering where the one had n over to domain was four kings so in this case he was really important one five and the last ones to cross are the ones I have zero he was so the most robust nightmare was about with Osteen's ups and all came out which is the one that in fact was use as initial experiment so we did some analytics in order to understand this a little bit better before we will plug in the system dynamics or something the system dynamics at every video T but now we wanted to do some analysis on the center you know better what happens with every B into T so effectively out that the period 2 T your system is in equilibrium because it's your your initial state is recovered that every 2 T so you always get the same initial state and rejected we know ever so it's very difficult or we were not able to obtain analytically the effective Hamiltonian analytical defective Hamiltonian for T but we were able to obtain it for 2t and no error which is that good thing as the what we realized with this room Antonius that it ensures the number of total number of domain walls and also the fire and we were able also to approximate for this same crappy Hamiltonian of 2t the approximate is not exact the Hamiltonian analytically when we had some ever and we realized that we were getting two local terms that were in fact raking the the concentration of the number of domain walls and parity symmetry so we there was a confirmation that what we had is as the error gets bigger and bigger and bigger and bigger we have our decouple subspaces that depend that are transferred by the number of things merged and the first ones to die are the more unstable ones which are the one had enough domain walls and the most robust ones are the ones that didn't happen so they made a video to complete melting pistol and how and I ordered the peritoneum a nice the basis of the comment I made using to see how we were getting hotel letters the network starts clustering with the error and at this point the crystal is said to be melted and that's with similar results and we was getting that whatever but you can see that it really has a Damien depending on the normal of the may walk there was a nice picture to see and last we propose the possible application of this system because we realized that for moderate levels of ephedrine we were getting preferential attachment mechanism of the nodes so the way the nodes start clustering for our preferential attachment that is a preparation for potential attachment mechanism that it's a property typical from some of Oban networks that causes the edges because as edges to be created between the nodes that are highly not most highly connected so the most you have what you get so the higher degree the highest degree nodes are the ones to get four four nodes connected to them and those who are property typical in CLP like structures can rely networks and mobile networks which have many applications in computer science social science so we thought that that would be a opposite a possible application would be the use of this platform for with moderate levels of error as a complex network from responding they were simulator and we showed that by calculating the degree distributions of the network one characteristic of this type of scale-free like structures and mobile networks do not tell the distributions we obtained the distribution for system and in fact when the error is moderate we get this long tail that we support no degree distribution which is members so we propose that possible so that brings me through the conclusions so we've got a simple approach and characterized not only nine crystals this was only an example under related phenomena not only melting we've been also working on transmutations are going from 39 to 49 crystal and studying it in terms of graphs but this kernel should be applied to any general forgivingly driven quantum system or strategy allows us to visualize what we call the kind crystalline order and understand the melting of the crystal as an increase in error is introduced and is understood here as temperature and we could identify the importance of the conserved quantities such as the number of Kings or number of domain walls and the breaking of symmetries in the melting of the crystal and as well we've proposed an application of a simulator as blogger to simulate scale-free like networks or Smallville members so if you take a disinfectant and you consider a business matter these are sort of like the good cases in which you can amend by the notes right your problem you're preparing a basis of an effective right yeah I see so the computation is expensive and so and you didn't buy the network well as the connection between these nodes which are not stronger than others can be negative right yes but the quality was something like the difference between the energy was smaller than so given its an editor as a week to say they seemed a sense whatever it's not a way smaller than sitting around I mean I was assuming that you came up with by interesting network if with a queen right systems are almost zero in our various one yeah you're saying that in the approximation can sometimes yes Irene is you matter if if r1 is 1.1 and you consider it as a being cut and yet one is 0.9 and has I think is quite a looker yeah I can we also put some sort of stress in there you can take that another way we also did the we represent on the networks without using that road so writing all the links and instead of doing that at the beginning of we're doing is putting weight you put weight the pages you see that you see the same structure you see the divers and you see and you see very very tiny tiny tiny edges when the errors it starts increasing so you can I think the approximation is correct for poor in that respect because of the ages were negligible they were very very very weak we saw Tony initially practicum in 2004 purple so you can literally be some utonium just that having the rule that you can evaluate this evolution yes times right okay so if you can actually terminate in evolution order a mentor yes it will be as long as you only look at the site and is it easy to initialization do something like stable transfer by the initializer for the energy in one mode of network and SP how the network is it to see such a nice a nice nice yes because for instance other in this pediment they were initializing the system with also peanuts that's one note of the network so because the networks are the basis states you can initialize in one node but you mainly should not even took a particularly many notes that reasons yeah yes these are the animals I you know I wasn't go to the basic spectrum on the basis of Christ we do find a stayfree distribution of the late sixties and it looks like that preparation transition to be that there should be regulations yeah we're working on that because if this that what we found is not enough certified that those are about scheduling hours so we need to yes apparently there's a lot of debates of this this could be fitted as a power law or a log normal distribution so and they both fit very well so we don't we still have enough they have to certify that scares me life but we are working on it with bigger systems because with any fillet never is never do still to make a question coming and they something biology politically neutral Network cities you have personal proteins called felony so different configurations of the networks and they may have essentially become political structures into seven different sequences happening instead of us percent of the speech of a set of Jhansi two sequences and the answers are connected with a point in the semester because of the same structures when the energy there is the quality is the same which is the energy said that there's and this is so the defense because states are meet and they stated that is equality of science such networks his name is on visions of innovation not even the percent of the states and probably the way states which I frankly think classes that we have techniques of some interesting cycle of the spectacles they that state of electrical system yeah I already have babies and sex of course the other thing we were very interested to use this type of approach for was to study environment in the system in that to be very useful but we think that those the way the edges are formed are very clean the questions

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