# 2018-03-14 - Dirac Medal Award Ceremony - Bennett, Deutsch, Shor

[Official](https://www.ictp.it/news/2018/3/2017-dirac-medal-ceremony)
[YouTube](https://www.youtube.com/watch?v=J7HeDX_7Heg)

Duration: 03:18:56

## Transcript
### Fernando Quevedo

00:10:00 - 00:10:35

Contributions regarding the popularization of science. He no doubt was the main figure for promotion of science physics, but in general science worldwide. So probably he is not an exaggeration 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 and 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.

### Dirac Medal ceremony audio artifact

00:10:54 - 00:11:56

You ...

### Fernando Quevedo

00:12:06 - 00:15:35

Thank you very much. So let me start. So ICTP Dirac's medal is given in honor of Paul Edwin Maurice Dirac, his distinguished theoretical physicist, a Nobel Prize winner and a staunch friend of ICTP. ICTP's founder Abdul Salam worked with Dirac at Cambridge University and long admired the professor and his work, which included conceiving the relativistic wave equation predicting the existence of antiparticles, particularly positron. And he was a regular visitor to ICTP and Salam usually recognized that one of the motivations he decided to do particle physics was his work with Salam, with Dirac, sorry. So the Dirac Medal 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, 27 years. And the recipients of the 2017 Dirac Medal award are Charles Bennett of the IBM Watson Research Center David Deutsch of Oxford University and Peter Shor of the Massachusetts Institute of Technology. All three are being honored for their groundbreaking work in applying fundamental concepts of quantum mechanics to solving basic problems in computation and communication. Bringing together the fields of quantum mechanics, computer sciences and information theory. The committee this year for this selection was kind of very unique because as you can see each of the awardees has a completely different background. One started as a chemist becoming a computer scientist at some point, the other one is a mathematician and the third one is a theoretical physicist. And the committee had a very difficult job to make the selection not because the awardees 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 covers many areas. And I can mention the names of the members of the committee is the very distinguished physicist. It's a Professor Michael Green from Cambridge, Professor David Gross from Santa Barbara, Professor Bert Halperin from Harvard, Professor Martin Rees also from Cambridge, Professor Ashok Sen from Allahabad in India and Professor Giorgio Parisi from Rome. So they were very pleased to come up with this selection which I think is very special and unique in the history of the Dirac Medal and we are all very pleased with the end result. So the ceremony will begin with the general talks by Peter Zoller who is a former Dirac Medalist which is a professor of the University of Innsbruck working quantum optics and also Artur Ekert, my former colleague from Cambridge and also now in 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 ceremony which each of the awardees will give a presentation. So let's ask Peter Zoller to start his presentation and please join me in welcoming Peter.

### Fernando Quevedo

00:15:36 - 00:15:38

Thank you.

### Peter Zoller

00:16:06 - 00:19:08

Okay, so let me start out by congratulating the winners of this actually last year's Dirac Medal and I just want to, I put down here the citation, you know, that was given for the prize. It says here for pioneering work in applying fundamental concepts of quantum mechanics to solving basic problems in computation, communication and in the application of quantum mechanics, in applying fundamental concepts of quantum mechanics to solving basic problems in computation, communication and therefore bringing together the fields of quantum mechanics, computer science and information. And I have to say that I could not more than agree with these prizes 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, I mean 30 years where many of these things started or where I got sort of, you know, influenced 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 whose 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 were just dreams, you know, in the meantime are a reality and as time is progressing and all these realities 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, interdisciplinary science that in the end is becoming something that's even sort of, you know, useful from the perspective of society. I could not, you know, refuse to sort of, you know, show very old photos. This is like political party meetings of quantum information 25 years ago. I have to say that two of the prize winners are here in this photo. I'm sure that Charlie Bennett actually put himself in Photoshop into this picture because you were always the one that took these pictures. Oh, you ran on the timer 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 talked for quite a while and you know, just because you see Artur Ekert, he's hiding a little bit here. David DiVincenzo and you can also see that I'm over here and Ignacio Cirac is hiding over here. This was, you know, we were just at this meeting there for two days and this was our first presentation, this idea of ion trap quantum computing that I will afterwards tell you a little bit more about.

### Peter Zoller

00:19:09 - 00:21:47

People were 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 physicists, I guess at all, you know. So this is Ignacio, how he really looked at this stage. Today's model has changed a little bit. And here's of course, you know, this is from the DiVincenzo blog, you know, all of the names here and many famous people and also people that are in the audience, you know, were sort of present at these meetings. 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, Artur Ekert has been very influential in all of these things. quantum simulation, quantum communication with quantum optics. It's a title with four 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 ion trap quantum computer as we have it at the moment in Innsbruck, you know, with a few qubits. This is the work by Rainer Blatt, he's an experimentalist, we have a very close collaboration and they will afterwards tell you how these ideas work but even also know what the perspective is behind some of that and what we are doing right now. And if the number of qubits that you would like to see is a little bit more, this is from a recent paper in Nature by Chris Monroe who also has a company now it's called IonQ so there's even a commercial version of building ion trap quantum computers now available and you might be 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 in atomic physics and quantum optics experiments was a talk that was given by Artur Ekert, 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, so it was entirely sort of, you know, my own conference but this 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 that would somehow bring new things into atomic physics and stimulate the field and this is, I have no idea who actually invited you, Artur to this conference, it was some clever guy in the program committee, must be, and so but Artur came and gave a talk that I would really say, you know, changed a lot of these things that were around.

### Peter Zoller

00:21:47 - 00:30:56

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 Artur 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're 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. They're sort of starting out by making this remark, computing is a physical process, you know, here's sort of a classical physical process, we're just moving beads around and so on and of course our present computers, you know, process information according to laws of classical physics whereas then of course, the germ is now over here, and obviously the fundamental nature is based on the laws of quantum physics and at the fundamental level therefore 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, in particular since, you know, Artur Ekert in his talk, he reported that the Shor algorithm was just invented, you know, a few months I guess before this thing and this was sort of, he 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 in physics quantum processor, 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 Artur's talk, it says here technology to beat Moore's law, yeah, I would still some extent agree with that, 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 Artur's talk that is that the basic element instead of the classical bit that only takes on value 0s and 1s is now the quantum bit which is a superposition of two quantum states 0 and 1, so we can have things like 0 plus 1 over here represented here on the Bloch sphere and this classical versus the quantum bit that can be in the superposition, I'm not sure exactly where I got this picture here from, I guess from Rainer Blatt, 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 than entanglement and of course what we are doing with our quantum computer sort of in the laboratory trying to breed little Schrödinger cats that are doing these computations for us, so entanglement superpositions of them avoiding decoherence as they're 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 two say 300 qubits you know 2 to the 300 this is the dimension of the Hilbert space the statement is that the Hilbert space is really huge and this is of course the point where people like Feynman came in originally in his seminal presentation 86 you know making the statement well if you're a quantum mechanical person and 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 leg 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 Artur mentioned in his talk was of course that the big challenge is how do we actually build a quantum computer because at that point nobody knew and what are the challenges to do so well if you want to build a quantum processor first of all you need a set of qubits you know that can be in a superposition state and tangle state and you need a way of manipulating these things that if you look inside these 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 so there's two kind of gates you know the single qubit gates that make certain rotations of your qubit on the Bloch sphere and if you combine these things with two qubit gates like a CNOT gate that's indicated over here if you control qubit and a target qubit and there's some unitary operation that conditional 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 in principle you 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 quantum mechanical superposition states what we now call quantum parallel processing sort of this was the envisioning part in this original idea behind the quantum information processing of course you know much of the motivation then was given by the Shor algorithm and there's also the Deutsch-Jozsa 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 this you know big Hilbert space where we take different computational paths but we can let them interfere and something like the Shor 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 this introduction and what sort of you know we walked out and Ignacio Cirac over here and I was sitting in his talk by Artur Ekert and we looked at this and 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 experimentalists what was the idea so you know people were building for atomic clocks ion traps and this is a single atom that's a single atom over here these are ions so they repel each other and you can put them in like a very an isotropic 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 qubit 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 qubit rotations on the Bloch 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 in 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 sort of you know of building the corresponding set of gates that constitute the quantum computer so on the left hand side we have this quantum logic network model all of these gates and we can sort 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 there 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 Shor algorithm was one of the killer applications initially 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 out there, 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.

### Peter Zoller

00:30:56 - 00:33:48

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 engineer a function of time, it uses certain time evolution which in a stroboscopic 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 Ising 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 factorize 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, entangling gates, single qubit gates you can mimic the time evolution of a quantum many body system and a few years ago we had these were the kind of things that experimentalists were playing with where you write down a Hamiltonian like a familiar say an Ising Hamiltonian over here and this comparison of 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 evolutions. 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 Schwinger model of one plus one dimensional quantum electrodynamics of course the hope at the end is to do something more non-trivial like maybe a non-Abelian 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 is experimentalists here and Christina Moshik is the theorist. You can sort of mimic these things and here is a comparison of theory and experiment to be honest it's only a few trotter steps but actually 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 might not be able to solve. What's really impressive in this experiment was the fact that there was only 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 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.

### Peter Zoller

00:33:48 - 00:40:47

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- and two-qubit 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 ion 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 excitation 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 and vice versa so you got sort of EPR type entanglement over here that's exactly what these experiments sort of are able to demonstrate so we have here possibilities 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 Hubbard 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 the whole 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 experimentalists 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 qubits separately so we have single-site control this is control on the level of single quanta 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 a new tools like the quantum gas microscope that these new tools allow you also then to do readouts on the level of single atoms or 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 Hubbard models the ions and also Rydberg's and so on built on theoretical ideas that we developed 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 this experimental progress and I want to summarize here by simply saying that well experimentalists have single-site control in these many-body systems and what's also coming in is this that they could 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 this leads to a whole new generation of experimental realizations and I will talk in particular about measuring entanglement as Renyi 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 you know these systems I've talked about ions have mentioned the Hubbard 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 in qubits I guess all of you know what the tweezers 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 cold 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 the 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 sort of this is filled this is filled this empty you can simply rearrange all of these things here together and if you for example you know pay the experimentalists a beer 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 bottom-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 here's an example so if I take now the system over here that can excite atoms to Rydberg states and I will not try to play the role of the atomic physicist then you can essentially design models that you want that build you know on basic interactions that you can engineer this atomic system so the bottom line of the story that sort of take home message is that from an experimental point of view, these systems have been developed down to the point where you can engineer quantum many-body systems. And these quantum many-body systems can be controlled on the level of talking to these atoms or spins or qubits individually, turning on interactions that we can really sort of design toolbox here of these quantum, 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 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.

### Peter Zoller

00:40:47 - 00:43:42

It started some time ago as purely theoretical ideas, but I will show you at the end of my talk now that we 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, you know, motivated one hand by new experimental possibilities, at the end then also leads to 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 like for example, you know, if I give you a quantum many-body system and it's in a pure state, then of course, you know, the von 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 that we subdivide in A and B and we would like to measure, for example, here, define the reduced density matrix but we trace it 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 is a von Neumann entropy. We'll be interested actually in the following, you know, in these Renyi entropies that are power of row to here to the power N. And this, if you are a quantum many-body person, then you will find this interesting because we might characterize here certain topological or strongly correlated quantum phases. So you would like to build new tools, you know, that are available in these experiments that answer interesting quantum many-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, we were interested in this story and as you will see, out there, we'll again now get credit for some of the earliest ideas in this context but we thought much more in a quantum computing context. Can we measure Renyi entropies with copies and the idea is this, that if I have here one copy of the system and then the second one, so I have a tensor product over here, but there's protocols that allow one to extract the trace of row A squared. And we wrote some theory papers over here, which then Markus Greiner picked up and we found certain protocols where 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 Hubbard 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 experimental, it's also much more friendly to implement so but I need this thing as a warm up here. So the story that Artur Ekert told us, you know, for quite some time ago was the following one.

### Peter Zoller

00:43:42 - 00:46:29

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 answer was that, well, if you introduce an operator Bn, and this is essentially a swap operator, then it simply reorders all of these indices that you have for V 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 Renyi entropy 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 that I introduce a swap operator which simply interchanges these two indices as you can see over here. Well, if you go through the mark 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 Artur 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 Hubbard models. And this led to, without telling you the details, so these papers here to these protocols that underlie these experiments. And these are seminal papers by Markus Greiner which by building two copies over here allowed one to measure now Renyi 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 Renyi 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 published in these papers over here and I want to give particular credit to Andreas Elben and Benoit Vermersch for all of that. And you can see my own collaboration with Ignacio Cirac sort of reviving over here. There's even one of the resident ICTP physicists here, Marcello Dalmonte, 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 underlying ideas are. What we would like to do is sort of play a replica trick. If you have two copies of a system, then we are able to measure Renyi entropies. So let's try to make a virtual copy.

### Peter Zoller

00:46:29 - 00:50:15

You will ask me what do you mean by 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. 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. So how does it work? Well, I go back to an old paper by Stephen Fanenck and he pointed out the following thing. Suppose that you got a spin system over here and you're interested 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, rho, 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, then of course the answer for these probabilities will be very boring because all of them will be, if I've done 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 Renyi entropy appearing. So there's a way of measuring Renyi entropies by looking fluctuations in the systems 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 unitary operator that we have over here belongs to a circular unitary ensemble, we 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 of at the end, allowing us sort of here to extract Renyi 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 possibilities for extracting interesting stuff like, for example, Renyi entropies as assigned as an indicator, quantifier of entanglement measurements. The question is, of course, how to realize and how many measurements and unitaries we need. This is getting a more technical discussion and I've just had a few slides that should sort of indicate you and then I'll show you some experimental results for that. So the measurement protocol, so that you know, at the end, it will be something like this where we have time and the next experimentalist has done an interesting quantum dynamics over here, preparing a certain interesting quantum state, maybe on the quantum computer or the quantum simulator. And then we would like to ask, can we measure trace row to this power n of a subsystem over here? And the way that they do it is this, the random unitaries, we simply build up by using the fact that I pointed out before, we have available in the laboratory, quantum many-body systems, that we have single-site addressing. So I can go in, for example, and make a random disorder, you know, and it becomes a programmable random disorder that we can use. 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-quenches with different disorder systems over here, the question is, how does this thing here converge to a circular unitary ensemble?

### Peter Zoller

00:50:15 - 00:53:11

How many of these disorder patterns do we need that we have to program in an experiment like that? And these answers answered over here by having, for example, an Ising model with a certain number of lattice sites and a certain disorder. All of these things are experimentally available, like in the Rydberg system. So 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, say in this case here, 10 disorder realizations in order to converge down to the fact that we have unitaries that approximate value, at least, on the second order correlation function, the circular unitary ensemble. All of these things are available in the lab. And if you ask yourself how fast does it converge, then the answer is simply that the number of necessary quenches also scales with the system size, which is your subsystem size that you want. And this works in 1D and in 2D. These are sort of theoretical checks that we do over here. So in that sense, we have an efficient generation of random unitaries for purity measurements. So all of these things that we do here 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 a measurement protocol out of these things so that P to the power N gives us this Renyi entropy, so the Nth power, and is 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 gates that people are trying to do. For example, we're superconducting circuits at the moment, but in our case, I would say we get these things essentially here for free in our systems. So the measurement protocol then sort of works like this that we have here, a sequence of random unitaries 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. 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 unitaries, then this is essentially for sufficient, 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 or that they can set the subsystem out of over here, in a system obeying the area law, it simply means that the entropy will scale proportional to the circumference of this area that you have over here. And indeed, if you make the system larger, love, this is sort of what you see ideally.

### Peter Zoller

00:53:11 - 00:56:08

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 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 you have entropy growth, entropy growth, which is logarithmic in these systems, and you would like to see that, again, we can use our protocol and we applied it, 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 see completely new physics in this context. You know, a few weeks ago, I got from Christian Rose in the Rainer Blatt Group, you know, this email over here, they have implemented these ideas, and what you can see here is results for Renyi entropy 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. 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 for these entanglement entropies to be in these quench dynamics that we have 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, where we do networking and protocols and all of that, but I'll do, I saw we'll give a talk afterwards that more on quantum communication, so we'll 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 the 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 to quantum technologies, and let me conclude by congratulating the medalists here again for their 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.

### Peter Zoller

00:56:08 - 00:56:58

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 when you hear discussions about the flagship, you know, the 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 we can see that there's a long history now behind it, and the time the engineers take these things over has not come yet. Okay, so congratulations again to the Dirac Medalists Prize winners this year, and with this I would like to conclude my talk.

### Dirac Medal ceremony audio artifact

00:56:58 - 00:57:00

[Applause]

### Fernando Quevedo

00:57:07 - 00:57:30

Thank you very much, Peter. It's a great presentation. Any question? We have very short time, but any urgent question will be welcome. Yes, a question there. Thank you.

### Audience questioner

00:57:40 - 00:58:00

Thank you very much, really. It's a perfect talk. Just about the notion of entanglement, can we find another correlation type than entanglement? I was reading something about the Discord, but I was reading that people are still sceptical about the Discord, so what can you say about this point? Okay, so you would like to measure Discord over here.

### Peter Zoller

00:58:00 - 00:58:28

Well, people have done these things of measuring Discord, but I would say that what we were interested in was the, I would say, real thing of really this entanglement, entropies, because this is the part that's sort of interesting from the many-body point of view if you are a condensed matter person. So this goes in a different direction, and I think that we are sort of measuring from a condensed matter point of view the real thing. It's like Coca-Cola and Pepsi.

### Fernando Quevedo

00:58:31 - 00:58:50

Yeah, thank you. So let's thank Peter again. Now we would like to call Artur Ekert. Please join me to welcome Artur for his presentation.

### Dirac Medal ceremony audio artifact

00:58:53 - 00:58:55

[Applause]

### Artur Ekert

00:59:17 - 01:03:00

How does it work? This goes... Oh, it's this one. Okay. Right, so thank you very much for inviting me here, and I should say Peter Zoller 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. You're only taken seriously when you convince experimentalists to do something in this particular area, and I thought that people like Peter Zoller and Ignacio Cirac were ideal people who... No, those are theorists who are working with experimentalists... 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 Ignacio for spreading the word and this kind of contaminating experimentalists who ventured into this field. Anyway, but I should perhaps start by congratulating the three people who got the Dirac prize, so Charlie and David and Peter. And I have to say that, you know, when I was asked to give this talk, 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 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. So then, of course, you know, through David I met Charlie Bennett and then I had also a pleasure to meet Peter. And the two of, the three of them, in fact, and the colleagues created a, not only they just made quantum information science a respectable thing and deep and profound subject, but also they created a very peculiar atmosphere in this field. So every sort of, everyone felt invited 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. So, you know, working with David, of course, was experience 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 talked to David about science, you know, universe, everything. In fact, you know, my first conversation with David had nothing to do with quantum physics, but it was all about Karl Popper. And so I just realized that I found a fellow Popperian in Oxford and I thought, yes, I like this guy, you know, I'm going to work with him. But, you know, all my students, almost all my students ended up working with David. So Adriano Barenco worked on universality issues. Then Patrick Hayden worked on reformulating Bell theorem and David Wallace worked on interpretations of probabilities.

### Artur Ekert

01:03:00 - 01:09:34

Now Chiara Marletta is working on constructor theory. 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. And, you know, it was already mentioned that this field exploded over the last few years. You know, at the very beginning it was pretty much like a family business. There were, you know, when you look at this picture that was, I don't know which year, it was taken in 1993 or so in a small place, Broadway in England. It 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 predating this particular meeting. But as far as I'm concerned, you know, at that time there were not so many people who were interested in the quantum aspects of computation. And then it exploded. And many of those sort of meetings, early meetings in quantum information science where David and Charlie and Peter attended was in Villa Gualino. Why Villa Gualino, Peter asked? There was a good reason. So what happened was that a person called Giuseppe Castagnoli, who was one of the directors of LSAC that is based in Torino, had a friend who was Mario Rosetti who was responsible for running an institute and Giuseppe Castagnoli who ventured into business. But he had some ideas about quantum computing. He wanted to somehow, you know, sponsor something. So LSAC, instead of giving money for yet another art exhibition in general, decided to sponsor a series of workshops in quantum information science. And Mario Rosetti somehow took care of it from the logistic point of view. So I think indirectly those people shaped this field. And as you can see, those pictures were mostly I think taken by Charlie who at some point cleverly used, I don't know whether it was Photoshop or whatever you used, but you know, various people came at different times and Charles wanted to have them all in the picture. So every now and then you can find this artificial head popping up. So that was Charles. Charlie wanted really to have everyone included in a true sort of 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. So I went to Northern Ireland 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 the word Catholic in terms of word embracing, but this sort of subconsciously I said, you know, come to this field. This is a very Catholic field. Imagine this. This talk is still remembered in the Queen's University. Anyway, so when I thought what should I really be talking about, I started permuting my transparencies and I think I symmetrized my talk so much that this morning when I sent those slides to the organizers of this meeting, I actually, I don't know whether I'll have any real control over this talk. So I'll just venture in the direction, in one aspect of quantum computation or quantum information processing has to do with data security, which is something that I had lots of personal interest in. As it happens for some reason or the other, the development of quantum information science had an impact on quantum, on data security. For one thing, Peter's algorithm, as you know, affects the security of public key crypto systems, such as RSA, but not only. For example, if you look at the cryptocurrency, say, bitcoins at the moment, 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 the mining process that can be seriously affected if you can do quantum search, for example. So quantum technology, those ideas that sort of, if they were, they have a serious impact on the future of information security. So in this sort of history of the development of cryptography, one can give a separate lecture on how it all started, how it all developed, how people wanted to design perfect ciphers 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 this, 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 systems that will resist attacks from quantum computers. And 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 as Gilles Brassard put it, you know, the quantum taketh away, but also the quantum giveth in the form of quantum crypto. So I'm going to talk about, you know, you can do quantum cryptography in all kinds of ways.

### Artur Ekert

01:09:34 - 01:14:47

Originally the idea came from Steven Wiesner, then Charlie Bennett, then Gilles Brassard turned it 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, device-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 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 at this. And usually in classical world, so to speak, it's very easy to test that something is random in the sense that it's 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 Alice and Bob. So this you cannot really do in a non-quantum scenario. Once you have those random sequences, you can communicate, for example, using the one-time pad, which is one of the oldest cryptosystems that was proposed. And so one way to make sure that 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 explore something that we call monogamy of entanglement or monogamy of quantum correlation. So it turns out that if you generate pairs of entangled particles, that the stronger they are correlated with each other, then the less they are correlated with anything else. And so 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 and therefore nobody outside those two entities knows anything about it. So one way to do it is to run the Bell test, the test that was designed to test for the local realism, but not necessarily going in this direction. I just simply use it in a very instrumental way as something that you have correlated particles, you measure a certain figure of merit, call it the Bell quantity, and on this basis 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 at this point you say fine, so you generated the key, you can assess how good it is, but it's all just the question of implementations. All good cryptosystems, fantastic cryptosystems usually fail because of some lousy implementation. So can you then somehow deal with the fact that experimental implementations may not be perfect? Can you somehow counteract on this? So, whoops. So this is actually not a purely hypothetical questions because there are experimental colleagues who actually exploit the imperfections in implementations of quantum cryptography. And that's a good work, so they're kind of quantum hackers. So I just pick up this photograph from Vadim Makarov who is probably the most known quantum hacker. So the guy is basically very clever experimentally is 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 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 test.

### Artur Ekert

01:14:47 - 01:18:57

If you reach a certain precision level with detections and with setting up this experiment in a certain way, then 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. We refer to this as a device independent cryptography. Then of course, you know, in order to do this, there are a few assumptions. So one of them is that Alice and Bob, the two people who want to establish this cryptographic key have access to some truly local random number generators. So just to be sure, so I'm talking about a scenario where Alice and Bob can then purchase devices from some kind of a dodgy dealer who comes to them and say, look, I'm selling you those at some discounted price. Those are good quantum devices and you can distribute cryptographic key and 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 that would work as long as you can trust those random number generators that you have, that Alice and Bob have to their disposal, otherwise it wouldn't work very well. So now the most dangerous scenario in this case is that you have this device-independent system, but so you purchase this device, those devices from someone whom you don't trust, but if by mistake you also purchase a random number generator from that person, so 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 you can trust or 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 those kind of random number generators that you can get today are probably not good because 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 genuine, that you can trust them. So the question is, can it be done? 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, suppose you want to get a random number generator and you are given, someone brings you a black box and says, well, 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 would like the string of zeros and one that is generated, be such that, you know, that that's a uniform distribution, that the frequency of zeros and one is the same, and the frequency of all pairs and subsets of zeros and ones is the same.

### Artur Ekert

01:18:57 - 01:23:36

This you can test. So those are sort of the regular classical well-established tests for randomness. But there's more. If you want to use it for cryptography, then you also like to test that this is truly unpredictable, that there's no copy of this device, so that you can easily imagine a situation where someone would just generate two identical random number generators and one would be stored 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 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 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 yourself, the end user, you open this box, you may look inside and you don't understand the physics, there's lots of electronics and gadgets there and you don't know what's going on. So how do you know? You wouldn't know basically, so you basically ask for a certifying authority to let you know whether this device is good or not. 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 it's 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 contrarian as I am, you may not trust the government, you may not trust the authorities, so you would like to test yourself 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 kinds 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 privacy amplification, for example. But we know that basically even sort of a source of randomness that is not good, most, there is really no classical way of improving a certain class of randomness. For example, in computer science, popular sources of randomness that computer scientists study are called the Santha-Vazirani sources and it's known that there 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 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 as long as there's a little bit of true randomness in your input, then you can amplify it and get a device that gives you not only uniformly distributed but also completely private sources of randomness. 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 this locally, you can actually amplify this randomness up to your satisfaction. And then, you know, there are many ways of doing this.

### Artur Ekert

01:23:36 - 01:27:24

I think I just wanted to say that, you know, you can use all kinds of Bell inequalities not only the most popular CHSH inequality, but, you know, the story basically is at the moment 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 get devices that you can test for security 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 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 tests 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 story of privacy to the limits, this is basically where we can, where we are today, at least, you know, in a very speculative way. I mean, I'm not saying that this is actually implemented. We can just about implement loophole free tests of the Bell inequalities. What is interesting though is that in my view, you know, even though 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, 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 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 if you assume, for example, that everything is quantum, then you have to somehow redefine the notion of secrecy in terms of relations between different universes so that, you know, how information in one particular part of the multiverse is restricted by people sort of, you know, the access, how the access is sort of restricted in different parts of the multiverse. So that's certainly one thing and then, you know, there's a 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 really objective things? Do we have truly random phenomena in nature? And so that would be, you know, a point of view taken by, say, the quantum world.

### Artur Ekert

01:27:26 - 01:29:52

The Epicureans 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 the Democriteans who were saying, well, you know, it's more subjective things. Atoms follow predetermined paths 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 relevant because if indeed it is the case that everything is quantum, then you know, what is really randomness in this sort of truly quantum universe and does it exist at all? And it may be the case 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 and I think you really said this, did you? Right, so, you know, it's just 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 develop, for example, physics where we don't use the notion of randomness and probabilities as we do it today, which is a very interesting question? And I think 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 generates lots of interesting questions and 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 a rather technical and precise language. So again, I would like to congratulate Charlie, David and Peter for their work. Helping to create this fantastic field and needless to say, this field will certainly thrive for years to come. Thank you very much.

### Fernando Quevedo

01:30:00 - 01:30:06

Any questions? Yes?

### Charles Bennett

01:30:06 - 01:30:38

Reminiscence, because I've taken a lot of these group conference pictures and one of the main reasons is that scientists in general are like herding cats. So you announced there's a group picture and a lot of the people miss it. And then you want to include them. I don't know if you were at that one, but we had a conference 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.

### Fernando Quevedo

01:30:45 - 01:52:34

Okay, so I'm sure there's plenty of things to think about after these presentations, but there is coffee outside. We are running very well on time, so there is 15 minutes for coffee and we come back at 4.15. Let's thank Arthur again. Thank you. Okay, let us continue. Okay, so now we will move to the next part of the event, which is awarding the medals and the presentations of the three awardees. So I will start with Peter Shor. So let me say some words about Peter. He received his B.S. in mathematics in 1981 for undergraduate work at Caltech and was a Putnam Fellow in 1978. He earned his Ph.D. in applied mathematics from MIT in 1985. His thesis was on probabilistic analysis of bin 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 encryption schemes. He thus proved that a quantum computer could solve a useful, hard computational problem exponentially faster than any known classical computer algorithm. Shor also introduced quantum error correcting codes and fault tolerant quantum computation, which are schemes for coping with effects of stray interactions, noise, disturbing qubits. Without robust quantum error correction, large scale quantum computation could be stymied by the extreme sensitivity of quantum states to noise. Instead, the theory of quantum error correction is now a well established branch of quantum information science, and the difficult path to developing large scale quantum computers appears open. 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 ask Peter to come here to, I can give you the Dirac Medal and everybody to give him a warm applause. Thank you.

### Peter Shor

01:53:02 - 01:57:20

Okay, so I want to talk about my inspiration for discovering the factoring algorithm and some reminiscences about what took place when I discovered it. So the outline of my talk is first I want to give the first few slides of my 1990s factoring talk, somewhat updated, because they'll show you why the factoring algorithm is such a surprise, and then I want to 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 a physics experiment? And of course back then that was like the joke, what's the difference between an elephant and an egg? It's so obvious. So first answer, a physics experiment is a big custom built finicky piece of apparatus, and a 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 is a computer, and here is a physics experiment. But if you go back 50 years before that, here is a computer, oops, and here is a physics experiment, and they start looking very much more alike. 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, the first computer that Von Neumann worked on. So here's the second answer. A physics, a computer? Okay. A computer answers mathematical questions, and a 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. And if you want to test whether 15, if you want to find 15 equals X times Y, you probably don't want to use physics experiments. So this is an ion trap computer at Rainer Blatt Group in Innsbruck, Austria, where he actually did the experiment of factoring 15 using an ion trap. And I'm always afraid when these papers come out that some headline is going to appear in a newspaper somewhere, physicists spend \$2 million to show that 15 equals 5 times 3. It hasn't happened yet, luckily. And a 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 produce computers. Well, it's hard to mass produce physics experiments. So for example, after the Tevatron 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 particle 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.

### Peter Shor

01:57:20 - 02:01:15

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 Kleene, 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. And what Church and Turing proposed was that this was really a very natural class of computational functions. But when people started building real computers, this turns out that the definition of computation was very different. Because this turns out that the definition of a function to be computable really wasn't that useful in practice. For example, if you have a function that can be solved and computed in 10 to the 30th years, well for practical purposes it might as well be uncomputable. So computer scientists made this rather, well from some points of view it's probably draconian compromise between theory and practice where they came up with the idea that efficient means it can be computable in polynomial time in the length of its input. So, I mean it's not really, it doesn't really correspond to the class of practically computable functions, but it's also something that computer scientists could prove theorems about. So once this was realized, once you have the definition of efficient as being polynomial time, this quantitative Church.s thesis, which was proposed many different times in the 1960s by various computer scientists, but I think Cobham is actually the first, a Turing machine can perform efficiently any computation that any device can perform efficiently. And I don't know 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, or several other people who pointed out a number of years before he did. So quantum computers can be built. The really surprising thing is that this would imply this folk thesis is not true. And in fact, the folk thesis has become, you know, has really become rooted in the consciousness of the public because one of the questions I get asked about quantum computers was, well, how much faster is a quantum computer than a classical computer? And this isn't really not 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 misconception is so widespread really means that the public had absorbed quantitative church's thesis.

### Peter Shor

02:01:15 - 02:05:22

I think we have now gotten 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 of planning to do. So 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 Bell Labs about quantum key distribution. Here is, actually I'm sure that Charlie is going to mention this in his talk, Charlie and John Smolin built, they got us, you know, basically on a tiny budget, a little quantum key distribution device. And this apparently is what it took for them to get physicists to take them seriously. So I, you know, I was very intrigued by Charlie Bennett's result and I went around and looked at papers about quantum computing and the literature and there really was not very many of them and most of them were written by David Deutsch. So looking at them, well, first neither Charlie nor David Deutsch convinced me that there was a mathematical rigorous description of quantum computing. Looking back at David's papers in retrospect, I was clearly wrong about that. But, 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 that was, I don't think David's papers had any really useful algorithms in them. So for that, next thing that happened is Umesh Vazirani 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, but which quantum computers really sped up the computation of classical computers. And the other thing is it had a rigorous definition of a quantum Turing machine. So after I saw Umesh's talk, I started thinking 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 Dan Simon's paper. So I was on the conference program committee and Dan Simon submitted the paper containing his algorithms to this conference. In fact, it was STOC in 1994, which occurred sometimes in the spring. So I saw it, I was very interested in it, 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 Vazirani and Ethan Bernstein's paper, which had appeared in a previous iteration of this conference. So, 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, I didn't go, I didn't jump up and down and they voted to reject it. So what is Dan Simon's algorithm?

### Peter Shor

02:05:22 - 02:09:13

Well, it takes place on a hypercube. So you have a hypercube, and you color the point. You color the points, vertices of the hypercube with one of two to the n minus one colors, so there are exactly two colors, or 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, and 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 hypercube with 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 wanna 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 random vertices, or 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 the hypercube, which is two to the D minus one, if this is D dimensional hypercube, and quantum mechanically, you can really solve it in D queries too. You ask D questions of points in superposition, and you get enough information to tell you what the distance is. Well that's an exponential speedup. 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 have periodicity, it's mod two. Discrete log algorithm uses the Fourier transform, Simon's algorithm uses the Fourier transform, it's mod Z two to the N instead of the integers mod Z. Integer is mod, I guess, some number. But I knew the discrete log 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, how does the factoring 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 it reflects off at, or the angle it makes when it goes through the diffraction grating depends on the color, and that's because at certain angles, all the wavelengths add up, so you get constructive interference, and at 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.

### Peter Shor

02:09:13 - 02:12:58

It separates the different possible periods of the periodic function, so each different period results in a different output of the quantum computer, and then from the output, you can figure out the period, and if you know some basic number theory, which is well known to cryptanalysts, 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 Bell Labs about the algorithm for discrete log on a Tuesday in April 1994. The next weekend, Umesh Vazirani, who was a professor at the University of California, called me. I was home in bed with a bad cold. And he said, I hear you can factor on a quantum computer. Tell me how it works. So you can notice that the talk was about the discrete log problem algorithm, and I had not actually solved the factoring algorithm yet. And well, I don't know if you know the childhood game of telephone, but somehow the result turned to factoring in, you know, people telling each other about it. This was five days later, 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, and I hadn't written it yet. So there were lots of different versions of various drafts of the paper spreading around, and people 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 factoring algorithm, I gave a talk at the Algorithmic Number Theory Symposium in Cornell. In June, Umesh gave a talk at the Santa Fe Institute Conference on Quantum Information. In August, I gave a talk at a conference in NIST, and I guess Artur Ekert gave a talk in Colorado on atomic optics conference. And in October, I gave a talk at Villa Gualino in Torino, and by that time the paper was actually written. I presented it at the FOCS Conference that November, which Dan Simon's paper also got into that conference, luckily. And it spread. And one interesting thing is that I started describing quantum computers as quantum Turing machines, which was what Bernstein-Vazirani paper talked about. But after I discovered the result, I started talking to physicists. It's absolutely impossible to explain a quantum Turing 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 Deutsch. And really how the quantum circuit model got to be the accepted model for quantum computation. And let's see, I'm probably out of time. Is that right?

### Peter Shor

02:12:58 - 02:15:41

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. And one of the biggest detractors of quantum computation was Rolf Landauer, who worked at the same place that Charlie Bennett and David DiVincenzo and some other people working on quantum computation. And I think Rolf Landauer described the situation there as, well, we have four people working on quantum computation and one person working against quantum computation. There are, you know, so what's the argument? Well, quantum computers can't be made fault tolerant. You can't use redundancy because of the no-cloning theorem, which says if you start with a quantum state, you can't make another copy of it. You can't measure to see if there's an error because the Heisenberg uncertainty principle means that if you measure the quantum computation, you inevitably disturb it. And then of course, 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. And 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. With this, there are fault tolerant threshold theorems which say you only need gates accurate to maybe one part and 10 to the fourth. This number really depends on the exact quantum fault tolerant techniques you use. And it's still unresolved as to what you're doing. What this number should be if you try to make quantum computers 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, which is very encouraging. And this is my last slide, so thank you.

### Fernando Quevedo

02:15:42 - 02:16:41

Thank you very much, Peter. So that was a very nice piece of history and it's a beautiful way to see how things develop. Any questions? Any comments or questions? Okay. So there's a question from a YouTube viewer for Peter. So what are the most significant reasons to think that factoring cannot be performed in polynomial time on a classical computer apart from the fact that many people have failed to do so?

### Peter Shor

02:16:41 - 02:17:20

Well actually I don't think there are that many reasons. If you talk to Peter Sarnak, who's one of the most famous and best number theorists around, he thinks it's entirely possible there's a polynomial time algorithm for factoring on a classical computer. So the only real reason we don't think there is one is that nobody has discovered it 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.

### Fernando Quevedo

02:17:20 - 02:20:33

Thank you very much, Peter. So let's thank Peter again and congratulations for the performance. Thank you very much. I will now continue with the next awardee, which is Charles Bennett. Charles Bennett is an intellectual leader in quantum information science. Born in 1943 in New York City, he earned a B.S. in chemistry from Brandeis University in 1964 and received his Ph.D. from Harvard in 1970 for molecular dynamics 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 under Aneesur Rahman at our laboratory. After joining IBM research in 1972, he built on the work of IBM's Rolf Landauer to show that general purpose computation can be performed by a logically and thermodynamically reversible apparatus. Let me add a small comment here that, I think, the idea of the thermodynamic code is not a good idea. In 1982 he proposed a reinterpretation of Maxwell's demon, attributing its inability to break the second law to the thermodynamic cost of destroying rather than acquiring information. And with Gilles Brassard, sorry, something is happening, you're receiving emails. I think it was Gilles Brassard from the University of Montreal, I think I have to mention, Bennett invented quantum cryptography where two distant parties share a secret encryption key with security from eavesdroppers guaranteed by the basic quantum limitations of measurements of incompatible observables. Bennett and Gilles Brassard, they were the first to create quantum cryptography. Their collaborators also introduced quantum teleportation, whereby entanglement and classical signals are used to transfer quantum states. He and coworkers proved that a quantity called the von Neumann entropy is the proper measure of entanglement for pure systems, an early result in the quantification of entanglement, which continues to be an active area of research. So please join me in applause for Charles for his Dirac medal.

### Dirac Medal ceremony audio artifact

02:20:33 - 02:21:23

[Applause]

### Fernando Quevedo

02:21:24 - 02:21:31

Okay, and then Charles will give us a presentation, Forging the Culture of Quantum Information Science.

### Charles Bennett

02:21:53 - 02:25:35

Yes, so I'm very glad to be here. I was here I think in the 1980s with Rolf Landauer, and it's a place where serious physics has been done for a long time. I'm going to talk about the culture of quantum, really the culture of information science, because when quantum is a very important part of the system, it's a very important part of the science, because when you, well, like I say, other parts of mathematics, information science was an abstraction from practical experience, but the information revolution that we're still in the middle of is from these two brilliant, I mean almost brutal abstractions by Turing, the idea of a hardware independent notion of computing, and by Shannon, an even more brutal idea that the theory of communication is best developed by ignoring the meaning of messages. So 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 questions of reversibility, which they thought were thermodynamic questions of not really much importance, 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, and all of the 20th century scientists were pretty, they knew about quantum mechanics, they'd been around for a while, and they certainly knew about thermodynamics, had 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, is sufficient and sometimes necessary to describe the states 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 kind of a nuisance, because people focused on the uncertainty principle causing quantum systems to behave less reliably than larger systems. And now, as we've heard from 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 Wiesner, who is 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, 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 the idea that the uncopyability of quantum information was something that could be useful.

### Charles Bennett

02:25:35 - 02:29:20

The other one was an even more direct application of that idea, a quantum banknote that cannot be copied. Now I guess I don't think the euro notes have this, but French and German banknotes used to have fine print explaining how many years in prison you would spend if you would copy the, duplicated the notes. Well anyway, I think this, he did, he wrote a manuscript which didn't get published until 15 years later about this in 1968 actually. And 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 physics for another decade. But I think this notes that I took in 1970 with him may be the first place where the notion of quantum information theory or the name theory even got mentioned. So then I went around talking to other people including David and we've heard a lot of the rest of the history. But of course in the beginning days it's sort of obvious that these were ideas that were so strange that most people, even the people who were working on them, didn't take them very seriously. Like Peter just said, oh well I was only working on it part time. So what's the difference between ordinary information and quantum information? People often ask me this and I sort of tried to say, well 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. So I came up with this other metaphor. Quantum information is like the information in a dream. If you try to explain your dream to somebody else you forget the dream and only remember what you said about it. And of course this means you can lie about your dream and not get caught unless you're trying to lie to your spouse. But unlike dreams there's 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 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. And so for the theory of communication and computation, what they did, we made an important improvement which may not be important yet in a technological sense but in a conceptual sense it's really an improvement. Oh, so 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 computer scientists and people that I'm not sure exactly what you'd call them like David began thinking about it they realized it 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 an idea that's as crisp and fruitful as the universal classical computer that Turing showed existed. So here's an example of something you can do with a quantum computer.

### Charles Bennett

02:29:20 - 02:32:57

We can take a, there it is, whoops, I want the laser, yeah. So let's take a vertical photon as a one and a horizontal photon as a zero and I have them in different colors so that I can keep tracking them. This is a conditional NOT operation or an exclusive or. So the first qubit controls whether the second one is left alone or whether it.s flipped. And when you put the first qubit 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 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 of itself. Well that's an idea that would bother a typical computer scientist of the 1980 very badly and they would say, you know, physicists don't even prove theorems, so how can I take what you're saying seriously? But actually in an earlier time in my life, I was in the Haight-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 hippies believed that with enough LSD everybody could be perfectly in tune with everybody else, but they were not really especially good at mathematics and now we have a quantitative theory of quantum information. We know that entanglement is monogamous and the more entangled two systems are with each other, the less of course the hippies weren't very good at monogamy either. So here's how it works. If we have two perfectly, 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 have a little bit more of this. So he entangles himself with Judy. Well the trouble with that is that that degrades his entanglement with Alice and his entanglement with Judy. So he's only classically correlated with each of them. But, and so that means if either of them leaves town, he just has a classical correlation that could be cloned or copied, but it's not very interesting. But a 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 a bit with one of two arbitrary orthogonal values. The classical wire is something that conducts classical information reliably but spoils superpositions. In other words, it's a quantum wire with an eavesdropper. And a classical computer is just a quantum computer that's handicapped by having eavesdroppers on all its wires. So instead of saying, why does a quantum computer speed up computations, a more sensible way of asking that question is why do some computations get horribly slowed down by having eavesdropping on every step of the way? So entanglement is ubiquitous.

### Charles Bennett

02:32:57 - 02:36:11

Why 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 environments that they tend 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 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 you 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 proposed by Wojciech Zurek. 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 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, I think Peter already talked about this. In classical computation, you can break all computations down into ands and ors and nots, 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. And we have now a well-developed theory of quantum computational complexity where we have 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 explored. Now, I'm gonna go back and talk a little bit about 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 sorts of bad ideas was Einstein. So Einstein really didn't like quantum mechanics, and because he's the only 20th century scientist most people can name, they have the attitude that if Einstein didn't like it and didn't understand it, what hope was 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 viewing entanglement as action at a distance, as some kind of influence of one particle on another. And the right way to think about it as an entangled state is that you have to give up the common sense idea that if the whole is in a definite state, then each part must be in it.

### Charles Bennett

02:36:11 - 02:40:25

It's just not true. And then once you've given up that idea, it's quite possible to understand how you can have this strong correlation, 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 early 80s, Nick Herbert published a paper, well actually he submitted it, I forget if it was Asher Peres, may have been the referee, and he said, this paper 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. So, but there's, so this gives you the idea that wrong ideas are very good for scientific progress. Conversely, and I'm going to be talking about this in the context of the reversibility in Maxwell's Demon, good ideas, indeed quantum mechanics itself, sometimes retard scientific progress. So, when we think about the idea between mathematics and physics, between dynamical motion and computation, and this is very nicely stated by Laplace in 1814, if the universe has deterministic laws, if we know the present state, then we know the entire future and past. Well, the next problem came up in connection with Maxwell's Demon. Who here has heard of Maxwell's Demon? Okay, well this was an idea of the discover, really, of the mathematics of random motion of atoms in a gas, and he said, if you had somebody who was able 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, as my science writer colleague, Aya Furuta in Japan puts it, Maxwell didn't solve the problem, he just gave it as a homework assignment to physicists after that. Now, actually, the time was ripe, right at the beginning of the 20th century, for someone to solve this problem, and it was Smoluchowski. And he considered a version of the Maxwell Demon problem, which was just a trap door, so that the molecules coming from one side 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 in the street with it for just using the energy of heat. And then he argued that if the door was light enough and the spring on it was small enough that it could be pushed open by a molecule, it would have its own random motion and it would work in reverse exactly as often as it worked forward. So he really solved the problem back in 1912. But, 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 that Laplace 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, Szilard's paper in 1929 was, so, 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 Rolf Landauer to say that computation could be reversible and it was an irreversible act of erasing information that keeps the demon from working. So here's my sermon, the sermon part of this history thing.

### Charles Bennett

02:40:25 - 02:42:37

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 was too kind to say, but I said to my colleagues, we didn't take him, I said to John Smolin, 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 too optimistic about what can be done right away. And my favorite example of this 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 Voyager Project and they had applied to make it go to all of 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 do 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 really needed to. And each one said, well you wouldn't want this thing to fail just because this part wasn't quite strong enough and he was working on the thermoelectric or power supply for it. So of course then once it was launched they could repurpose it and go to all of those. So the moral of the story is sometimes you have to lie to the politicians, but 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.

### Fernando Quevedo

02:42:52 - 02:43:12

Thank you very much Charles. It's a lot to learn from these expressions and from this way to behave with politicians also. So, comments, questions? Yes?

### Audience questioner

02:43:23 - 02:43:49

Yes, so you spoke about entanglement. So, do you think in the quantum computational speed up, is there any clear sign that entanglement plays a role rather than superposition? Well, it's hard to separate the two because from the superposition principle you get entanglement.

### Charles Bennett

02:43:49 - 02:44:40

But it's an important question because people have asked, does every useful quantum computation where there's some advantage over classical involve entanglement? And I think actually Peter would know the answer to that better. I think Grover's algorithm doesn't involve entangled states, right? Well, it does. Grover's algorithm involves entangled states, but it doesn't look like entanglement states are central to Grover's algorithm. But 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 an efficient way of simulating quantum computation. So, yes?

### Audience questioner

02:44:40 - 02:45:12

You 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 Tumulka and other people have spoken, I have derived the no cloning theorem two years before. Two years before Wootters and Zurek and Dieks. Oh, and there was also before that, there was this... Two years before.

### Charles Bennett

02:45:12 - 02:45:15

Yeah. It was even more than two years before.

### Audience questioner

02:45:16 - 02:45:35

I can send you the next... Yes. No, I was saying it was discovered in a paper that was cited by Wootters that had been written for like 10 years before, but it was not noticed. My proof is exactly identical to Wootters.

### Charles Bennett

02:45:35 - 02:45:37

That has the proof in it too. That's the earlier one.

### Audience questioner

02:45:37 - 02:45:39

And it is a very rare one too.

### Charles Bennett

02:45:39 - 02:45:57

Yeah, so you got there almost at the right time for it to be noticed. Yeah, so this is almost most scientific discoveries occur this way. They're discovered three or four times, sometimes very well, and it's not the part of the discoverer that was not noticed. It's just the time wasn't right.

### Fernando Quevedo

02:46:01 - 02:49:08

Okay, so let's thank Charles again for his wonderful talk. So now the last medalist is David Deutsch. David was born in Haifa in Israel in 1953, the son of Oscar and Tikva Deutsch. He attended William Ellis School in Highgate, North London, before reading natural sciences at Clare College in Cambridge and taking part three of the Mathematical Tripos. And he went to Wolfson College Oxford for his doctorate in theoretical physics. And I have to say that his supervisor was Dennis Sciama, who was the well-known figure here in Trieste, and also the supervisor of big scientists like including Stephen Hawking and Martin Rees. And he wrote his thesis on quantum theory in curved spacetime. David 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 Bennett, Shor and co-workers showed that sequences of one qubit gates and one simple type of reversible classical two-bit gates. Working alone and with Richard Jozsa from the University of Cambridge, Deutsch proposed the first quantum algorithms known as the Deutsch and Deutsch-Jozsa algorithms, showing that quantum computation could solve certain problems faster than any known classical computer algorithm. So please, let's all congratulate David for the award. Thank you. So David will give us a presentation called the mathematician's misconception. Do you have slides? No.

### David Deutsch

02:49:51 - 02:54:19

Hi. Can everyone hear that? Yeah. Okay, well, nice to be here. A couple of years ago, the mathematician Hannah Fry made a TV documentary about Ada 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, 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 one could call arithmetical universality. In his previous design, the difference engine could compute polynomials in one fixed point variable, so a very limited kind of universality, it's universal for those. 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 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, instantiate or simulate or emulate all possible motions 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 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.

### David Deutsch

02:54:19 - 02:58:36

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 Feynman remarked, they thought they understood paper, but they didn't. And 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. I also had a referee problem.

### David Deutsch

02:58:36 - 03:02:44

The referee of the paper in which 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. It turned out it was as much of a mystery to them as to me. Some of them said it was metamathematical 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. 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 mathematician's misconception, the denial that proof is physical is one way of putting it. By the way, the Rolf 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 metamathematical 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 that's how the mathematician's 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 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 Gandy 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.

### David Deutsch

03:02:44 - 03:06:51

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 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 vindicating 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. Again, they think that there's a mathematical definition of information out there somewhere independent of physics. 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 physical world is actually being computed on a vast computer belonging to God or to supernormal aliens. Because there's no reason other than the misconception why the alien 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.

### Fernando Quevedo

03:07:07 - 03:07:25

Thank you. That was a thought provoking talk. Any questions from any mathematician? I have a very simple question.

### Audience questioner

03:07:25 - 03:07:26

What is physical?

### David Deutsch

03:07:29 - 03:08:22

Yes. It's a bit like asking what is real. There seem to be various, I don't know is the answer, but there seem to be various levels of reality and there's a level that's only accessible by experiment and then there's the level to find out what the laws are. And then there's the level that is independent of the laws. So we know that Fermat's Last Theorem is true and if somebody comes and finds that general relativity has a flaw or quantum theory has a flaw, nobody will worry that maybe Fermat's Last Theorem isn't true. Laws of physics are things unlike that. They are things that could be overturned at any moment. We guess at them. So I can't provide an answer better than that. It's a deep question.

### Fernando Quevedo

03:08:29 - 03:08:39

More questions? Yes. Yes.

### Audience questioner

03:08:46 - 03:09:06

Yes. I think I am confused. Can you explain the difference between what is like mathematical, like which is like in the top, mathematical proof or physics proof from what I understood is the physics one, I think.

### David Deutsch

03:09:06 - 03:09:54

Well, you have to draw a distinction between what issues of what we can know, how do we know things. Their physics is at the top. We conjecture laws of physics, we test them from our physical intuition, we then develop mathematical intuitions from there, we learn about mathematics. However, 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 truth goes, mathematics is at the top. Its truths are necessary. But our knowledge is the other way around. It comes via physics. Is that clear?

### Fernando Quevedo

03:10:00 - 03:10:16

I have a couple of minutes to 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 that quantum mechanics most probably is not the last word. Can you combine the two thoughts?

### David Deutsch

03:10:17 - 03:11:18

Well, I think that the multiverse interpretation is on the same level of, I mean, the existence of the multiverse. It's on the same level as the existence of the dinosaurs. You know, that is not going to be proved false. What is going to be proved false is what the multiverse consists of, 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 different people won the prize and so on. We know that is true, but the details are going to change because quantum theory is in many ways totally unsatisfactory. Look at quantum gravity, for example.

### Fernando Quevedo

03:11:19 - 03:11:26

But just some people do not support this multiverse interpretation, so you say they're simply wrong or this?

### David Deutsch

03:11:27 - 03:11:30

Well, they're all wrong in different ways, but yes.

### Audience questioner

03:11:30 - 03:11:51

Well, I'm going to ask David about something that I think he thinks. Could you describe yourself as a technological optimist?

### David Deutsch

03:11:51 - 03:11:52

Yes.

### Audience questioner

03:11:52 - 03:12:45

Okay. Well, I used to be a technological optimist, but I then started studying a little bit of cosmology and maybe thinking too hard about the Copernican principle, and it occurred to me that perhaps the universe is infinite, but the self-destructive tendencies 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 many other bubbles where they do better. We're just not in the good one. But I think you think maybe one of those bubbles 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?

### David Deutsch

03:12:46 - 03:13:10

I think the mistake there is when you said the evidence of our self-destructive nature. By our you meant our civilization or our species or whatever. Really, basically what Schopenhauer said, that the argument that suggests that we're all possible worlds and if we're a little worse, it would destroy itself.

### Audience questioner

03:13:10 - 03:13:11

Yes. Very close to that.

### David Deutsch

03:13:12 - 03:14:29

Well, it's obvious 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. I was going to say something. Because if we had destroyed ourselves, we wouldn't be here to complain about it. Well, okay, 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 solved problems. And our particular civilization is different from all other ones, previous ones in that respect. So you can't extrapolate from them either. All civilizations basically other than our current scientific, technological, 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 pessimists suggest ours will be destroyed. So there's again a disconnect. So it doesn't work. Well, just a very quick question because.

### Audience questioner

03:14:31 - 03:14:48

How you said the provability as well as the validity which is true in all interpretation, both are physical. How you make the distinction? Because one is semantics essentially. The other part is purely syntactical which is the provability.

### David Deutsch

03:14:48 - 03:15:26

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 seems fundamentally hidden from us.

### Fernando Quevedo

03:15:28 - 03:16:51

Very good. So let's thank David again for this wonderful talk. Thank you. 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 Savoy Excelsior Palace in Trieste. And it's a moderated roundtable discussion with Hartmut Neven, who is Google's Director of Engineering. He's here. Alessandro Curioni, who is the Vice President of IBM Europe and Director of IBM Research Lab in Zurich. And Tommaso Calarco, the Director of the Institute for Complex Quantum Systems in the University of Ulm and a leading figure for this European Commission Quantum Technology Flagship Project. So you're all welcome to participate. It's for the general public. And there is a bus that we hired that will take 50 people. So all of the 50 of you who want to go, it's the first come, first served. And then we will see you there. So it will be an interesting discussion about the importance of quantum technologies. Okay, well, thank you very much. And congratulations again to all the awardees.