 Okay, please take your seats and so we can start in one minute Okay, so we are ready to start so Welcome to all of you for this is very special event Today is a unique day for several reasons we are here to celebrate the Dirac medal, which is one of the major events for ICTP in the year every year and it's one of the most prestigious awards in just so in theoretical physics worldwide and We have three great Scientists as winners and we have two top scientists also that will give presentations for us and But let me start with the South Park As you may all know today, Stephen Hawking passed away he's It's hard to emphasize or to ever emphasize the impact he has had in many generations of physicists I personally consider him a very good friend and colleague in Cambridge for many years This is a very sad moment for all the scientific community. I Can say that he he's a unique human being in many respects. He was Especially because There has never been anybody like him in the history of the humankind and there will never be anybody like him in the Future because the condition he had it was such in such a way that That the way he survived in a way that nobody else has survived But also the technology was ready only at the time when he needed to be able to communicate with people and so on In the future other people may find other ways to communicate and so in that sense even in that regard He was also a pioneer We know his many contributions to physics in particular to black holes to gravity and cosmology in general so his impact in science will be Remember for many many years to come I would say many generations of hundreds of years because that he's discovered is first of all from the results were painless about the Generous general existence of singularities in general relativity Then the thermodynamics of black holes the Hawking radiation the way forms of the universe and many other Contributions that he has been producing over the years even recently. He has been working very closely to Solve the problem that he created he pointed out for the whole community, which is the information Lost paradox that you can have it's more than 40 years of several generations of physicists trying to solve and He would also be remembered and The influence that he has had had to measure for his great contributions Regarding the popularization of science. He's no doubt was the main figure for promotion of science physics, but in general science Worldwide, so probably is it's not a suggestion the best known scientist in the world and So he has many legacies that For us it would be invaluable to measure the impact he has had in our lives in the community in physics in general So I will ask all of you you don't mind to stand up and join with me for a minute of silence So let me start So I see people the Rax medal is giving in honor of all the green Morris the rank is distinguished theoretical Physicist and Nobel Prize winner and a staunch friend of ICTP A CPS founder of the salon work with Iraq at Cambridge University and long admired the professor and his work Which included conceiving the relativistic wave equation predicting the existence of Antiparticles in particular the positron and He was a regular visitor to a CTP and Salam you solely recognized that one of the motivations he decided to do Particle physics was his work with Salam with the direct sorry Hmm, so the direct man recognizes scientists who have made significant contributions to theoretical physics And you have seen a list of very prestigious theoretical physicists over the past 26 26 27 years and the recipients of the 2017 direct medal award are Charles Bennett of the IBM Watson Research Center David Deutsch of Oxford University and Peter short of the Massachusetts Institute of Technology All three are being honored for their groundbreaking working applying fundamental concepts of quantum mechanics to solve the basic problems in Computation and communication Bringing together the fields of quantum mechanics computer sciences and information theory The committee this year for the this election was kind of very unique Because as you can see each of the hour days has a completely different background When I started as a chemist becoming A computer scientist at some point do a master mathematician and the third one is a theoretical physicist and the committee had a very difficult Job to make the selection not because there were these was Difficult to select because they needed extra help for the selection because the expertise of the committee is usually more into theoretical physics And this cover many areas and I can mention then the names of the members of the committee is the distinguished physicist It's a person Michael Green From Cambridge the president David Gross from Santa Barbara So Bert Halperin from Harvard or some Martin Reese also from Cambridge Professor Ashok Sen from Allahabad and HRI in India and Professor Giorgio Parisi from Rome So they were very pleased to come up with this selection, which I think is Very especially unique in the history of the of the the Iraq medal And we are all very pleased with the end result So the ceremony will begin with the general talks by Peter Zoller who's a former direct medallist and Which is a professor of the University of Innsbruck working quantum optics and also Arthur Ecker Former colleague from Cambridge and also not an Oxford a professor of quantum physics and cryptography at Oxford University And then after that we have a coffee break and we start with the awards of the ceremony Which each of each of the awardees will give a presentation so let's As a pity solar to start His presentation and please join me in welcoming Peter Okay, so let me start out by congratulating the winners of this actually last year's direct medal and I just want to I put down here the citation, you know that was given for the price It says here for pioneering work in applying fundamental concepts of quantum mechanics So solving basic problems in computation communication and therefore bringing together the fields of quantum mechanics computer science and Information and that to say that I could not more than agree With these prices to these people here that represents the whole spectrum of what defines quantum information which is by definition very you know interdisciplinary and What I would like to do in my talk here today is this that I would like to sort of you know Give you a part historical talk going back 25 years or maybe 30 years where many of these things started Or where I got sort of an influence by all of these ideas here And then sort of in the second part of my talk give you a snapshot of what we are doing at the moment So I'm somebody who's background is quantum optics So I was interested or became interested. How do we actually build? Quantum computers or quantum communication devices quantum networks and all of these things from a theoretical perspective And I will say that many of these ideas that 25 years ago, which are screams, you know in the meantime our reality and Time is progressing and all these realities were becoming also quantum technologies And might have actually quite an important impact on our you know life even in the future So I think that this is one of the prime examples of basic science in the disciplinary science that in the end is Becoming something that's even sort of you know useful from the perspective of society. I could not Refuse to sort of show very old photos. This is like political party meetings of quantum information 25 years ago And I have to say that two of the price winners are here in this photo I'm sure that Charlie Bennett actually put himself at Photoshop into this picture because you were always the one that took these pictures Or you ran on the title because okay. Yes, and Peter Shor is over here And I'm not sure exactly why these meetings happened in Torino But actually they were really sort of you know very interesting ones because people came together from all different communities and talk For quite a while and you know just this because he out to Eckhart. He's hiding a little bit here David even Jenso and you can also see that I'm over here and Ignacio Sirac is hiding over here This was you know, we were just at this meeting there for two days And this was our first presentation of this idea of I entrap quantum computing that I will afterwards tell you a little bit more about People are asking me Ignacio Why were you hiding and his answer was that I was a little bit embarrassed by being surrounded of people that were all a Little bit weird, but I guess that's sort of the definition of this of physicists. I guess at all, you know So this is Ignacio how he really looked at this stage Today's money is changed a little bit here. Of course, you know, this is from the TV channel block You know all of the names here and many famous people and also people that are in the audience and over sort of No present that is meeting. So these were historical meetings where These things were sort of starting and one thing that sort of started from my perspective is that during this year It was actually 1994 I learned about quantum computing in a way that I will summarize now and as you will see out to Eckhart has been very influential All of these things quantum simulation quantum communication with quantum optics. It's a title bit for quantum So I mean damn it, you know, it cannot go more quantum than that And you might ask yourself, you know, what's this thing in the background over here and this thing in the background here is actually an I am trapped quantum computer as we have it at the moment in this book, you know with a few cubits This is the work by Rainer Platt is an experimentalist We have a very close collaboration and I will afterwards tell you how these ideas work but even more so, you know what the perspective is behind some of that and what we are doing right now and If the number of cubits that you would like to see is a little bit more This is from a recent paper in nature by Chris Monroe who also is a company now. It's called I and Q So there's even a commercial version of Building I to have quantum computers now available. You might buy able to buy some of these devices in the future As I said, you know for me actually the moment where You learn these things and then somehow is the point where you take a different turn in science As an atomic physics and quantum of expression was a talk that was given by Otto Eckhardt He will be the second speaker after me At the iCAP conference in Boulder iCAP is a very prestigious international conference in atomic physics usually very experimentally dominated But so it wasn't highly sort of, you know, my my own conference But these iCAP had, you know, one very particular feature They always try to invite people that one or two not too many that were sort of a little bit outside It would somehow bring new things into atomic physics and stimulate the field and this is I've no idea who actually invited you Otto to this conference. It was some clever guy in the program committee must be and so But Otto came and gave a talk that I would really say, you know changed a lot of these things that were around It's really diverted. I would say The interest in atomic physics to quantum information processing and I've sort of a few old slides that They're not precisely the presentation that Otto gave but I guess very close So I stole them from you from some of your later talks And let me go through these things very quickly because they are a little bit historical slides that show you, you know What the kind of things were that were around the questions being asked what the challenges were This sort of signing out by making this remark computing is a physical process, you know Here's sort of a classical physical process. We are just moving beats around and so on and of course our present computers You know process information according to laws of classical physics There's then of course Deutsche is now over here. You know, we can see that at the fundamental nature Nature based the laws of quantum physics and at the fundamental level of that for information science must also be a quantum information science I think this is sort of the starting point You know of all of these things were happening and the question is is it at the end more powerful and we believe that the answer is Yes, the particular since you know Otto Eckhardt in his talk over here reported that the show algorithm was just invented, you know A few months I guess before this thing and this was sort of you finally had the killer application You know, that was a very true and deep motivation for pursuing these kind of things So here's this information and physics quantum process and when you look inside You have now here a set of qubits and all of these things that I will explain now here briefly But sort of why do we want to do these things and again? This is from autostalk. It says your technology to be more slow. Yeah, we would still some extent agree with that Yeah, computer science new complexity classes. We still hope for that Physics to learn more about quantum theory. This is always true by definition So it's kind of a win-win situation over here And of course what we learned from autostalk That is that the basic element instead of the classical bit that only takes on values series and one Is now the quantum bit, which is a superposition of two quantum states zero and one So we can have things like zero plus one over here represented here on the block sphere and This classical versus the quantum bit that can be in your superposition I'm not sure exactly where I got this picture here from I guess from Reiner plot if you look at it You know, there's an old woman and there's a young girl at the same time sort of symbolizing this thing of a qubit As being in a superposition state Don't take this thing too literally, of course And of course we have quantum registers and this is where entanglement comes in that We can store of course in the sense of superposition states in our quantum register Superposition of all these different numbers at the same time. This is nothing else in Entanglement and of course what we're doing with our quantum computers sort of in the laboratory trying to breed little shredding Cats that are doing these computations for us. So entanglement Superpositions of them avoiding decoherence as the coupling to the environment is sort of essentially all of these things And of course the statement well quantum memory. How big is it that if you take something like to say 300 Cubits, you know Two to the 300. This is that the mention of the Hilbert space the statement is that the Hilbert space is really huge And this is of course the point where people like fine man came in originally In his same in L presentation 86 You know making the statement well if you're a quantum mechanical person You would like to simulate something on a quantum computer Hilbert space is pretty big and it's hard to do so Why not turn things around and build a quantum device that can actually you know Simulate quantum devices as a programmable system. This was sort of the Second lack of which all of these things built and this is sort of the starting point of what we today call quantum simulators So but one of the things that out dimensionally stock was of course that the big challenge is how do we actually build the quantum computer? because at that point nobody knew and What are the challenges to do? So well if you want to build a quantum Processer first of all you need a set of cubits, you know That can be in a superposition state and tangled state and you need a way of manipulating these things that if you look inside This quantum processor that you can see that there's sort of if you read these things like a kind of a world line There will be gates that operate on these things that there's two kind of gates You know the single cubit gates that make certain rotations of your cubit on the block sphere And if you combine these things with two cubit gates like a C naught gate that's indicated over here They feel controlled cubit and the target cubit and there's some unitary operation that Condition to the state of the first one you operate on the second one if you can build these kind of gates The second one being the entangling gates that you can just put all of these things together And you principally have your functioning quantum computer provided you have a way at the end to read these things out So the historical challenge was to come up in different implementations You know with ways of implementing these kind of gates and what we talk about is of course a network model And of course what's behind all of these things is that these gates operate on two quantum mechanical superposition states What we now call quantum parallel processing sort of this was the envisioning part You know in this original idea of behind the quantum information processing Of course, you know much of the motivation then was given by the shore algorithm And there's also the Deutsch-Joseph algorithm as an example where we have a certain quantum advantage And it's always based on the fact that what the quantum computer does is it's like a big interferometer But in these you know big Hilbert space where we take different computational bars But we can let them interfere and something like the shore algorithm for example Just really uses this thing in order to get the corresponding advantage out So with this I'm sort of at the at the end of these introduction and what sort of you know We walked out and Ignacio Sirac over here and I was sitting in his talk by out to a cut and we looked at each other I said I guess we know how to actually build something like this because we were just working on trapped ions you know that were developed for atomic clocks and We had some ideas how to build these gates and let me just give you the qualitative Insight and then I would like to show you where we are right now In the laboratory in our collaboration with experimentalist where we are what was the idea? So you know people were building for atomic clocks iron traps and this is a single atom That's a single atom over here. These are I am so they repel each other and you can put them in like an very unisotrotic Harmonic oscillator so that they essentially go to an equilibrium situation if you cool them down to very low temperatures Okay, so we cool away all of the phonons. This can be done by laser cooling and You can see this as some sort of being representative as the quantum register see that it spins up and spin down And of course there will be a superposition of all of this and this is the cubits You know the quantum register that you would like to manipulate and how do we manipulate it? Well, if you would like to do single cubic rotations on the plot sphere You can do these things by just shining lasers on one of them and the distance between these ions is something like a few Micrometers so you can actually do this and an experiment But there's also phonons and you can try to quantum control the motion of these phonons And this is part of the building blocks then a sort of you know of building the corresponding set of gates That constitute the quantum computer so on the left hand side We have these quantum logic network model all of these gates and because of you know all of these elements We can build with hardware which is here on the right hand side and there's many groups out there that are pursuing these things Where are we at the moment in the lab? So if you go to experimental papers from recently, you know these experimentalists have developed a sort of a complete Gate set over here on very simple lasers that are shining all these things but just based on this original idea And what's kind of interesting is that we have now Like a little quantum compiler So if you have some unitary some quantum algorithm that you have you can decompose it You know in the different bits and pieces and we have quantum compilers that tell us, you know What sequence of laser pulses you have to shine on these ions to represent a certain quantum computation? Of course the short algorithm was one of the killer applications Sillishly and it still is but I would say the point of course is that the number of qubits and the number of Operations and here we talk not about doing error correction at the moment It's just horrendous So we have to wait a little bit except we want to factorize 21 or so where some people might even know the answer So I would say that a lot of interest has focused in recent years on quantum simulation And this is like taking a many-body system that we have an Outday a quantum many-body system like a spin system And you would like to for example Calculate on a universal quantum computer here the time evolution of a many-body system That's represented as a set of spins and let me sort of point out This is what we call digital quantum simulation. That would also be analog quantum simulation at the end Think of this like having a many-body system Which is available some spin up and spin down and you specify a certain Hamiltonian and by shining laser pulses you can hear as a function of time it uses certain time evolution Which in a strobiscopic sense mimics a certain Hamiltonian over here and to illustrate to you What I mean by that for example if you take a simple Hamiltonian of two spins like an easy model here and over the transverse field These operators will not Commute here. We can always decompose the unitary time evolution in little steps And we can trotterize them by decomposing these two parts that we have over here in these Hamiltonians And we can write them as gates So if you know how to do gates, you know entangling gates single cubic gates you can mimic the time evolution of a quantum many-body system and A few years ago, you know these were the kind of things that experimentalists were playing with They write down a Hamiltonian like a familiar say an easy Hamiltonian over here And this was comparison theory and experiment was only up to about six spins and in the meantime As I said before they can do it up to about 20 or maybe even 50 of these spins But you can also write down very exotic Hamiltonians like the one over here Which is a six-body interaction and you can just program these things on your device to mimic the corresponding time evolution So this was a few years ago More recent work and I'm not going to explain all of the details here Is this that we can take models that become sort of interesting like you know a Schlinger model of one plus one dimensional quantum Electro dynamics Of course The hope at the end is to do something more non-trivial like maybe a non-nebillion lattice gauge theory in two dimensions but this is I can tell you a little bit in the future and We can sort of take a model like this and we can map it to a certain number of qubits over here And you know this nature paper here and the people who should get the credit these days mentalists Here and Christina Moschik as the theorist You can sort of you know mimic these things and here's a comparison theory and experiments to be honest It's only a few trotter steps, but actually you see you should see these things as the starting point of Development where these devices you know are at the point where at one point we might be able to solve some Difficult problems that classical computers now might not be able to solve What's really impressive in this experiment was the fact that it was only a four qubits But 220 quantum gates were possible So these gates became so accurate in the meantime that you can do 220 gates before the whole system falls apart and that's quite an amazing development I mean given that you could write your nature paper, you know 15 years ago if you are able to do a single gate Now we talk about 220 so things are becoming sort of a certain maturity in this context There's also another way of doing quantum simulation and I just want to mention this because I will afterwards refer to this Which is what we call analog quantum simulation so far. I've talked about quantum computing about gates You know single to cubit gates and all of these things You can also try to sort of you know imitate quantum many-body dynamics By simply designing your system in such a way that you mimic directly the corresponding Hamiltonian Not this you know this digitized version that we had here before and you can also do that with ions and the way that you do It is that you can sort of shine in lasers and these lasers will distort these iron crystals And if you eliminate this thing you get effective spin-spin interactions out from this whole thing Allowing you to realize a model of this type and here's an example of you know If I take all spin downs I take a model like an XY model sigma plus sigma minus if I flip one spin over here You can see now that the spin acceleration moves here to the left and moves also here to the right And you can try to see the entanglement because if I give you one spin over here Which is at the same time moving to the right and to the left It means that if the spin up is on the right then there's a spin down on the left advice versa So you got sort of EPR type entanglement over here and that's exactly what these experiments sort of are able to demonstrate So the FDA possibility is to build all of these very exotic spin models for example And of course that's here in the case of 1d, but we can also do more generally So let me sort of try to summarize you know what after all of these years the experimental situation is on the atomic physics side On the atomic physics side. We have now systems available The ions is just one example Where we can essentially have complete control either in the sense of building little Harvard models or In building for example with Rydberg atoms Rydberg arrays over here And what these Rydberg arrays do is this that they allow one sort of to really one by one build quantum systems and Engineer their corresponding interactions So we have to hold toolbox available in the laboratory and whenever you have a favorite You know, Hamiltonian that you would like to implement There's a good chance that the experimentalist at the moment, you know will be able to do that And of course here the ion traps is one example What's really interesting is that in these atomic systems that we have you have complete control by being able to talk to the individual Cubits separately. So we have single side control. This is control on the absolute You know level of single quantum of your system. You cannot get more quantum control than something like that And of course it comes with the fact that if you take the new tools like the quantum gas microscope That these new tools allow you also then to do readouts on the level of single atoms on the level of single spins So I would say this is sort of achieving in the quantum many body system complete control over these systems And of course we in Innsbruck are quite proud because many of these ideas like these havert models the ions and also Rydbergs and so on Built on theoretical ideas that we developed You know in Innsbruck some time ago in collaboration, of course with many people And this sort of you know now takes me to the Little bit new part of my talk where you might ask yourself what do we want to do now? What do we what can we do now based on these experimental progress and I want to summarize here by simply saying that well Experimentalists have single side control in these many body systems And what's also coming in is that they can do these experiments with very high repetition rates And then of course you as a theorist start to think about these things What should we do with that? You know we have new tools available What should we do and I will give you now one example that we are working on at the moment again in collaboration with the experimentalists that we have new theoretical ideas and at the end these leads that do a whole new generation of experimental realizations and I will talk in particular about measuring Entanglement as rainy entropies and of course I have to explain to you in detail what it means But before I do that I want to sort of you know highlight one very recent development That I find is very exciting related to Rydberg atoms know in these systems I've talked about ions have mentioned the habit models a little bit and this is sort of a new toy in this context and It's a very beautiful example of kind of an bottom-up, you know engineering that one does of really being able to control single systems and qubits I guess all of you know what the tweezer is you know from biology where you focus a laser and they able to trap a particle But you can do the same thing also with atoms so you can trap atoms you can cool laser cool them down And if you do any of them which is very easy to do You know some of them will have an atom some of them not called What you do now is this that you can actually remove entropy by hand by simply finding out which ones are occupied or not By simply seeing the fluorescence So this allows you in a way sort of to you know Build a quantum system kind of bottom up and I want to show you examples The first line you know is sort of this is filled this is filled this empty empty empty You can simply rearrange all of these things here together and if you for example, you know Pay the experimentally appear you can even you know have your name written or so This context and you can do these things also In 2d so these are really sort of button up design You know you want an atom there, you know with this kind of interaction you can do these things now in the lab Okay What's really promising is the fact that the next generation will have you know About 1000 of these atoms in 1d 2d and 3d So we're getting at the point where we can maybe really make these things useful, you know in a completely new context Uh Here's an example So if I take now this system over here and I can excite atoms through rootberg states And I will not try to play the role of the atomic physicist Then you can essentially design models that you want that built, you know On basic interactions that you can engineer in this atomic system So the bottom line of the story that you should sort of take is a take home message is that From an experimental point of view these systems have been developed, you know Down to the point where I can engineer quantum many body systems And these quantum many body systems can be controlled, you know on the level of talking to these atoms or spins or qubits individually Turning on interactions that will we can really sort of design toolbox Here of of these quantum of of general quantum many body systems So given all of that and I mean this thing comes back now to theorists and you have to Provide now ideas and sort of you know come up. Can we answer now questions based on these things that are maybe interesting? And I would like to present now a few slides on ideas that we are working on at the moment that started some time ago It's purely theoretical ideas, but I will show you at the end of my talk now That you know be convinced the experimentalists go to the lab and try it they tried it and it works So I will tell you now a story that sort of, uh, you know motivated One hand by newer experimental possibilities At the end then also leads to you know experimental realization and all of these things happen just within one year And I would like to ask now a question which is very important You know whenever we talk about quantum simulation and all of these things we talk about entanglement in these systems and the question is this Can we actually measure as a protocol entanglement in systems? Uh, like for example, you know if I give you a quantum any body system and it's in a pure state Then of course, you know the for Neumann entropy will have entropy zero But if I partition it the partitioning and the entropy will then be a mixed state and this mixed state will have an entropy Which is not equal to zero. So these are the kind of things that we are asked and So if you have quantum many body system, uh, that is subdivided a and b And we would like to measure for example here, uh, define the reduced density matrix where we trace, you know Over the second part defining this row a here, for example, it's the ground state of a certain system And then we have here, you know an entropy This either as a for Neumann entropy will be interested actually in the following, you know in these Rainy entropies that are power of row to here to the power n And this if you're a quantum any body person then you will find this interesting because Might characterize here Dopological or strongly correlated quantum places. So you would like to build new tools, you know that are available In these experiments that answer interesting quantum any body questions that so far could not be answered So the question is can we actually measure things like these things over here? Well, some time ago, uh, we were interested in the story and as you will see out there I can will again now get credit for some of the earliest ideas in this context, but you thought much more in a quantum computing context Can we measure any entropies with copies and the idea is this that if I feel one copy of a system and then the second one So I've had tens of product over here But there's protocols that allow one to extract the trace of row a squared um And we wrote some theory papers over here, which uh, then marcus geiner picked up and we found certain protocols We actually these things could be implemented and here's an example where you have two copies, you know one over here and one over here These are habit models that are being implemented and I would like to tell you now a little bit What the underlying ideas are but then replace this protocol by something which is now Maybe much easier and for the experimentally is also much more friendly to implement So but I need this thing is a warm up here So the story that alto echo told us, you know, quite some time ago was the following one Well imagine that you're interested in trace of row to the power n But you have the ability to make n copies of a quantum system like this thing over here How do you get from this thing here this trace of row to the power n and the the answer was that well If you introduce an operator b n and this is essentially a swap operator Then it simply reorders all of these indices that you have over here in such a way That the trace of row to the power n, you know is acting with the swap operator or this tensor product of these density matrices here Just the expectation value of this quantity over here So if you can measure this expectation value and sort of implement this swap operator You have here the trace of row to the power n which are these rainy entropies that one is interested in Here's sort of a simple example that illustrates what we mean by that if I take two copies here Below and I introduce a swap operator. We simply interchanges these two indices as you can see over here Well, if you go through the math down here trace of, you know, the swap operator row one tensor row two Converts these things at the end to row one row two and that's exactly what we would like to do in our systems Well, it turns out that what Otto had in mind originally was the whole quantum circuit And actually these things would be pretty tough to build and you need a real quantum computer for doing these things Now we came up with ideas how you can actually avoid all of these complications at least in the case of Harvard models And this led without telling you the details. So these these papers here to these protocols that underlie these experiments That these are seminal papers by Marcus Geiner which by building two copies over here allowed one to measure now rainy entropies and In principle this exists, but let me now give you a version which is actually very cute physically But at the same time, I think it is also something that's experimentally much simpler And this is I would like to measure rainy entropies via random measurements And it works for a single system So these were theoretical ideas that are not even one year old Sort of you know published in these papers over here and I want to give in particular credit to Andreas Elven and Benoist for all of that And you can see my old collaboration with Ignacio Siarac sort of reviving over here And there's even one of the resident ICTB physicists here Marcello that participated in this work So I find these ideas behind this actually very cute and as I said also useful So let me tell you what the what the underlying ideas are What we would like to do is sort of play a replica trick You know if you have two copies of a system Then we are able to measure rainy entropies. So let's try to make a virtual copy They will ask me what do you mean by a virtual copy and I'll say that the virtual copy is exactly The replica tricks that we know so well from the work of parisi for example You know, that's usually more mathematical trick But out of this mathematical trick we make something over here, which at the end becomes a real measurement protocol And so how does it work? Well, I go back to an old paper by Stephen Fanang here and He pointed out the following thing that Suppose that you got a spin system over here And you're interested, you know in a certain subsystem that we call a over here And let's apply now over here Some ua which is some random unitary operations on the spins that we have here of interest If you make measurements after that then you can see that the probabilities that we find over here Are just given by this formula, you know row then you scramble it up by these random unitaries And then you do your measurement. This gives you the probability But now let's do the following suppose that I average now this thing over all possible unitaries And of course the answer for these probabilities will be very boring because all of them will be if I've done a very good scrambling All of them will be the same but just equal to a constant But what's very interesting is that if you look at the square of this probability and then you average Then you find that indeed here is your rainy entropy appearing So there's a way of measuring rainy entropies by looking fluctuations in the systems and with random measurements Okay And if you ask yourself why is it the case? Well, let me just write down the p squared over here And I write it now just taking the formula over here twice But I write it under one trace and now you can see it's like by having this square over here We're sort of making two virtual copies of the system here And if our you know unitary operator that we have over here belongs to a circular unitary ensemble You get like if you have gaussians for example cross correlations this u will be correlated with that here But there will also be cross correlations between these two different virtual copies And this is the one that makes the magic the magic of at the end You know allowing us sort of here to extract rainy entropies from that In quantum information, this is called two design or t design in a more general context And so you can see that if in a system like that we're able to perform random measurements There will be no possibilities for extracting interesting stuff like for example rainy entropies Is designed as an indicator or quantifier of entanglement measurements The question is of course how to realize and how many measurements in unity there is we need This is getting a more technical discussion and I've just had a few slides that should sort of indicate to you And then I'll show you some experimental results for that So the measurement protocol sort of you know at the end It will be something like this where we have time and the next for mentalist has done an interesting quantum dynamics over here Preparing a certain interest in quantum state maybe on the quantum computer or the quantum simulator And then we would like to ask can we measure trace road to this power n of a subsystem over here And the way that we do it is that the random unit there is we simply build up by using the fact that I pointed out before We have available in the laboratory in quantum many body systems There we have single site addressing so I can go in for example and make random disorder You know and it becomes a programmable random disorder that we can add to our systems And what we have at the very end is this that if I do sort of a series of mini branches You know with different disorder systems over here the question is how does this thing here converge to a circular unitary ensemble How many of these you know these order patterns that we need that we have to program in an experiment like that And this answer is answered over here by having for example an easy model You know with a certain number of lattice site and a certain disorder All of these things are experimentally available like at the Rydberg systems And you can see that if I do about 10 disorder patterns then these things have converged down here Essentially to the value that we want so it takes about you know Say in this case here 10 you know these order realizations in order to converge down To the fact that we have unit areas that approximate value at least on the second order correlation function the circular unitary ensemble All of these things are available in the in the lab and if you ask yourself how fast does it converge Then the answer is simply that the number of necessary trenches sort of also scales with the system size Which is your subsystem size that you want and this works in 1d and into these these are sort of theoretical checks that we do Over here, so in that sense we have an efficient generation of random unit areas for purity measurements So all of these things that we do here is essentially is that in our controlled quantum many body system We can sort of do chaos by design and by this chaos by design Construct and measurement protocol out of these things so that p to the power n gives us these rainy entropy to the end power And it's based on the fact that we have these correlation functions over here That we imitate with our random disorder that should approximate as well as possible the circular unitary ensembles over here Well, these results are sort of consistent with random With random gates that people are trying to do for example with super Conducting circuits at the moment But in our case I would say we get these things essentially here for for free in our systems So the measurement protocol then sort of works like this that we have here Low a sequence of random unit areas that we have to implement and then we do our standard measurement And here the quantum gas microscope comes in all of these tools are available in the laboratory And we have to repeat these things and the question is I mean how often do we have to repeat all of that And the answer is well, there's a certain scaling over here and I will not enter the details behind it What it simply means is that in these experiments if you do about 100 measurements And if you do about 100 unit areas, then this is essentially for sufficient No for the system sizes that we can do in our context What's this thing now enabling Well, maybe you would like to see something like an area law All of you I guess know that if you have a quantum system and I think a certain subsystem out of over here In a system obeying the area law It simply means that the entomies will scale proportional To the circumference of this area that you have over here And indeed if you make this system larger love This is sort of what you see ideally if you apply our protocol in this context Then you can see that with a sufficient number of these disorders we are right on top So this is would be a way of experimentally measuring area law It's never done before and I think this is now sort of constructing tools that will allow us to do so Or if you're interested in say many body localization and you would like to see that That you have entropy growth, you know Entropy growth, which is logarithmic in these systems And you would like to see that again We can use our protocol and be applied it, you know And you can see this is sort of the simulated data points And this would be a simulated measurement over here So we see the possibilities that these new tools that we have available Will allow us to do to see completely new physics in this context You know a few weeks ago I got from from christian rose in the reinerplatz group, you know this email over here They have implemented these ideas and What you can see here is results for rainy entropies in the system first of all for 10 ions And this is supposed to be a product state initially so down here. They are doing some quench dynamics You know the total system should be pure So this thing should go down to zero on the right hand side over here This is exactly what you expect, you know for these entanglement entropies to be In these quench dynamics that we have you know in quenches and They can even do it for 20 ions sort of as a result over here And I would say that we have the tools now available If you can do these things for larger system towards testing what we call this quantum supremacy And the nice thing is that these protocols that we have here, of course are available for many systems I had a few more slides on quantum networks and quantum computers, you know Maybe do networking and protocols and all of that But otherwise, so we'll give a dog afterwards that won quantum communication So it will basically skip these things, you know instead of satellite links We would like to talk about say networking of quantum computers with these things here So this would be an extra talk But I guess you sort of got the idea here of a snapshot of these developments triggered 25 years ago That led now to experimental programs That are now at the point I guess where we get New and interesting physics out and at the same time, you know We are sort of opening the door also do quantum technologies and let me conclude by congratulating the medallists here again For the pioneering work, you know, it started all by the ideas of these gentlemen And I just want to make as a last Remark here the sentence very often these days we hear essentially about quantum technologies. I think we should not forget There's a synergy and there's an intimate connection between basic science and quantum technologies If somebody tells you that building a quantum computer is just now an engineering task and nothing more These people are wrong. I would say that a lot of the basic science questions both on the hardware side But also on the conceptual side are still open And keeping these synergies in mind. I think is something which is fundamental And then you hear discussions about the flagship, you know flagship for quantum technology My personal wish would have been that it was a flagship for quantum science and quantum technologies and This is sort of the last remark because you can see that there's a long history now behind it and Time the engineers take these things over has not come yet Okay, so congratulations again to the direct medalist prize winners this year and With ease I would like to conclude my talk. Thank you very much. Peter is a great presentation Any question? We have very short time, but any origin question will be welcome Yes, a question then Thank you very much. Really. It's a perfect talk Just about the notion of interanglement Can we find another correlation type than interanglement? I was reading something about the discord But I was reading that people skeptical about the discord. So what can you say about this point? Okay, so you would like to measure discord over here People have done these things of measuring discord, but I would say that you know what we were interested in was the I would say real thing of Really this entanglement entropy is because this is the part that's sort of interesting From the many body point of view if you are connex meta person, so This goes in a different direction and I think that you're sort of measuring from a connex meta point of view the real thing, you know, it's like coca-cola and pepsi, you know Okay Yeah, thank you Very good. So let's thank the Peter again Now we like to call Arthur a current Please join me to welcome Arthur Much for inviting me here and I should say Peter solar gave me probably too much credit than I deserve because you know When it comes to this particular field at some point, it was absolutely essential To be taken seriously only taken seriously when you convince experimentalist to do something in this particular area and I thought That people like Peter solar and Ignatius iraq were ideal people who no those are Theories who are working with experimentalist and experimentalists are trusting that kind of people They wouldn't trust those wacky individuals working in this quantum information science at the very beginning So I thought, you know, all kudos goes to Peter and Ignatius for spreading the word and this kind of contaminating Experimentalists who ventured into this field anyway, but um, I should Perhaps start by congratulating the three people whom Who got the dirac prize of charlie and david and and peter And I have to say that, you know, when I was asked to give this talk I I really didn't know how to structure this talk because you know on one hand I wanted to say something about Their work at the same time, you know, there's such a vast area of Of papers that were produced by them and that would you know, it was very difficult to find a theme that would somehow Incorporate everything that they did and also, you know, I was kind of biased because david was Effectively my supervisor back in oxford and he is the person who in many ways changed my life um, so Then of course, you know through david I made I met charlie bennett and then I had also a pleasure to meet peter and that the two of the three of them in fact and and and and the colleagues created a Not only they just made quantum information science respectable thing and and debent profound subject But also they created a very peculiar atmosphere in this in this field So every sort of everyone felt invited and and and was helped and Somehow this area of quantum information science is still the area where people are, you know Very friendly very willing to work together and collaborate and that's sort of a It started from the very beginning Um, so, you know working with david, of course was was was experienced and I would have too many anecdotes to tell But I'm not going to tell them don't worry david But it's not only me, you know, but also whenever I got a phd student sooner or later they sort of Moved in the direction of david and talk to david about science You know universe everything in fact, you know my first conversation with david with nothing to do with quantum physics But it was all about carl popper And so I just realized that I found a fellow popperian in oxon. I thought yes, I like this guy, you know I'm going to work with him Um, but but you know all my students almost all my students ended up working with david so Adriano Barenco worked on the universality issues then Patrick Hayden worked on reformulating bell theorem and David Wallace worked on interpretations of probabilities now Chiara Marletta is working on constructed theory So so in sort of in a way It's kind of very easy for me to supervise students in oxford sooner or later. I said, why don't you just go and talk to david, you know Um, and you know it was already mentioned that this field exploded over the last few years Um, you know few at the very beginning was pretty much like a family business They were you know, when you look at this picture that was I don't know which year it was taken 1993 or so in in a small Place broadway in in England was just you know pretty much everyone who was working this field at the time Well, charlie may actually give you a little bit more History of predating this particular meeting but as far as I'm concerned, you know At that time were not so many people who were interested in the quantum aspects of computation And then it exploded and many many of those sort of meetings early meetings in quantum information science were David and and charlie and peter attended was in villa gualino. Why villa gualino peter asked actually there was a good reason So what happened was that A person called Giuseppe Castagnoli who was one of the directors of elsac that is based in torino I had a friend who was mario razzetti who was responsible for We're running an institute and and Giuseppe Castagnoli who Vertured into business, but he had some ideas about quantum computing. He wanted to somehow, you know sponsor something So elsac instead of giving money for yet another art exhibition in general I decided to Sponsor a series of workshops in in quantum information science And mario razzetti somehow took care of it from the logistic point of view So so I think Indirectly those people shaped this field and as you could see Those pictures were mostly I think taken by charlie who at some point cleverly Used was I don't know whether it was photoshop or whatever you used charlie But but you know the various people came at different times So and charles wanted to have them all in the picture so every now and then you can find them I got an artificial head popping up so that So that was charles charlie wanted really to have everyone included in in a in a true So all embracing spirit of the field So which by the way, I remember that you know once I was invited to give a lecture to a popular lecture in university of belfast in In So I went to northern island and I just gave a talk and I wanted to encourage everyone to Join this field no matter what sort of directions you are coming from and you know I never use a word catholic in terms of word embracing, but that you know at this sort of some consciously I said, you know come to this field. This is a very catholic field And you know imagine this So this talk is still remembered in the queens university Anyway, so I'm I When I when I when I thought what should I really be talking about? So I I started permuting my transparencies and I think I symmetrized my talk so much that this morning when I sent those slides to To the organizers of this meeting. I actually I just I don't know whether I'll have any real control over this talk So I'll just I'll just venture in the direction in one aspects of quantum computation or quantum information processing It has to do with data security, which is something that I had lots of personally interesting As it happens for some reason or the other the development of quantum information science had an impact on um on quantum on on data security to you know for one thing Peter's algorithm as you know, um affects the security of public key crypto systems And such as rsa, but not only you know For example, if you look at the cryptocurrency say bitcoins at the moment And that the two important components For the whole thing to work are digital signatures, which are based on elliptic curves Which can be broken with peter's algorithm And there's also that you know the mining process that can be seriously affected if you can do quantum search for example and so so Quantum technology or those those ideas that sort of if they were if you know They have a serious impact on on the future of information security and so the so in this sort of history of the development of Cryptography that that you can one can give a separate lecture on the how it all started how it all developed how people wanted to Design perfect cyphers and how most of the time they failed And go through the public key crypto systems ending up with sort of a quantum crypto So i'm not going to go into those details because that's probably not important But maybe i'll just say a few words about how we can take the ideas of Quantum correlations and quantum entanglement to the extreme And design a system Which comes as close as one can possibly come to perfectly secure communication and so so this So so the fact that on one hand when you have a quantum computer you destroy public key crypto systems And it's a big thing now to design possibly new generation of public key crypto system That will resist attacks from quantum computers and you know people as you probably know national security agency and some other people are Looking to replacement of rsa going in some directions possibly lattice-based cryptography But another candidate For that is quantum cryptography, of course So it's gilbrassat put it, you know what the quantum take it away But also the quantum give it a bet in the form of Quantum crypto So i'm going to talk about you know, you can do quantum cryptography in in all kind of ways Originally the idea came from steven visner than then charlie bennett and gilbrassat turned into quantum key distribution I had a slightly different approach based on quantum entanglement Which i will take not because it is my approach, but because it has it leads in some way into Something that i would consider maybe an interesting part of cryptography today devise independent cryptography and also It will take me to some speculations about randomness and probability at the end So probably Most of you know that For any two individuals to communicate In a secure way, it's probably enough if they share a private randomness. So if If the two individuals we always call them Alice and Bob Have the same random sequence of zeros and ones and it's known only to them and not to anyone else Then they can build secure communication very easily out of this And usually you know in classical world so to speak it's very easy to Test that something is random in a sense that is uniformly distributed But it's almost impossible to Make sure that those sequences are really unpredictable so that they are not known to anyone, but elis and bob So this you cannot really do In a in a non quantum scenario The ones you have those Um Random sequences you can communicate for example using a one-time path, which is one of the oldest cryptosystems that was proposed And so one way to To make sure that that that's you know, Alice and bob ended up with the strings of binary strings of zeros and ones that are Not known to anyone else Is to use the properties of quantum entanglement and And explore something that we call monogamy of entanglement or monogamy of of quantum correlations it turns out that if If you generate pairs of entangled particles that the stronger they are correlated with each other than the less they are correlated with anything else And so if you can randomly test and see that the two entities are really strongly correlated very very strongly correlated then By this rule of the monogamy of Entanglement then there's no correlation with anything else that therefore nobody outside Those two entities knows anything about it. So one way to do it is to run The bell test the you know the test that was designed to test for The local realism, but i'm not necessarily going in this direction. I just simply use it in a very instrumental way As something that you know you you have correlated particles you measure a certain figure of merit Call it the bell quantity and on this basis you can You can decide how secure is the key that you generated how good it is for cryptographic purposes So that's kind of an old story But then you know at this point you say fine So you generated the key you can assess how good it is, but you know it's It's all just you know The question of implementations all good Cryptosystems fantastic cryptosystems usually fail because of some lousy implementations. So can you then somehow Deal with the fact that Experimental implementations may not be perfect. Can you somehow counteract on this? um so um whoops so, you know, this is actually not a sort of a purely hypothetical questions because there are experimental colleagues who actually Exploits the imperfections in implementations of of quantum cryptography And that's that's a good work. So they kind of quantum hackers So I just pick up this photograph from Vady Makarov, who is probably The most known quantum hacker. So so the guy is basically very clever experimentalist who knows that Currently you cannot really implement all those things ideally and therefore he is using his tool his famous suitcase that you can see here and to crack some supposedly secure Quantum key distribution methods But you know, in fact You can You you can Deal with the situations where you have imperfections as long as you can reach the level of implementation of those bell Inequalities, which are called sort of the loophole free A test so if you reach a certain precision level um With the dections and with Setting up this experiment in a certain way then What what is interesting is that the hardware doesn't matter anymore. It's just by correlation alone You can by measuring the degree of correlations alone You can say whether something is secure or not. So in other words, there's no you know that there are no side channels to this game So that we we refer to this as a device independent Um cryptography That of course, you know in order to do this there are there are few assumptions. So one of them is that That aliz and bob the two people who want to establish this cryptographic key have access to some truly local um random number generators So so just just to to be sure so we I'm talking about a scenario where aliz and bob can then purchase devices from You know Some kind of a dodgy dealer who who comes to them and say look I'm I'm I'm I'm selling you those at some discounted price Those are good quantum devices and you can distribute cryptographic key and you you don't trust this person at all But nonetheless If you take those devices you can without knowing really what they are doing As long as they generate correlations up to a certain degree You don't care what is inside. You just simply say okay fine. I can use those correlations to generate cryptographic key So that's sort of a beauty of this result so In order to do this in order to run this test, of course, you have to also rely that you have a source of truly random numbers locally and So so the that would work as long as you can trust those random number generators that you have Add to that aliz and bob have to the disposal. Otherwise it wouldn't work very well so now the the most dangerous scenario in this case is that You have this device independent system But so you purchase this device those devices from from someone whom you don't trust But if by mistake you also purchase a random number generator from that person So that that that unfortunately wouldn't work. So somehow you have to make sure that your local randomness your local random number generators are either devices that that you can trust all those are Or you can do something about it so For example, you can just purchase a quantum random number generator and plug in but you know Those kind of random number generators that you can get today are probably Not good because you know, even if you get those random number generators, you also would like to Usually you don't produce them yourself. You would just get them. You also would like to self test Do some kind of run some kind of a simple test and see whether those random number generators are Genuinely, you know that you can trust them. So the question is can it be done? um So this brings us to sort of like A question that is basically the question that I want to address here is of this time. So given So suppose you want to get a random number generator and you are given a someone brings you a black box And says well, you know go ahead and use this random generator for cryptographic purposes Would you be able to check that this random number generator is Doing what it's supposed to be doing So what do you request from this random number generator? So you you would like the string of Zeroes and one that is generated be such that you know that that's a uniform distribution that the frequency of Zeroes and one is the same and the frequency of all pairs and subsets of zeros and ones is the same This you can test. So those are sort of the regular classical well established as for randomness But there's more if you want to use it for cryptography that you also like to test that this is a truly unpredictable That there's no copy of this device so that you know, you can easily imagine a situation where Someone would just generate two identical random number generators and one would be Start and would generate exactly the same sequence And it will pass, you know, you look at yours and it will just pass all the statistical tests for for randomness But in fact, it's not a private randomness. So this is not Unpredictable because there is a person somewhere who can actually tell exactly what kind of randomness you are getting there So so today When you buy a random number generator And you want to use it say for cryptographic purposes. Usually it comes with some kind of certificate Because you know you you yourself as the end user you just you open this box you may look inside and you don't understand the physics It's just lots of electronics and gadgets then you don't know what's going on. So how do you know you can You wouldn't know basically so you you basically Ask for a certain certifying authority to let you know Whether this device is good or not. So for example, I'm showing you one of quantum random number generators here that is Produced by a company called id quantique and usually when you get it you can get a certification from relevant Swiss agencies saying yeah, you know We look into this and we can certify that is done and produced in such and such way that it Generates randomness that is kind of a private randomness to the best of our knowledge, right? The question I'm asking now is it You know, you may not trust those authorities and if you sort of like a bit contrary and as I am you may not trust the governments You may not trust the authorities. So you would like to test yourself whether whether this device does what it's supposed to be doing And So the question is can you do it? One thing you may consider is you know computer scientists have all kind of ideas how to Amplify randomness how to take something that is less private for example and make it a bit more private So you can use private amplification for example and But we know that basically Even sort of a source of randomness that is not good most that really There are really no classical way of improving a certain class of randomly for example in computer science Popular sources of randomness that computer scientists study are called the Santa Vasirani sources and it's known that the is basically no way There's no classical randomness There's no classical processing of this randomness that would allow you to expand it or to make it more private So it's a well established result However, you know if you then construct the Random you know this can be bypassed by using again monogamous correlations So if you design a quantum random number generator in such a way that It can you can just you know get Two outputs and you can measure the correlations between those two outputs and then Basically pretty much by the same argument about the monogamy of entanglement or monogamy of certain correlations You can then sample from one of the outputs and be actually quite confident that That as long as there's a little bit of true randomness In In your input and you can amplify it and and get A device that gives you not only uniformly distributed but also completely private sources of randomness So so basically pretty much it is pretty much the case that even if you get a lousy random number generator that you don't trust with a little bit of Post-processing, you know using using this in locally you can actually amplify this randomness up to your satisfaction And then you know There are many ways of doing this. I think I just wanted I have to say that you know you can use all kinds of Belling the qualities not only the most popular chsh inequality But but but you know the story basically is At the moment if you if you if you take this path To secrecy where you use quantum entanglement you can show not only that By testing for correlations for monogamous correlations you can You can get devices that You can test for security of of the data that you obtain you can Also, you know test for The sources of the local randomness So that means that you can push the concept of privacy very much to your own domain. So it's Basically, you don't have to know Anything about the underlying physics in this device All you have to do is just to make some statistical test And no matter what is the underlying physics there You will be able at least to make statements about privacy of this data, which is actually quite remarkable but you know So this is actually the story where if you want to push cryptography or the The story of privacy to the limits. This is basically where we can Where we are today at least, you know at the very speculative way I mean, I'm not saying that this is actually implemented we We can just about implement Loophole free test of the value inequalities And what is interesting though is is that in my view, you know Even though I can I like this narrative and I can develop it into some more coherent And I can give more technical or more consistent review of this field Quite often when I do this, I feel that you know, there's a little bit of a superficial Approach to this and somehow we are cheating at some level Because it's it's you know, very nice mathematically. It's sort of simplified But if you go to the bottom of it, I don't think it is it is as simple as that There's lots of you know, lots of interesting questions or fundamental questions that you can ask for example You know those input output boxes Surely it is not the case that they are just mathematical devices and They are real physical things and if you look at them and they have to be quantum And the question is, you know, how do you operate this and how do you understand the whole notion of secrecy in terms of say the Everett Multiverse where where if you assume for example that everything is quantum Then then you have to somehow redefine the notion of secrecy in terms of relations between different universes so that you know, how How information in in one particular part of the multiverse is restricted by by people sort of But you know the access how the access is sort of restricted by different in different parts of the multiverse So that's that's certainly one thing and And then you know, there's the whole thing about the randomness the randomness always provoked lots of interesting discussions Going back to the past, you know, the question was well, is it is it really objective things? Do we have truly random phenomena in nature? And so that would be You know point of view taken by say Epicurus who would say yeah atoms, you know swerve every now and then so there's no predetermined thing and you know that was sort of Perhaps on the other side of the spectrum was democraters who was saying well, you know, it's most objective things atoms follow predetermined path And it's just what is random is due to the lack of your knowledge. Maybe You know take this discussion where you want but the question is It is still irrelevant because if if it needed is the case that Everything is quantum Then you know, what is really randomness in this sort of truly quantum universe and and Does it exist at all and and it may be the case that That it doesn't in fact, probably I would like to finish with This statement from David. I took it from the new scientist article. You gave this interview I think you really said this did you? Right, so so so, you know, it's it's just you know a valid question at this point To go in that direction and think how the whole Discussion the historical thing about randomness and probabilities Is going to end up so do we can we can we develop for example physics where we don't use the notion of randomness and Probabilities as we as we do it today, which is a very interesting question um, and I think I will I will probably stop at this point because as you can see it was sort of like A talk where I was trying probably to take this notion of security and the idea of pushing Privacy to the limits Creates generates lots of interesting questions in fundamental questions and I think What is great about this field is the fact that somehow more and more often we can address those Questions in in in a rather technical and precise language. So again, I would like to congratulate Charlie David and peter for Helping to create this fantastic field and and this needless to say this field will certainly thrive for years to come Thank you very much Thank you very much Arthur. Thank you for the very inspiring presentation any Questions Yes Reminiscence because I've taken a lot of these group conference pictures and one of the main reasons is that is that Scientists in general are like herding cats. So you announce there's a group picture and a lot of the people miss it And then you want to include them And I was I don't know if you were at that one that we had a conference in in capri And there was a beautiful swimming pool and a lot of people Failed to show up for the group picture which was around the swimming pool So I took them later on and then just cut their heads and had them floating around in the water Okay, so I'm sure there's plenty of things to to think about after all these presentations, but there is coffee outside We are running very well on time. So there is a 15 minutes for coffee and we come back at 4 15 Let's say thank Arthur again Okay, let us continue Okay, so now we will move to the next part of the of the event which is awarding the medals and and the presentations of the three hour days So I will start with Peter short So let me say some words about Peter He received his bs in mathematics in 1981 for underguided work at caltech And was a putnam fellow in 1978 He earned his phd in applied mathematics from mit in 1985 His thesis was a probabilistic analysis of bean packing algorithms Peter boosted the field of quantum computation by designing efficient quantum algorithms for factoring large numbers and computing discrete logarithms Each of which can be used to break classical encrypting schemes He does prove that a quantum computer could solve a useful hard computational problem exponentially faster than any known classical computer algorithm Sure also introduce quantum ever-correcting codes and full tolerant quantum computation Which are a scheme for copying with effects of stray interactions noise is disturbing cubits cubits Without robust Quantum ever correction large-scale quantum computation could be Stimulated by the extreme sensitivity of quantum states to noise Mistake the theory of quantum ever-correction is now a well-established branch of quantum information science And the difficult path to developing large-scale quantum computers appears open and Peter will give the presentation and the title will be I will just read it the discovery of the factoring algorithm But before that I will uh as Peter to come here to I can give you the The rack medal and everybody to give him a warm award inspiration for discovering the factoring metal and some reminiscences about You know what took place when I discovered it around 20 years ago So the outline of my talk is first I want to give the first few slides of my 1990s factoring talk somewhat updated because well They'll show you you know why factoring algorithm is such a surprise And then I want to talk say a few words about how I actually Discovered the factoring algorithm and then I want to say a few words about what happened after I discovered it So first the slide I opened my question Asking what is the difference between a computer and physics experiment? And of course back then that was like the joke. What's the difference between an elephant and an egg? It's you know, so obvious So first answer A physics experiment is a big custom built finicky piece of apparatus And the computer is a little box that fits in your briefcase So for example And you can see neither of these existed 20 years ago when I discovered the factoring algorithm Here's a computer and here's a physics experiment if you go back, you know 50 years before that Here is a computer hopes And here is a physics experiment and they start looking very much more And you can even see that the technicians were in the same uniform You're interested. This is the Berkeley particle accelerator and this is eniac First computer that von Neumann worked on So here's the second answer a physics a computer A computer answers mathematical questions and if physics experiment answers physical questions So for example, if you want to test whether all bodies fall at the same rate, you probably don't want to use computers If you want to test whether 15, you know, what you want to find 15 equals x times y You'll probably don't want to use physics experiments So this is um an ion trap computer Reiner blotz group in innsbruck austria where he actually did the experiment of Factoring 15 using an ion trap. I'm always afraid when these papers come out that some Headline is going to appear in a newspaper somewhere Physicists spend two million dollars show that 15 equals five times three It hasn't happened yet third answer Is that you don't need to build a new computer for each mathematical question you want answered and this is really a very actually it's a fundamental fact about computation and what that means is that you can mass compute produce computers Well, it's hard to mass produce physics experiments. So for example after the tebitron It's solved all the particle physics questions it was capable of People built the lhc and When the lhc solves When people discover all the physics they can at the lhc They're going to have to come up with a lot of money to build a new one or stop running practical accelerator experiments so No one would think of building more than one lhc because that would be really quite useless And then there's a lot of physics Condensed matter physics that the lhc is completely useless for Whereas if you have one big computer You can pretty much run any mathematical problem you want on it And this is related to the universality of computation. So back in the 1930s There were three people. There was Alonzo church Alan Turing and Cleaney And they all had completely different looking definitions of computation What does it mean for a function to be computable? But it turned out they gave the exact same class of computational functions What church and Turing proposed Was that this was really a very natural class of computational functions When people started building wheel computers This turns out that the definition of computational for Definition of for a function to be computable really wasn't that useful in practice. For example, if you have a Function that can be solved computed in 10 to the 30th years Well for practical purposes it might as well be uncomputable so computer scientists made this Rather um From some points of view, it's probably Braconian compromised between 30th practice where they came up with the idea that efficient means it can be computable in polynomial time In the length of its input It's not really doesn't really correspond to the practically computable functions But it's also something that computer scientists could prove the remiss about once, you know this It was realized once you have the definition of efficient as being computational time um this church quantitative churches thesis which you know was proposed Many different times in the 1960s by various computer scientists, but I think Cobham is actually the first You know what Turing machine can perform efficiently any computation that any Device can perform efficiently Well, how widely recognized was that this is really a statement about physics rather than about Computation rather than about mathematics But in fact if you have different laws of physics you might be able to compute different things efficiently as David Deutsch was one of the people to point out. I believe were several other people who pointed out Number of years before he did So a quantum computers can be built The really surprising thing is that this would imply this fault basis is not true and in fact this fault thesis has The no has um really become rooted in the consciousness of the public because One of the questions I get asked About quantum computers as well. How much faster is a quantum computer than a classical computer? And this isn't really Oh very born An answerable question because quantum computers speed up some problems By exponential amounts and they speed up other computational problems not at all so This you know the fact that this is conception is so widespread It really means that the public had absorbed quantitative churches thesis. I think we have now Got to the point where we have convinced the public That quantum computers don't Just speed up everything By one number But that was you know that took a long time Planing to do part two What led up to the discovery? So my first exposure to quantum computing was when I heard a talk by charlie bennett At the labs about quantum key distribution in here is Actually, I'm sure that charlie is going to mention this in this talk charlie and Don smolin Built the out of Basically on a tiny budget a little bottom key distribution device And this apparently is what it took For them to get physicists to take them seriously. You know, I was very intrigued by charlie bennett's result and I went around and looked at papers about quantum computing The literature and there really was not very many of them and most of them were written by david deutsch So Looking at them first neither charlie nor david deutsch convinced me that there was a Mathematical rigorous description of quantum computing Now looking back at david's papers in retrospect I was Clearly wrong about that and I also was not convinced at all that it was at all useful And I'm not going to say that I mean I was wrong about that too, but um That was um I don't think david's papers had any really useful algorithms in them For that Next thing that happened is umesh vasrani gave a talk at bell labs about the paper quantum complexity theory he wrote with ethan bernstein And this had two Really great inventions in it first it had a problem Which was a problem that no one would actually really ever want to solve and um But which quantum computers really sped up the computation of the classical computers And the other thing is it had a rigorous definition of a quantum return machine So after I saw umesh's talk I started thinking of seriously about quantum computing and whether it would be possible to speed up some Real problems with quantum computers But I didn't get anywhere with this until I saw dimes simons paper So I was on the conference program committee and dan simons and submitted the paper containing His algorithm to this conference in fact it was stock 1994 which occurred sometimes in the spring So I saw it I was very interested in And I'm very embarrassed to say that the conference program committee rejected it So I was not able to persuade the committee that this was a big enough advance over Umesh vasrani and ethan bernstein's paper which had appeared in a previous iteration of this conference So um I mean in retrospect clearly I should have been jumping up and down and yelling at them That this was the biggest mistake you could ever make But I didn't know that at the time and I was um I didn't jump up and down and they voted to reject it So what is dan simons algorithm? Well, it takes place on a hyper cube So you have a hyper cube and you color the point you color the points courtesy of the hyper two with one of two to the n minus one colors So there are exactly two colors Are two points labeled with each color And these points have to be periodic so To get from a green point to the other green point you say what you do is you take a vertical horizontal and right diagonal edge Let's try that with a different point Vertical horizontal right diagonal edge that gets us to the same color and here vertical horizontal Right diagonal the same color So now you have this hyper cube All these colors on it And what you're allowed to do is you're allowed to ask On what color is this point? And you want to find this path from one Point of a color to another point of a color now classically The only thing you can do Keep asking vertices are maybe Nearly random vertices. You can do a little bit better than random Until you get two vertices of the same color And then you're done because you know what the path looks like quantum mechanically So that takes the number of points on a hyper cube, which is You know two to the d minus one if this is d-dimensional hyper cube and one mechanically you can really solve it in d queries you ask d questions of points in superposition And you get information to tell you What the um distances So that's an exponential speed up Simon's algorithm really gave me all the hints I needed to discover Well the discrete log algorithm discrete logs as periodicity Simon's algorithm has periodicity. It's mod two discrete log algorithm uses the Fourier transform Simon's algorithm uses the Fourier transform. It's mod z2 to the n instead of The integer is mod z Or integer is mod I guess some number But you know, I knew the discrete problem would be solved by using periodicity Simon's algorithm used periodicity And I started thinking about it and eventually I figured out how to do it But what happened after that? Well first, no, how does the fact algorithm work? You can think of the factoring algorithm as a computational interferometer Maybe a computational diffraction grating. So what a diffraction grating does is it has a lot of lines on it and when you shine Colored light the angle that reflects off our The angle It makes when it goes through the diffraction It becomes on the color and that's because at certain angles all the wavelengths add up So you get constructive interference and all the other angles the wavelengths Don't add up. So you get destructive interference So the colors are separated by the angle they make coming out of the diffraction grating And the quantum Fourier transform really does the same thing for a periodic function It separates the different possible periods of the periodic function. So each different period Results and a different output to the quantum computer and then from the output you can figure out the period and if you know You know some basic number three, which is well known to Crypt analysts You can turn factoring into a problem of finding a period of a function Okay, so what happened after the discovery? Well, so the news of this spread Amazingly fast So this was I gave a talk at Bellaggs about the algorithm for discrete log on a Tuesday in April 1994 The next weekend Umesh Vasarani called me I was home in bed with a bad cold And he said I hear you can factor in a quantum computer. Tell me how it works So you can notice that the talk was about the discrete log problem Other than and I had not actually solved the factory algorithm yet Well, I don't know if you know the childhood game of telephone, but somehow The result turned to factoring telling each other about it Five days there and in those five days I had managed to solve factoring as well So I could tell Umesh how to factor And the news spread remarkably fast I kept getting you know email requests for the paper. I hadn't written it yet So there were lots of different versions of various drafts of the paper Spreading around and people kept you know kept asking me questions about outdated drafts, which I had to answer by sending them the latest draft And in May Which was only a few weeks after I discovered the factory algorithm I gave a talk at the algorithmic number 30 symposium in Cornell In June Umesh gave a talk at a Senefe Institute Um conference on quantum information In august I gave a talk at a conference in mist and I guess Arthur Eckert gave a talk in Colorado on um Atomic optics conference And in October I gave a talk at Vila Guelino in Torino and By that time the paper was actually written I presented it at the thoughts conference that november, which Dan Simon's paper also got into that conference luckily and um Red one interesting thing Is that I started describing quantum computers as quantum turning machines, which was what burnstein baserani paper talked about But you know after I discovered the result I started talking to physicists It's absolutely impossible to explain the quantum turning machine to a physicist They can't understand it because it's you know mathematics. It doesn't really correspond to any actual experiment So I started using the quantum circuit model instead Which I think was first described by david doge Out of the quantum circuit model got to be the accepted model for quantum computation Let's see. I'm probably out of time. Is that right? Am I out of time? Okay, so one objection to the factoring result was if you needed to do 10 to the ninth steps on a quantum computer Each gate had to be accurate to one part in 10 to the ninth Of course, this is completely out of the question experimentally one of the biggest um Detractors of quantum computation was A rulf landauer who worked at the same place that charlie bent and david divin chenzo and some other people working on quantum computation and I think rulf landauer Described the situation there as well. We have four people working on quantum computation and one person working against quantum computation so there are you know so So what's the argument? Well Quantum computers can't be made fault tolerant You can't use redundancy because of the node cloning theorem which says if you start with a quantum state You can't make another copy of it Can't measure to see if there's an error because the heisenberg uncertain answer means that if you measure the quantum computation inevitably disturb it and then of course if if the computation is disturbed it won't give you the right answer So the resolution of this is Though the quantum error correcting codes exist And quantum computers can be made fault tolerant by using them How do they work? Well, you arrange the codes so that likely errors are orthogonal to the encoded state And what that means is you can measure the errors Without disturbing the encoded state And once you've measured the errors You can correct the errors this There are fault tolerant threshold theorems, which Say you only need gates accurate to maybe one part and ten to the fourth This number really depends on the exact quantum fault tolerant techniques you use and it's still Still unresolved as to what this number should be if you Try to make a quantum computers in you know fault tolerant without using too much overhead So this is still Very difficult Experimentally, but in the last few years Various groups are coming really close to this number. I'm encouraging. This is my last slide. So thank you Yeah, but thank you very much Peter. So that was a very nice piece of history It's a beautiful way to see how things develop Any questions anyone comment or question? So, um, there's a question from a youtube viewer Um for peter So what are the most significant reasons to think that factoring cannot be performing polynomial time on a classical computer? Apart from the fact that many people have failed to do so um Well, actually, I don't think there are that many reasons If you talk to peter sarnac who's One of the most famous and number theorists around he thinks it's entirely possible There's a polynomial time algorithm for factoring on a quantum on a classical computer So the real only the only the I mean the only real reason we don't think there is one is Nobody has discovered yet and we think that we're smart enough that if that existed it would have been discovered Which is of course probably completely wrong Well, thank you very much peter so let's Thank peter again and then congratulations for the path Now continue with the the next Our d which is uh charles bennett Charles bennett is an intellectual leader in quantum information science Born in 1943 in new york city He earned the bs in chemistry from brian das university In 1964 and received his phd from harvard in 1970 For molecular dynamic studies computer simulations of molecular motion At harvard he worked for james watson One year as a teaching assistant about the genetic code For the next two years. He continued his research on the anisura raman at argon laboratory After joining research in 1972 He built on the work of ibm's rough land hour To show that general purpose computation can be performed biologically and thermodynamically reversible apparatus And let me add a small comment here That uh In 1982 he He proposed a reinterpretation of marchwell's demon Attributing its inability to break the second lot to the to the thermodynamic cost of this trojan rather than acquiring information with the Jill's brass art, sorry It's something something you're receiving. He may I think uh, yes, it was jid brass art from the university of montreal. I think i have to mention Bennet invented quantum cryptography where two distant parties share a secret Secret encryption key with security from evers ifs droppers guarantee by the basic quantum limitations on measurements of incompatible observables Bennet and collaborators also introduced quantum teleportation Whereby entanglement and classical signals are used to transfer quantum states He and co-workers Proved that a quantity called the voimon mon entropy is the proper measure of entanglement of four pure systems And nearly resolved in the quantification of entanglement which continues to be an active area of research So, please join me to to the Uh, jonah plus for for for charles for his director Okay, and then charles will give us a presentation building a culture of quantum information Yes, so i'm very glad to be here. I was here. I think in the 1980s with with rough land hour And it's a place where a serious physics has been done for a long time of I'm going to talk about the culture of quantum of really the culture of information science because when you when you well, like like well, I say other parts of mathematics information science was an abstraction from practical experience, but And and there the information revolution that we're still in the middle of is is from these two brilliant I mean almost brutal abstractions by Turing of the idea of a hardware independent notion of computing and by shannon the an even more brutal idea that That that there the theory of communication is best developed by ignoring the meaning of messages So they they did a tremendous Service to humanity by making these brutal abstractions, but they were a little bit too brutal. They left out a couple of essentially mathematical Properties, which they thought were just physical stuff that wasn't really necessary to think about and these were the reversibility questions of reversibility which leads look they thought were Thermodynamic questions of not really much importance and superposition Which was the idea that was left out of Turing's theory when he thought of it as a theory of computation. These were both I mean in all of the 20th century scientists were We're pretty they knew about quantum mechanics They've been around for a while and they certainly knew about thermodynamics have been around for over a century But they just thought that wasn't so important well, conventionally The information carriers are what a physicist would call a classical system their states are reliably distinguishable And you can measure it without disturbing them and then to specify the joint state of two objects Like what's in my left pocket and what's in my right pocket? It's sufficient and and and sometimes necessary to describe the states of of both each one separately But of course quantum systems don't behave that way But for most of the 20th century this was regarded as it's kind of a nuisance because People focused on the uncertainty principle causing quantum systems to behave less reliably than the larger systems And now as we've heard from from from as several of the speakers today There are positive consequences of quantum mechanics for information processing Now the first that I found out about it is by my conversation with steven weasner who was my college classmate And he had some ideas that Things you could do with information that were not covered by shannon's theory One of them was to combine two messages Into a form where if you transmitted that message you could nowadays we would say multiplex them together So that the receiver can receive either one of them, but not both Now that's impossible in shannon's theory because you just make a copy and you decrypt it one way and you decrypt it the other way So this the idea that the uncopyability of quantum information was something that could be useful The other one was an even more direct Application of that idea of the quantum banknote that cannot be copied now I guess I don't know think the euro notes have this but French and german banknotes used to have Print find print explaining how many years in prison you would spend if you would copy the Duplicated the notes. Well, anyway, some of I think this He he he did the He wrote it in a manuscript which didn't get published until 15 years later about this in 1968 actually Uh, and I think he I think he submitted it to IEEE But then didn't follow up on it because he became interested in sort of political activism and not in in physics for another decade so Uh, but I think this notes that I took on in 1970 With him maybe the first place where the notion of quantum information theory or the name even got mentioned So then I went around talking to other people including david and and and and we we've heard a lot of the rest of the history, but of course in the beginning days it's sort of Sort of obvious that these were ideas that were so strange that most people Even the people who are working on them didn't take them very seriously like peter just said Oh, well, I was only working on it part-time uh So what's the what's What's the difference between ordinary information and quantum information people often ask me this and I I've I sort of tried to say well if you if you think of A space of four dimensions then you can explain the notion of an entangled state But this doesn't work very well at a dinner party Uh, so I came up with this other metaphor That uh quantum information is like the information in a dream Uh, if you try to explain What your dream to somebody else you forget the dream and only remember what you said about it Uh, and of course this means you can lie about your dream and not get caught unless you're trying to lie to your spouse uh, but unlike dreams there's a A well-known and well understood theory of how the quantum information behaves And that's what the people in our field have been developing for the the last several decades and it's really Exciting because it's the right Oh, this is a very arrogant statement to say it's the right basis for the theory of communication and computation Well, it's a better basis than what we had before thanking Turing and Shannon for what they did we made a an important improvement which may not be important yet in a in a in a uh Technological sense, but in a conceptual sense. It's really an improvement Oh, but there so one of the constant one of the Things that came out of this is that physicists and chemists used to think of quantum Mechanics as part of their subject and when when computer scientists And and uh people that i'm not sure exactly what you'd call them like david began thinking about it Uh, they were realizing was very parallel to the theory of classical computing Just as all classical information can be reduced to bits All quantum information can be reduced to qubits and you only have to work on them one and two at a time in order to Do any computation. So this idea of a universal I think that's david's idea a universal quantum computer As as an idea that's as crisp and and fruitful as the universal classical computer that Turing showed existed so here's uh Here's an example of something you can do with a quantum computer We can take a Oops, I want the laser. Yeah Yeah, so let's take a like a vertical photon is a one and a horizontal photon at zero And I have in different colors so that I can keep track of them. This is a a conditional Not operation or a Exclusive or so the first the first qubit Controls whether the second one is left alone or whether it's flipped and then you put the first qubit in in in the Intermediate quantum state you get an intermediate state between both of them being horizontal and both of them being vertical And that's an entangled state that has no analog and classical theory So you could say It's a state of sameness of polarization even though neither photon has a polarization itself Well, that's an idea that that Would would bother a typical computer scientist of the 1980 very badly and they would say, you know You physicists don't even prove theorem. So how can I take what you're saying? Seriously But actually in an earlier time in my my life I was in in the hate ashbury district of san francisco in 1967 And there it was easy to find people who thought they were perfectly in tune with you even though they had no opinion about anything Now the The hippies believed that with enough lsd everybody could be perfectly in tune with Everybody else, but they were they were not really especially good at mathematics And now we have a quantitative theory of of quantum information We know that entanglement is monogamous And the more entangled two systems are with each other the level of christmas hippies weren't very good at monogamy either So here's how it works if we have two uh two perfectly and Well, we get two separate systems We go through a very simple quantum operation and we can get an entangled state And then suppose bob likes the fact that he's entangled with alice and he decides well Let's let's have a little bit more of this. So he entangles himself with judy Uh, well the trouble with that is that that degrades his is entangled with alice and his entangled judy So he's only classically correlated with each of them But uh, and so that means if either of them leaves town He just has a classical correlation that could be cloned or copied. You know, but it's not very interesting Uh, but and more interesting thing happens if they both stay in town And that is that he becomes entangled with the now non-trivial relationship Between the two of them that he's brought about which I would say is an appropriate punishment And so now we've developed the quantum theory of information and information processing We have to explain what we mean by classical bits and a classical bit is just one uh, Bit with one of two arbitrary or orthogonal values the classical wire is something that conducts Uh classical information reliably, but spoiled superpositions In other words, it's a quantum wire with an eavesdropper And a classical computer is just a quantum computer It's handicapped by having eavesdroppers on all its wires So instead of saying why does a quantum computer speed up computations a more uh Sensible way of asking that question is why do some computations get Horribly slowed down by having eavesdropping on on every step of the way So, uh entanglement is ubiquitous why uh almost every interaction between two systems produces entanglement Why wasn't it discovered till the 20th century? Well, because of monogamy Most systems of nature other than little ones like photons Interact so strongly with their environment is to become entangled with them almost immediately And that means that the relation between the parts of the system is degraded to mere classical correlation It's a little bit like the life of celebrities where you know, they if you read the people magazine You find out what they had for breakfast and then you read the next issue of people magazine and find out what they had for lunch And so they have no private life because they're being eavesdropped on continuously Well How does entanglement hide itself? This is sort of a quick version of decoherence theory in the version of proposed by Vojcik Zurich And it says as most systems in the kind of world we inhabit are continually eavesdropped on by multiple different eavesdroppers For example, the photons of light are bouncing off off all of us and some of them are going out the window and never coming back And they certainly don't interact with each other afterwards. So what happens is For a typical thing in our world other than this microscopic thing the environment eavesdrops on it and creates multiple redundant copies of some properties while obfuscating other properties Now this is this is I think peter already talked about this in in classical computation You can break all computations down into ands and ores and knots But you may need a lot of them to do a problem like this factoring problem And if you had a quantum computer you could do it much faster Uh And we have now a well developed theory of quantum computational complexity where we have your origin Our earlier theory of classical complexity classes like p and np And we've got the new quantum ones that sort of interpolate between them in an interesting way that's still being being explored I'm going to go back and talk a little bit about the The way ideas develop in a way that's not in a straightforward way in fact Bad ideas are sometimes extremely good for advancing scientific progress and good ideas sometimes slow it down So and one of the biggest source of bad ideas was einstein So einstein really didn't like quantum mechanics And because he's the the the the only 20th century scientists most people can name They they'd have the attitude that if einstein didn't like and it didn't understand it What hope was in it for me? Well Now we know he was wrong and I would say Although i'm not really a historian of science at all. I think his mistake was the viewing entanglement as action at a distance uh Is some kind of influence of one one particle on another And the right way is to think about it as an entangled state is that you have to give up the The common sense idea that if the whole is in a definite state then each part must be in it It's just not true And then once you once you've given up that idea it's quite possible to understand how you can have this strong correlation Which uh Which doesn't mean that either particle is influencing the other now, but Many people continue to follow this bad path and I think in the in the early 80s Nick herbert published a paper. Well, actually he he submitted it. I forgot if it was asher peris may have been the the Referee and he said this paper is Is so wrong that we must publish it immediately And it turned out to be the right thing to do because it stimulated the refutation of the idea that entanglement can be used for long distance communication uh so But there's there's uh So this gives you the idea that wrong ideas are very good for scientific progress so Conversely, and I'm going to be talking about this in the context of the reversibility in maxville's demon Uh good ideas indeed quantum mechanics itself sometimes retard scientific progress so We think about the idea between analysis between mathematics and physics between dynamical motion and uh and uh And computation uh, and this is very nicely stated by laplace in 1814 that it's that If the universe has deterministic laws if we know the present state that we know the entire future of the past Well The next problem came up in connection with the maxwell's demon who here has heard of maxwell's demon Okay, well, this was an idea of the discover really of the of the Mathematics of random motion of atoms in the gas And he said if you had somebody who was able to To look at the gas molecules You could get all the hot ones on one side and all the cold ones on the other side Or you could collect them all on one side and you could violate the second law of thermodynamics and he sort of uh as as my uh of science writer Colleague ira fruit aya fruta in japan puts it Maxwell didn't solve the problem. He just gave it as a homework assignment to physicist after that now Actually the time was right right at the beginning of the 20th century for someone to solve this problem And it was small khatski Uh, and he considered a version of the maxwell demon problem Which was just a trap door so that the molecules coming from one side Uh could push the door open, but if they hit the door from the other side They couldn't go through and eventually all the gas would collect on the right And you could run your pneumatic drill and make holes on the street with it for just using the energy of heat And then he argued that if the door was light And Enough and the spring on it was small enough that it could be pushed open by molecule It would have its own Random motion and it would work in reverse exactly as often as it worked for it. So he really solved the problem back in 1912 but uh Then quantum mechanics happened and people realized that measurement was a problematical thing Which they thought was a straightforward thing and then somehow they got timid in a way that I don't understand Which is the plus already imagined that everything in the universe including all of our thoughts are mechanistic And now but by the mid 20th century after quantum mechanics had discovered people started worrying if an intelligent being could somehow do something that a Trap door couldn't do so zillard's paper in 1929 was uh It was actually mathematically and physically correct But it got gave people a lot of wrong ideas because of its title and because it didn't Quite clearly stay in words as well as in the equations Why the demon doesn't work and finally it was felt to Ralph Landauer to say That computation could be irreversible and it was the irreversible act of erasing information that keeps the demon from working So here's my Sermon the sermon part of this history thing basic science in the future haste makes waste scientific progress. I think is mostly Incremental rather than breakthroughs There was a guy who came from another part of IBM and said he wanted to work with our group so he could make breakthrough discoveries And I I was too kind to say but I said to my colleagues We didn't take him. I said to John Smoll and I said that's like making a firm decision to be spontaneous So here we are in a situation where for years People didn't take the subject seriously and now maybe they're they're Too optimistic about what can be done right away And my favorite example of this was was about 20 years ago I met a scientist at jet propulsion laboratory And he was saying the most proud accomplishment in his life was on the voyage of project And they had Applied to make it go to all the outer planets But the word came back from washington most people don't know anything besides jupiter and saturn just go to jupiter and saturn And they said but you know the planets won't be lined up in the right way for another 200 years And the word came back from washington congress understands about two years not about 200 years just due to jupiter and saturn So he says he and all of the other scientists working on it and engineers conspired to make everything last Twice as long as it was as it really needed to And each one said well he wouldn't want this thing to fail just because this part was wasn't wasn't quite strong enough and he was working on the the thermoelectric power supply for it So of course then once it was launched they could repurpose it and said go to all of them So the the moral of the story is Sometimes you have to lie to the politicians But if if you do it in the right way and you don't do it too often that may be the best thing for science Okay, this is my summary of the subject Thank you very much Charles A lot to learn from these expressions and from this way to behave with politicians also So Comments questions. Yeah, so you spoke about entanglement So Do you think in the In the quantum computational speed up Uh Is there any clear sign that entanglement plays a role? Rather than superposition It's it's it's hard to separate the two because from the superposition principle you get entanglement but They it's it's it's a an important question because people have asked Are Is it does every Useful quantum computation that where there's some advantage over over classical Involve entanglement and I think actually peter would know the answer that better I think it does a grover's algorithm doesn't involve entangled states, right? It does oh it does grover's algorithm involves entangled states, but it's you know, it's not really It doesn't look like it entanglement states are central to grover's algorithm But I don't think I don't think it will work without entanglement Yeah Well, one argument you make is if you don't have entangled states, there's a there's a A efficient way of simulating a quantum computation. So so there yes You very happen to be very right The only problem that I wanted it's just a stupid remark But since all of you have mentioned the no cloning theorem I would like to call your attention that everybody now knows After tumul can that other people have spoken I have derived the cloning theorem two years before Two years before would the sensoric antics Oh, and and there was also before that there was two years before yeah It was even more than two years before I can send you yes. No. No, I think it was discovered in a paper that was cited by Wooters that had been written for like 10 years before but it was not noticed That has the proof in it too. That's the earlier one Yeah, yeah, so you didn't you got there almost at the right time for it to be noticed Yeah, so this is this is almost most scientific discoveries occur this way They're discovered three or four times sometimes very well And it's not a part of the discoverer that it was not noticed. It just the time wasn't right Okay, so well let's let the charles again So now it's The last medalist is a david dodge David was born in high fine israel in 1953 the son of oscar and digva dodge He attended william ellie school in high gate north london Uh Before reading natural sciences at clear college in cambridge and taking part three of the mathematical triples And he went to waltz some college oxford for his doctorate in theoretical physics And I have to say that his supervisor Was denny shama was a well-known figure here in trieste and also the supervisor of big scientists like including Stephen Hawking and martin riz and He wrote his thesis on quantum field theory in color space times There is one of the founding fathers of quantum computing He introduced the notion of a quantum Turing machine that will operate on arbitrary superposition of states that is on qubits the concept of the quantum logic gate and quantum circuit as well as the Network model of quantum computation He showed that all possible operations on a quantum computer could be generated by combining sequences of a single kind of three qubit logic gate Later benet sure and co-workers show that sequences of one qubit case and one simple type of reversible classical qubit case surface Working working along and with the richard just said from the university of cambridge Doge proposed the first quantum algorithms known as a doge and doge just algorithms Showing that quantum computation could solve certain problems faster than any known classical computer algorithm And so please Let's all congratulate David for the world So David was given a presentation called the mathematicians misconception Do you have slides? Okay, well nice to be here a couple of years ago The mathematician hannah fry made a tv documentary about aida lovelace The 19th century computer theory pioneer It was about an episode in the history of ideas Which would have been absolutely pivotal if anybody had noticed it at the time Or in other words if lovelace hadn't died young because Well from the evidence in that documentary I suspect that the first person to get The universality of computation Was actually lovelace and not her colleague charles babbage the designer of The universal computer that she was theorizing about the uh, that babbage's analytical engine never built But like many of these computers the significance was in the design and the theory rather than actual building The thing is The analytical engine would have had two kinds of universality And babbage was obsessed with one of them He Had perhaps been the first human being to understand what what one could call arithmetical universality In his previous design the difference engine could compute polynomials in one fixed point variable So, you know very limited kind of universality is universal for those but babbage realized that if he added just a few more features Conceptually very simple The machine would make the jump to universality becoming the analytical engine universal for Any arithmetic function of any number of variables of any finite precision basically What we would today call computable functions So this was arithmetical universality What lovelace understood i think was the significance of the analytical engine's ability to compute Not just any arithmetic, but anything in the world in the physical world She envisaged all sorts of applications like computer music and art and chess and and so on But this wasn't just a matter of usefulness The abilities of the analytical engine As a physical object Depend on a momentous property of the laws of physics themselves all of them namely While the analytical engine could instantiate a tiny fraction of all An infinitesimal fraction of all mathematical objects and relationships It could also apparently Apparently instantiate or simulate or emulate all possible notions Of all possible physical objects and their laws not just a tiny subset This physical universality Is an intrinsic property of the laws of physics It doesn't follow from babbage's Mathematical arithmetical universality It has nothing to do with mathematics In fact neither of the universalities follows from the other Yet it seemed that both of them were exhibited by the same machine Why? Well, whatever the reason It's in the laws of physics It would make no sense to try to prove this other than from the laws of physics This unity of the two universalities was also conjectured later Explicitly by Alan Turing in the 20th century. It's just Turing's conjecture Sometimes called the church Turing thesis. It has various names But the usual way that this conjecture is described is not That it's the unity of those two universalities Why not? Well Turing's great paper presenting his conjecture Had an application as he put it To a fundamental puzzle posed by the mathematician David Hilbert Basically what is the relationship between a true mathematical statement and a provable one Hilbert had hoped that one could define a system of proof Such that a mathematical statement was true if and only if it could be proved under that system In the 1930s mathematicians converged from several directions on the realization that that is impossible Notably, Kurt Gödel proved that there can be no method of proof that identifies all true mathematical propositions Now Turing's approach Did exactly the same in that respect But it had wider implications as we now know because of these physical objects computers The reason Turing's approach had this additional reach Was that Gödel's model of proof Was a model inside the arithmetic of the integers so nothing to do with computation He simply defined proofs as finite sequences Of symbols drawn from a finite set and all that stuff But there was no Gödel's conjecture It was Turing who realized that that notion of what proving something means isn't self evidence So he acknowledged it as a substantive conjecture The Turing conjecture The model of proof that he used was computation And the model of computation that he used was physical Strips of paper divided into squares with symbols and a finite set of discrete operations on them the universal Turing machine And when he conjectured That this machine was universal for proofs The phrase he used was that it could compute anything which would naturally be regarded as computable Naturally At the time the word computer meant a human being it wasn't one of these things A person whose job was to manipulate symbols on sheets of paper And the manipulators obeying the rules human beings are physical systems So by Anything that would naturally be regarded as computable He meant computable in nature by physical objects And by provable he meant provable by physical objects Now that conjecture Unlike Gödel's proofs Might have been false But it turned out to be true in nature or rather very nearly true As richard finally remarked They thought they understood paper But they didn't And when when I When I proved Turing's conjecture from quantum theory In 1985 it was with the slight correction that the universal machine is not Turing's paper machine Nor Babbage's brass gear machine, but the universal quantum computer But I soon found out That not everyone saw it that way The referee I also had a referee problem the the referee of the paper in which I I presented that proof Insisted that Turing's phrase would naturally be regarded as computable Referred to mathematical naturalness mathematical intuition Not nature And so what I had proved wasn't Turing's conjecture it was about physics So I asked some mathematicians what mathematical intuition is Turned out it was as much of a mystery to them as to me Some of them said it was meta mathematical intuition Fair enough, but they couldn't tell me what that was either Some kind of mathematical mysticism I think But one thing they were all adamant about nevertheless was that Turing's conjecture was about whether his mathematical model of proof matched Not the physical world, but something else Like mathematical intuition or something now Turing's basic insight was that proof is computation and computation is physical and hence proof is physical That it isn't physical seemed to me a philosophical absurdity But it was an absurdity that all the mathematicians I asked insisted on And most not all most non-mathematicians who thought about computation Didn't So I called it the mathematicians misconception the denial that proof is physical is one way of putting it By the way, the Ralph Landauer Charles Bennett's old boss had been campaigning for years with the slogan computation is physical and proof also Just to be clear Mathematical facts like Fermat's last theorem aren't physical That there is a difference between truth and provability Was the main point of all those 1930s discoveries still In my paper I had to defer to prevailing usage So I changed it to define Turing's conjecture as that vague meta mathematical idea And the referee at least agreed to let me call my result a proof of the Turing principle To distinguish it from the conjecture The principle that there can be a physical object whose motions contain those of all other objects Nevertheless Now people sometimes call that The church Turing-Deutsch principle And and that's how that's how the mathematicians conception Ended up giving me credit for something Alan Turing did And arguably Ada Lovelace did A few years later I gave a talk in oxford arguing that it makes no sense to regard Turing's conjecture in any form As something one might hope to prove one day from from logic like Fermat's last theorem But that it could be proved to be a property of quantum mechanics Sitting in the front row was Robin Gandhi who'd worked with Turing And he got a bit agitated and at the end he stood up And declared With good humor but very emphatically I've never heard such a load of rubbish in my life I tried to explain further but he seemed implacable He'd also given a talk at the same event and at the dinner afterwards he came over to where I was sitting and he said You know, I think there might have been a grain of truth in there somewhere Let's talk about it later and we did discuss it later But unfortunately we did not reach a resolution He was a mathematician He had the misconception Unfortunately in the bigger picture The mathematician's misconception has done more than just cause amusing anecdotes It expresses the idea Acknowledged or not That somewhere out there in in the world of mathematical abstractions or in some supernatural world of mathematical intuition There is the authentic official Though ineffable Now we know that Hilbert was wrong ineffable definition of proof And if some physical process that doesn't conform to that definition Turns out to allow us to know some new necessary truth That process wouldn't constitute a proof of that truth There's the misconception It so happens That a quantum computer's repertoire of Integer functions is the same as the Turing machines. They differ only in speed So some people view this as of indicating the mathematician's misconception, but no First of all, we only know that they only differ in speed from physics from quantum theory And second Quantum theory won't be the final theory of physics And even if it is you can't prove that either from mathematical intuition In reality, we only have Physical intuition never provable always incomplete always full of errors The misconception also affects thinking about information For example A quantum cryptographic device may perform a classical Information processing task that is provably impossible classically So the misconception makes people say well quantum cryptography isn't an information processing task It's just an engineering task like building a washing machine Why because Turing machines couldn't perform it They think that there's a mathematical definition of information out there somewhere independent of physics Um the same holds for probability by the way Similarly again the answer to Eugene Wigner's famous question about why Mathematics is unreasonably effective as he put it in science Is not that the math that the physical world is actually being computed on a vast computer belonging to god Or to super normal aliens Snellions because There's no reason Other than the misconception Why the snellions computer? Should itself generate that particular tiny piece of mathematics that we call computable Purely mathematical intuition will never reveal anything about proof Or computation or probability or information If you want to understand any of those things fundamentally you must start with laws of physics And in particular with what is currently the most fundamental theory in physics quantum theory It won't always be the most fundamental But its replacement Will not come from mathematics or logic Or the supernatural Okay, that's it. Thank you. Thank you very much for that provoking talk Any questions from any mathematician? I have a very simple question. What is physical? Oh Yes It's a bit like asking what is real There there seem to be various I don't know is the answer but there seem to be various levels of reality And there's the level that's only accessible by experiment And then there's the level it's to find out what laws laws the laws are and then there's the level that is independent of the laws so we know that firmats last theorem is true and if if somebody comes and and Finds that general relativity has a flaw or quantum theory has a flaw nobody will worry that maybe firmats last theorem isn't true Laws of physics are things are unlike that. They are things that could be overturned at any moment. We we we guess at them So I can't provide an answer better than that. It's it's um a deep question Yes More questions. Yes, um, I think uh, I am I am confused. Can you um Can you explain the difference between what is like mathematical like like Which is like in the top the a mathematical proof of physics proof for what I understood is the physics one I think well, you have to draw a distinction between um, what Issues of what we can know How do we know things? Their physics is at the top Uh, we we conjecture laws of physics. We test them from our physical intuition We did then develop mathematical intuitions from uh, from there we learn about mathematics Uh, however, um There are necessary truths which are independent of the laws of physics And they don't become any less necessary if we don't know them So as far as the necessity of truths goes um Mathematics is at the top its truths are necessary, but our knowledge is the other way around it comes via physics That clear Okay, we still have a couple of minutes. Let me ask a question myself I know that you are a great advocate of the Multiverse explanation for quantum mechanics, but now you also say the quantum mechanics most probably is not the last word can you Combine the two thoughts well, um, I think that the the multiverse interpretation um is on the same level of of um I mean the existence of the multiverse is is on the same level as as the existence of the dinosaurs You know it's that is not going to be proved false What what is going to be proved false is what the multiverse consists of what the what the structure of it is We don't actually have a very good idea of what the structure of it is at the moment within quantum theory. We kind of know how to Do calculations and we know that As we sit here in the lecture room there are other copies of us Watching a different lecture and listening to you know different people won the prize and so on So we know that is true but The details are going to change because quantum theories in many ways totally unsatisfactory look at quantum gravity for example But just some people do not support this multiverse Interpretation so you said they're simply wrong or this Well, they're all wrong in different ways, but yes Well, I'm going to ask david about something that I think he thinks In if Would you describe yourself as as a technological optimist? Yes Okay. Well, I used to be a technological optimist but I then Started studying a little bit cosmology and maybe thinking too hard about the kippurikin principle and it occurred to me that perhaps the universe is infinite, but the Self-destructive tendencies of of the civilization that we're in our particular bubble Suggest that it may not last more than a few thousand years And that's okay because there are infinitely infinitely many other bubbles where they do better We're just not in the good one Uh, but I think you think maybe one of those bubbles will get will get it right well enough So that it can spread its beneficent influence throughout Everywhere whatever that means. What's your reaction to that question? I think the mistake there is is when you said The the the evidence of our self-destructive nature By our you meant our civilization or our species or whatever Yes Well, it it's obvious that all that all of our past was worse than the present and the evidence that we're self-destructive is all what you might call extrapolation It's extrapolating and in order to reach that conclusion you've got to extrapolate selectively Well, okay, that's that's one argument on the other side, but it's not very convincing because it could always be made no matter how good things are If you look at the actual details We have time and again solve problems and our particular civilization Is different from all other ones in that previous ones in that respect. So you can't extrapolate from them either All civilizations basically other than our current scientific technological or whatever you call it civilization have in fact been destroyed And it's another interesting thing is that none of them were destroyed by the ways that By the ways that pessimists suggest ours will be destroyed. So there's again a disconnect. So it doesn't work How you you said the probability as well as the validity which is true and all interpretation Both are physical. How you make the distinction because one is semantics essentially the Validity and the other part is purely syntactical, which is the probability. I don't think mathematical truth is syntactical Well, in that respect, I'm a Platonist or something Yeah, I think there are mathematical objects out there only in a different sense to the sense in which there are physical objects out there but you have to distinguish between the necessary features of the things that are out there And the method by which we find out about them in the case of the mathematical truths We definitely only have access to an infinitesimal proportion of them But with physical truths we seem to have access. There's nothing that that Seems fundamentally hidden from us Very good. So let's thank David again for this wonderful talk I just to finish the event So let me remind you that this is not yet over There's a special event that was a post-ceremony public event this Afternoon starting at 6 30. So it's a few minutes from now In the Savoia Excelsior Palace Interesting And it's a moderated roundtable discussion with a hardwood nevin who is at google's director of engineering here Alessandro Curioni who's the vice president of IBM Europe and director of IBM research lab in sonic and tomas o calarco the director of the institute for complex quantum systems in the university of um and a leader figure for this The european commission quantum technology flagship project. So you're all welcome to participate It's for the general public And there is a boss that we hire That will take 50 people So all of the 50 or you who want to go It's the first come first serve And then and then we will see you there. So it will be an interesting Discussing about the importance of quantum technologies. Okay. Well, thank you very much and congratulations again to all the awardees