00:07:45.000 to top scientists also that will give presentations for us.
00:07:52.480 As you may all know, today, Stephen Hawking passed away.
00:08:01.640 the impact he has had in many generations of physicists.
00:08:10.680 But this is a very sad moment for all the scientific community.
00:08:16.360 I consider that he, he's a unique human being in many respects.
00:08:22.560 He was special because there has never been anybody
00:08:31.240 and there will never be anybody like him in the future,
00:08:41.560 but also the technology was ready only at the time
00:08:44.960 but he needed to be able to communicate with people and so on,
00:08:48.240 in the future all the people may find other ways to communicate.
00:08:59.000 in particular to black holes, to gravity, and cosmology in general.
00:09:12.080 I would say many generations of hundreds of years
00:09:17.800 from the results were painters about the general existence
00:09:24.400 then the thermodynamics of black holes, the hockey
00:09:29.600 and many other contributions that he has been producing
00:09:32.840 over the years, even recently he has been working very closely
00:09:40.640 for the whole community, which is the information,
00:09:47.000 of several generations of physicists trying to solve.
00:09:56.560 And the influence that he has had had to make sure
00:09:59.040 for his great contributions regarding the popularization
00:10:06.640 for promotion of science, physics, but in general,
00:10:32.800 to stand up and join with me for a minute of silence.
00:12:26.040 a Nobel Prize winner and a staunch friend of SDP.
00:12:29.040 SDP's founder, Adus Salan, worked with Dirac at Cambridge
00:12:31.600 University and love admired the professor and his work,
00:12:34.520 which included considering the relativistic wave equation
00:12:37.320 the diagnosis of anti-particles, particular the possibility.
00:12:46.400 and Salan used to recognize that one of the motivations
00:12:53.080 who's worked with Salan, with the Dirac, sorry.
00:12:59.920 who have made significant contributions to theoretical physics.
00:13:05.960 theoretical physicists over the past 26, 27 years.
00:13:11.040 And the recipients of the 2017 Dirac-Meidel Award
00:13:14.760 are Chancellor Bennett of the IBM Watson Research Center,
00:13:22.040 Peter Schor, of the Massachusetts Institute of Technology.
00:13:25.680 All three are being honored for the groundbreaking,
00:13:28.120 working applying for the mental concepts of quantum mechanics
00:13:31.160 to solve the basic problems in computation and communication.
00:13:35.120 Bringing together the fields of quantum mechanics,
00:13:45.000 was kind of very unique, because as you can see,
00:13:48.160 each of the awardees has a completely different background
00:13:51.760 when they started as a chemist, becoming a computer scientist
00:14:07.880 to make the selection, not because the awardees
00:14:10.640 was difficult to select, because they needed extra help
00:14:15.200 for the selection, because the expertise of the committee
00:14:25.000 as the distinguished physicist as Professor Michael Green
00:14:30.400 from Cambridge, Professor David Gross from Santa Barbara,
00:14:39.520 Professor Ashut Sen from Alahabad in Asia-Rang, in India,
00:14:47.520 So they were very pleased to come up with this selection,
00:14:51.400 which I think is very special, unique in the history
00:14:55.320 of the Dirac Merelle, and we are all very pleased
00:15:01.240 So the ceremony will begin with the general talks
00:15:03.520 by Peter Zoller, who's a former director of Middle East,
00:15:06.480 and which is a professor of the University of England,
00:15:09.000 working in quantum optics, and also art to occur,
00:15:12.480 for my colleague from Cambridge, and also not for Professor
00:15:16.200 of quantum physics and cryptography at Oxford University.
00:15:27.000 So let's, as Peter Zoller, to start his presentation,
00:16:17.400 the winners of this actually last year's Dirac Merelle.
00:16:32.880 to solving basic problems in computation, communication,
00:16:38.040 of quantum mechanics, computer science, and information.
00:16:41.480 And that's to say that I could not more than agree
00:16:46.480 that represents the whole spectrum of what defines quantum
00:16:49.800 information, which is by definition very interdisciplinary.
00:16:54.520 And what I would like to do in my talk here today
00:16:57.200 is this that I would like to sort of give you a part historical
00:17:06.680 I got sort of influenced by all of these ideas here.
00:17:11.680 And then sort of in the second part of my talk,
00:17:13.720 give you a snapshot of what we're doing at the moment.
00:17:16.640 So I'm somebody whose background is quantum optics.
00:17:26.280 or quantum communication devices, quantum networks,
00:17:29.080 and all of these things, from a theoretical perspective.
00:17:32.520 I would say that many of these ideas that 25 years ago
00:17:35.480 were just dreams, in the meantime, are reality.
00:17:43.840 And might have actually quite an important impact
00:17:49.080 So I think that this is one of the prime examples
00:18:09.120 This is like political party meetings of quantum information
00:18:14.120 And I've to say that two of the prize winners are here,
00:18:17.760 And show that Charlie Bennett actually put himself
00:18:20.040 in Photoshop into this picture, because you were always
00:18:24.000 They didn't have Photoshop very much in that frame.
00:18:27.960 Or you ran on the title, because OK, you're so.
00:18:37.280 But actually, they were really sort of very interesting ones,
00:18:40.080 because people came together from all different communities
00:18:45.000 And you know, just because you're out to Eckhart,
00:18:58.280 This was, you know, we were just meeting there for two days.
00:19:01.640 And this was our first presentation of this idea
00:19:06.440 will afterwards tell you a little bit more about.
00:19:09.440 People were asking me, Ignacio, why were you hiding?
00:19:12.160 And these answers was that I was a little bit embarrassed
00:19:14.600 by being surrounded by people that were all a little bit weird.
00:19:17.360 But I guess that's sort of the definition of physicists
00:19:24.240 So this is Ignacio, how we really look at this stage.
00:19:29.800 in this, of course, you know, this is from David Jenssel block,
00:19:44.160 And one thing that sort of started from my perspective
00:19:47.440 is that during this year at what's actually in 1994,
00:19:56.040 And as you will see, after academia has been very influential,
00:19:59.040 all of these things, quantum simulation, quantum communication,
00:20:01.600 with quantum optics, it's a title with four quantum.
00:20:04.400 So I mean, damn it, you know, it cannot go more quantum than that.
00:20:14.520 an iron trap quantum computer, as we have at the moment
00:20:22.000 an experimentalist, where I have a very close collaboration
00:20:24.400 and then we love to work, tell you how these ideas work.
00:20:29.520 behind some of that and what we're doing right now.
00:20:32.040 And if the number of qubits that you would like to see,
00:20:34.600 it's a little bit more, this is from a recent paper
00:20:36.720 in Nature by Chris Monroe, who also is a company now.
00:20:39.720 It's called, I am curious, so there's even a commercial version
00:20:43.320 of building iron trap quantum computers now available.
00:20:47.080 You might be able to buy some of these devices in the future.
00:20:58.160 is the point where you take a different tone in science.
00:21:01.400 It's an atomic physics and quantum optics version,
00:21:03.640 what's it talk that was given by outdoor aircraft.
00:21:10.920 ICAP is a very prestigious international conference
00:21:13.720 and atomic physics, usually very experimentally dominated.
00:21:20.920 But this ICAP had, one very particular feature.
00:21:23.800 They always try to invite people that want to, not too many,
00:21:37.720 It was some clever guy, the program committee must be.
00:21:42.920 that I would really say changed a lot of these things
00:22:00.000 So I stole them from you, from some of you later talks.
00:22:02.920 And let me go through these things very quickly,
00:22:13.080 They're sort of starting out by making this remark,
00:22:17.160 you know, here's sort of a classical physical process,
00:22:29.480 We are saying, of course, the doorages now over here,
00:22:32.440 and obviously here, that the fundamental nature,
00:22:37.560 and at the fundamental level of that for information science
00:22:48.320 more powerful and we believe that the answer is yes.
00:22:54.200 the historical behavior reported that the show algorithm
00:23:03.040 you know, that was a very true and deep motivation
00:23:08.360 So here's this information and physics quantum process
00:23:11.400 and then you will look inside, you have now here,
00:23:24.600 we would still some extent agree with that there.
00:23:38.600 And of course, what we learned from outer stock
00:23:46.800 is now the quantum bit, which is a superposition
00:23:51.120 so we can have things like zero plus one over here,
00:23:56.160 and these classical versions of the quantum bit
00:24:01.000 I'm not sure exactly where I got this picture here
00:24:03.000 from, I guess, from behind the block, if you look at it,
00:24:07.920 at the same time sort of symbolizing this thing
00:24:14.280 don't take this thing too literally, of course.
00:24:28.240 of all these different numbers at the same time,
00:24:33.240 and of course, what we're doing with our quantum computers
00:24:45.000 avoiding decoherence as the coupling to the environment
00:24:50.240 And of course, the statement, well called the memory,
00:24:52.360 how big is it, that if it takes something like two,
00:24:58.720 two to the 300 pieces that the mention of the Hilbert space,
00:25:01.640 the statement is that the Hilbert space is really huge.
00:25:04.800 The piece is of course, the point where people like
00:25:06.920 five men came in originally in its seminal presentation,
00:25:15.560 you'd like to simulate something on a quantum computer,
00:25:17.960 Hilbert space is pretty big and it's hard to do so,
00:25:20.640 why not turn things around and build a quantum device
00:25:33.880 of what would be today called quantum simulators.
00:25:40.120 in his talk was, of course, that the big challenges,
00:25:52.400 first of all, you need a set of qubits, you know,
00:25:54.400 that can be in a superposition state and parangostate,
00:25:57.880 and you need a way of manipulating these things.
00:25:59.920 And if you look inside these quantum processor,
00:26:04.920 if you read these things like a kind of a world line,
00:26:07.520 there will be gates that operate on these things,
00:26:11.680 the single qubit gates that make certain rotations
00:26:16.240 And if you combine these things with two qubit gates,
00:26:21.960 then if you control qubit and then target qubit
00:26:26.000 and then conditional to the state of the first one,
00:26:34.040 that you can just put all of these things together
00:26:35.920 and you principally have your functioning quantum computer
00:26:51.240 And of course, what's behind all of these things
00:26:53.480 is that these gates operate on two quantum mechanical superposition states,
00:27:04.600 of here, I'm the quantum information processing.
00:27:07.680 Of course, you know, much of the motivation then
00:27:13.920 is an example where we have a certain quantum advantage.
00:27:29.840 And something like the shore algorithm, for example,
00:27:37.040 So with this, sort of at the end of this introduction,
00:27:44.040 and I was sitting at his talk about how to echo
00:27:48.160 I guess we know how to actually beat something like this
00:27:52.480 you know, that were developed for atomic clocks.
00:27:58.320 So let me just give you the qualitative insight
00:28:00.600 and then I would like to show you where we are right now
00:28:08.560 So, you know, people were building for atomic clocks,
00:28:17.520 and you can put them in like an unisotropic harmonic oscillator
00:28:22.720 so that they essentially go to an equilibrium situation
00:28:25.480 if you cool them down to very low temperatures, okay?
00:28:32.320 And you can see this as sort of being representative
00:28:35.920 as the quantum ratchers see that it spins up and spin down.
00:28:39.480 And of course, there will be a superposition of all of this
00:28:43.320 the quantum ratchers that we would like to manipulate
00:28:47.760 Well, if you would like to do single qubit rotations
00:28:54.200 and the distance between these ions is something
00:28:56.880 like a few micrometers, so you can actually do this
00:29:00.520 But there's also phonons and you can try to quantum control
00:29:07.120 and sort of, you know, of building the corresponding set
00:29:13.680 So on the left-hand side, we have this called the logic network model.
00:29:17.480 All of these gates, and because sort of you know,
00:29:19.480 all of these elements we can build with hardware,
00:29:24.240 And there's many groups out there that are pursuing these things.
00:29:29.160 So if you go to experimental papers from recently,
00:29:33.080 you know, these experimentalists have developed sort
00:29:35.920 of a complete gate set over here on very simple lasers
00:29:43.640 And what's kind of interesting is that we have now
00:29:48.400 So if you have some unitaries, some quantum algorithm
00:29:54.840 And we have quantum compilers that tell us, you know,
00:29:59.720 on these ions to represent the certain quantum computation.
00:30:06.720 of the killer applications, initially, and they still
00:30:11.360 is that the number of qubits and the number of operations
00:30:13.880 and here it's not about doing error correction here
00:30:27.600 has focused in recent years on quantum simulation.
00:30:32.640 that we have out there called the many-body system,
00:30:52.840 that would also be analog quantum simulation at the end.
00:31:09.320 in a strawberry-scopic sense mimics a certain Hamiltonian
00:31:12.520 over here, to illustrate to you what I mean by that.
00:31:15.680 For example, if you take a simple Hamiltonian of two spins,
00:31:19.400 like an easing model here and over the transverse field,
00:31:26.280 You can always decompose the unitary time evolution
00:31:31.520 by decomposing these two parts that we have over here
00:31:34.400 in these Hamiltonians, and we can write them as gates.
00:31:37.520 So if you know how to do gates, and tangling gates,
00:31:40.520 single cubic gates, you can mimic the time evolution
00:31:45.560 And a few years ago, this were the kind of themes
00:31:52.600 like a familiar, say, an easing Hamiltonian over here.
00:32:02.400 can do it up to about 20, or maybe even 50 of these spins.
00:32:05.640 But you can also write down very exotic Hamiltonians
00:32:08.480 like the one over here, which is a six-body direction.
00:32:11.240 And you can just program these things on your device
00:32:23.120 is that they can take models that become sort of interesting,
00:32:26.400 like, you know, a schminger model of one plus one,
00:32:28.800 that makes you a quantum electrodynamics, of course,
00:32:31.800 you hope at the end is to do something more non-trivial,
00:32:34.760 like maybe a non-thebillion lattice stage theory
00:32:38.120 But this is, I can't tell you a little bit in the future.
00:32:43.600 and we can map it to a certain number of qubits over here.
00:33:03.800 But actually, you see these things as the starting point
00:33:07.720 of a development where these devices, you know,
00:33:12.280 we might be able to solve some difficult problems
00:33:15.240 that classical computers might not be able to solve.
00:33:26.240 So these gates became so accurate in the meantime,
00:33:29.360 that you can do 220 gates before the whole system falls apart.
00:33:35.400 I mean, given that you could write your nature paper,
00:33:38.160 you know, 15 years ago, if you're able to do a single gate,
00:33:43.400 So things are becoming sort of a certain maturity
00:33:49.480 There's also another way of doing quantum simulation,
00:33:56.280 which is what we call analog quantum simulation.
00:34:12.440 that you mimic directly the corresponding Hamiltonians,
00:34:24.640 and these lasers will distort these ion crystals,
00:34:28.680 you get effective spin interactions out from this whole thing,
00:34:33.280 allowing you to realize the model of this type.
00:34:47.440 moves here to the left and moves also here to the right,
00:34:56.520 to the left, it means that if the spin up is on the right,
00:34:59.560 then there's a spin down and the left advice versa,
00:35:02.080 so you get sort of EPR type entanglements over here,
00:35:04.760 and that's exactly what these experiments sort of
00:35:08.040 So we have the possibilities to build all of these very
00:35:14.400 and of course that's here, in the case of one D,
00:35:23.440 the experimental situation is on the atomic physics side,
00:35:26.480 on the atomic physics side, we have now systems available.
00:35:33.840 where we can essentially have complete control,
00:35:37.320 either in the sense of building little half of models,
00:35:40.240 or in building, for example, with rigberg atoms,
00:35:42.920 rigberg arrays over here, and what these rigberg arrays do
00:35:46.360 is that they allow one sort of to really one by one
00:35:49.680 build quantum systems, and engineer their corresponding
00:35:52.960 interactions, so we have to hold two box available in the laboratory,
00:35:59.160 that you would like to implement, there's a good chance
00:36:01.920 that the experimentalists at the moment will be able to do that,
00:36:05.280 and of course, here the ion traps is one example.
00:36:08.920 What's really interesting is that in these atomic systems
00:36:11.800 that we have to have complete control by being able to talk
00:36:18.560 This is control on the absolute level of single-quanta,
00:36:22.640 of the system, you cannot get more quantum control
00:36:29.000 that if you take new tools like the quantum gas microscope,
00:36:41.200 in the quantum, many body system complete control
00:36:45.720 in this program quite proud, because many of these ideas,
00:36:48.520 like this, how about models, the ions, and also rigbergs,
00:37:00.640 And this sort of now takes me to the little bit new part
00:37:08.200 What do we, what can we do now based on this experimental progress?
00:37:11.960 And I want to summarize here by simply saying that, well,
00:37:21.040 could do these experiments with very high repetition rates.
00:37:39.560 And at the end, these leads that do a whole new generation
00:37:53.320 But before I do that, I want to sort of highlight
00:37:59.280 is very exciting related to rigbreak atoms in these systems.
00:38:11.320 And it's a very beautiful example of kind of an bottom-up
00:38:15.080 kilo engineering that one does of really being able to control
00:38:33.320 And if you do any of them, which is very easy to do,
00:38:35.520 hello, some of them will have an atom, some of them not called.
00:38:41.320 remove entropy by hand by simply finding out which ones
00:38:44.240 are occupied or not by simply seeing the fluorescence.
00:38:47.320 So this allows you in a way sort of to build a quantum system,
00:38:52.040 kind of bottom-up, and I want to show you examples.
00:38:55.040 The first line, you know, is sort of this is film,
00:38:59.480 You can simply rearrange all of these things you together.
00:39:05.480 play the experimentalist appear, you can even, you know,
00:39:15.440 So these are really sort of bottom-up design, you know.
00:39:19.960 with this kind of interaction, you can do these things
00:39:32.560 So we're getting at the point where we can really, really
00:39:46.360 and I will not try to play the role of the atomic physicist,
00:39:50.120 then you can essentially design models that you want
00:39:57.360 So the bottom line of the story that you should sort of take
00:40:00.640 as a take-home message is that, for the next moment,
00:40:03.640 point of view, the systems have been developed, you know,
00:40:08.760 many body systems, and it's called the many body systems
00:40:11.800 can be controlled, you know, on the level of talking
00:40:14.760 to these atoms or spins or qubits individually,
00:40:18.360 turning on interactions that will, if you can really sort
00:40:30.360 Now, given all of that, and the main thing comes back now
00:40:33.240 to theorists, and you have to provide now ideas,
00:40:36.960 and sort of, you know, come up, can be answered
00:40:38.760 now questions based on these things that are maybe interesting.
00:40:42.360 And I would like to present now a few slides on ideas
00:40:47.280 that started some time ago, it's purely theoretical ideas,
00:40:53.080 that, you know, we convinced the experimentalists go
00:40:55.480 to the lab and try it, they tried it, and it works.
00:40:57.720 So I will tell you now a story that sort of, you know,
00:41:00.600 motivated one hand by new experimental possibilities
00:41:06.800 experimental realization, and all of these things
00:41:17.280 and all of these things, we talk about entanglement
00:41:43.320 So these are the kind of things that they are asked.
00:41:46.040 And so here, we are called the many body system
00:41:50.200 that is subdivided A and B, and we would like to measure,
00:41:54.040 for example, here, define the reduced density matrix,
00:42:00.600 For example, it's a ground state of a certain system,
00:42:11.640 it's that our power of row to here to the power n.
00:42:14.840 And this, if you are a quantum antibody person,
00:42:21.200 set the biological or strongly correlated quantum crazy.
00:42:26.360 you know, that are available in these experiments
00:42:34.360 So the question is, can we actually measure things
00:42:39.040 Well, some time ago, we were interested in the story,
00:42:42.200 and as you will see, our black had been again now
00:42:52.840 And the idea is that if I have to one copy of the system,
00:42:56.280 then the second one, so I've had tensor product over here,
00:42:59.960 there's protocols that allow one to extract the trace
00:43:13.280 where actually these things could be implemented.
00:43:15.560 And here's an example that you have two copies,
00:43:20.200 These are Harvard models that are being implemented,
00:43:39.640 you know, quite some time ago, was the following one,
00:44:06.840 that the trace of row to the power n, you know,
00:44:12.280 or this tensor product of this density matrices here,
00:44:14.960 just the expectation value of this quantity over here.
00:44:25.400 which are these many entropy that one is interested in.
00:44:45.080 converts these things at the end to row one, row two.
00:44:47.800 And that's exactly what we would like to do in our systems.
00:44:51.360 Well, it turns out that what I'd like to add in mind,
00:44:57.880 and actually these things would be pretty tough
00:44:59.800 to build and you need the real quantum computer
00:45:03.680 Now, we came up with ideas how you can actually avoid
00:45:10.360 And this led to, without telling you the details of this,
00:45:14.960 to these protocols that underlie these experiments,
00:45:17.560 that these are same middle papers by Malcolm's gliner,
00:45:32.160 But at the same time, I think it is also something
00:45:37.320 And this is, I would like to measure rainy entropies
00:45:45.200 So these were theoretical ideas that are not even one year old,
00:45:53.080 to our previous evidence, Benoit Vermez for all of that.
00:45:58.840 with the Ignat CCRX sort of reviving over here,
00:46:01.160 and there's even one of the resident ICTP physicists here,
00:46:05.640 a large trailer that participated in this work.
00:46:09.920 So, I find these ideas behind this actually very cute.
00:46:14.640 so let me tell you what the underlying ideas are.
00:46:18.320 What we would like to do is sort of play a replica trick.
00:46:21.640 You know, if you have two copies of the system,
00:46:39.840 You know, there's usually more mathematical trick,
00:46:44.960 which at the end becomes a real measurement protocol.
00:46:50.400 Well, I go back to note paper by Stephen Fanank,
00:46:55.880 that suppose that you got a spin system over here,
00:47:16.280 that we find over here are just given by this formula.
00:47:32.280 then of course the answer for these probabilities
00:47:34.480 will be very boring because all of them will be,
00:47:41.960 But what's very interesting is that if you look at the square
00:47:47.040 then you find that indeed here is your rainy entropy appearing.
00:47:58.040 Okay, and if you ask yourself why is it the case?
00:48:01.720 Well, let me just write down the P squared over here,
00:48:04.320 and I write it now just taking the formula over here twice,
00:48:09.400 And now you can see it's like by having this square over here,
00:48:12.800 the sort of making two virtual copies of the system here.
00:48:16.560 And if our unitary operator that we have for we here
00:48:32.440 And this is the one that makes the magic of it,
00:48:40.840 In quantum information, this is called two-design
00:48:46.480 And so you can see that if in a system like that,
00:48:54.680 interesting stuff like some example rainy entropies,
00:48:57.600 a scientist, an indicator, a quantifier of entanglement
00:49:04.800 and how many measurements the unitary is we need.
00:49:12.920 and then I'll show you some experimental results for that.
00:49:27.880 maybe on the quantum computer or the quantum simulator.
00:49:38.240 And the way that we do it is that the random unitaries
00:49:51.680 So I can go in, for example, and make a random disorder
00:50:07.560 you know, with different disorder systems over here,
00:50:18.400 that we have to program in an experiment like that?
00:50:29.520 are experimentally available like a derivative system.
00:50:32.040 So you can see that if I do about 10 disorder patterns,
00:50:56.560 And if you ask yourself how fast as it converged,
00:51:04.280 with the system size, which is your subsystem size
00:51:10.120 These are sort of theoretical checks that we do over here.
00:51:13.560 So in that sense, we have an efficient generation
00:51:29.280 construct a measurement protocol out of these things
00:51:49.800 with random gates that people are trying to do,
00:51:58.280 But in our case, I would say we get these things,
00:52:07.720 that we have here a sequence of random unitaries
00:52:13.880 and here the quantum Gauss microscope comes in.
00:52:16.400 All of these tools are available in the laboratory.
00:52:21.480 The question is about how often do we have to repeat all of that.
00:52:25.560 And the answer is, well, there's a certain scaling
00:52:31.880 What it simply means is that in these experiments,
00:52:39.800 no, for the system sizes that we can do in our context.
00:52:47.320 Well, maybe you would like to see something like an aerial
00:52:52.960 that take a certain subsystem out of over here,
00:52:58.360 it simply means that the entropy will scale proportional
00:53:02.160 to the circumference of this area that you have over here.
00:53:06.440 And indeed, if you make the system large enough,
00:53:18.080 So this is would be a way of experimentally measuring
00:53:22.720 And I think this is now sort of constructing tools
00:53:30.480 and you would like to see that you have entropy growth,
00:53:39.400 it can use our protocol and be applied it, you know,
00:53:42.720 and you can see this is sort of the simulated data points,
00:53:45.440 and this would be a simulated measurement over here.
00:53:48.360 So we see the possibilities that these new tools
00:54:21.840 so this thing should go down to zero on the right-hand side
00:54:30.880 in these crunch dynamics that we have for, you know,
00:54:39.680 And I would say that we have the tools now available,
00:54:44.320 to it's testing what we call this quantum supremacy.
00:54:50.280 that we have here, of course, are available for many systems.
00:54:55.680 and quantum computers, so they'll be doing networking
00:55:10.600 networking of quantum computers with these things here.
00:55:19.640 of the snapshot of these demands triggered 25 years ago
00:55:30.200 I guess we've got new and interesting physics out
00:55:42.080 the medalist here again for the pioneering work.
00:55:47.080 You know, it started all by the ideas of these gentlemen.
00:55:56.600 we hear essentially about quantum technologies.
00:55:59.200 I think we should not forget, there's a synergy.
00:56:03.160 There's an intimate connection between basic science
00:56:07.960 If somebody tells you that building a quantum computer
00:56:11.040 is just now an engineering task and nothing more,
00:56:15.000 I would say that a lot of the basic science questions
00:56:19.560 but also on the conceptual side are still open.
00:56:27.160 And then you hear discussions about the flagship,
00:56:41.040 because you can see that there's a long history now
00:56:43.720 behind it and the time the engineers take these things
00:56:57.680 Thank you very much, Peter, as a great presentation.
00:57:15.840 We have very short time, but any other question
00:57:24.240 Thank you very much, really, it's a perfect talk.
00:57:51.280 but I was reading the people's discussion about the Discord.
00:57:57.920 Okay, so you would like to measure Discord originally.
00:58:02.000 of measuring Discord, but I would say that, you know,
00:58:07.320 I would say, real thing of really this entanglement
00:58:12.360 that's sort of interesting from the antibody point
00:58:23.200 from a condensed matter point if you would real thing,
00:58:25.800 you know, it's like Coca-Cola and Pepsi, you know.
00:59:33.640 too much credit that I deserve because, you know,
00:59:36.640 when it comes to this particular field, at some point,
00:59:39.640 it was absolutely essential to be taken seriously.
00:59:44.640 And when you convince experimentalists to do something
00:59:47.640 in this particular area, and I thought that people like
00:59:51.640 Peter Solar and Ignatius Iraq were ideal people who,
00:59:59.640 experimentalists are trusting that kind of people.
1:00:01.640 They wouldn't trust those wacky individuals working
1:00:03.640 in this quantum information science at the very beginning.
1:00:08.640 oh, could those go to Peter and Ignatius for spreading
1:00:11.640 the word and this kind of contaminating experimentalists
1:00:23.640 congratulating the three people who got the direct prize,
1:00:37.640 And I have to say that, you know, when I was asked to give
1:00:39.640 this talk, I really didn't know how to structure this talk
1:00:42.640 because, you know, on one hand, I wanted to say something
1:00:47.640 that's such a vast area of papers that were produced
1:00:54.640 it was very difficult to find a theme that would somehow
1:01:01.640 And also, you know, I was kind of biased because David
1:01:04.640 was effectively my supervisor back in Oxford
1:01:07.640 and he's the person who, in many ways, changed my life.
1:01:12.640 So, then, of course, you know, through David,
1:01:16.640 I made Charlie Bennett and then I had also pleasure
1:01:20.640 to meet Peter and the two of the three of them, in fact,
1:01:29.640 they just made quantum information science respectable
1:01:33.640 think and deep and profound subject, but also they created
1:01:45.640 And somehow, this area of quantum information science is still
1:01:49.640 the area where people are, you know, very friendly,
1:01:52.640 very willing to work together and collaborate.
1:01:55.640 And that's sort of, it started from the very beginning.
1:02:00.640 So, you know, working with David, of course,
1:02:03.640 was experienced and I would have too many anecdotes to tell,
1:02:07.640 but I'm not going to tell them, don't worry David, I haven't.
1:02:12.640 But it's not only me, you know, but also whenever I got a PhD
1:02:16.640 student, sooner or later, they sort of moved in the direction
1:02:19.640 of David and talked to David about science,
1:02:25.640 In fact, you know, my first conversation with David
1:02:31.640 And so, I just realized that I found a fellow
1:02:40.640 But, you know, all my students, almost all my students ended up
1:02:44.640 So, Gianna Barranco worked on the universality issues.
1:02:50.640 Then Patrick Hayden worked on reformulating
1:02:55.040 in Bell theorem, and David Wallace worked on interpretations of
1:03:01.040 Now, Chiara Marletta is working on construct theory.
1:03:04.040 So, in a way, it's kind of very easy for me to supervise
1:03:09.040 So, why don't you just go and talk to David, you know?
1:03:12.040 And, you know, it was already mentioned that this field
1:03:22.040 And, you know, few, at the very beginning, it was pretty much
1:03:26.040 There were, you know, when you look at this picture that was,
1:03:29.040 I don't know which year it was taken in 1993 or so,
1:03:37.040 it was just, you know, pretty much everyone
1:03:41.040 Well, Charlie may actually give you a little bit more
1:03:44.040 history of predating this particular meeting,
1:03:47.040 but as far as I'm concerned, you know, at the time,
1:03:50.040 there were not so many people who were interested
1:03:58.040 early meetings in quantum information science,
1:04:01.040 where David and Charlie and Peter attended,
1:04:07.040 why do you like, well, you know, Peter asked,
1:04:14.040 Giuseppe Castanioli, who was one of the directors
1:04:30.040 but he had some ideas about quantum computing.
1:04:33.040 He wanted to somehow, you know, sponsor something.
1:05:08.040 But, you know, various people came at different times,
1:05:12.040 and Charles wanted to have them all in the picture.
1:05:17.040 I got an artificial head popping up so that,
1:05:30.040 So, which, by the way, I remember that, you know,
1:05:35.040 to a popular lecture in the University of Belfast.
1:05:39.040 So, I went to Northern Ireland and I just gave a talk
1:05:47.040 No matter what sort of directions you are coming from.
1:06:06.040 This talk is still remembered in the Queen's University.
1:06:29.040 I actually, I don't know whether I'll have any real control
1:06:43.040 which is something that I had lots of personal interest in.
1:06:47.040 Now, as it happens for some reason or the other,
1:06:50.040 the development of quantum information science
1:06:52.040 had an impact on quantum, on data security too.
1:07:03.040 affects the security of public key crypto systems,
1:07:11.040 for example, if you look at the cryptocurrency,
1:07:19.040 for the whole thing to work, are digital signatures,
1:07:24.040 which can be broken with Peter's algorithm.
1:07:32.040 that can be seriously affected if you can do quantum search,
1:07:45.040 they have a serious impact on the future of information security.
1:07:52.040 So, in this sort of history of the development
1:07:57.040 of cryptography that you can give a separate lecture
1:08:01.040 on how it all started, how it all developed,
1:08:04.040 how people wanted to design perfect size first,
1:08:11.040 and go through the public key crypto systems
1:08:24.040 how we can take the ideas of quantum correlations
1:08:31.040 that's a quantum entanglement to the extreme,
1:08:36.040 which comes as close as one can possibly come
1:08:42.040 And so, this, so the fact that on one hand,
1:08:53.040 to design possibly new generation of public key cryptosystem
1:08:57.040 that will resist attacks from quantum computers
1:09:02.040 national security agency and some other people
1:09:08.040 going some directions possibly lattice-based cryptography,
1:09:14.040 for that is quantum cryptography, of course.
1:09:30.040 you can do quantum cryptography in all kinds of ways.
1:09:34.040 Originally, the idea came from Stephen Visner
1:09:47.040 which I will take, not because it is my approach,
1:10:04.040 and also it will take me to some speculations
1:10:30.040 have the same random sequence of zeros and ones,
1:10:34.040 and it's not only to them and not to anyone else,
1:10:37.040 then they can build secure communication very easily at them.
1:10:54.040 that those sequences are really unpredictable
1:11:15.040 using a one-time path, which is one of the oldest
1:11:29.040 with the strings of binary strings of zeros and ones
1:11:38.040 is to use the properties of quantum entanglement,
1:11:41.040 and explore something that we call monogamy
1:11:45.040 of entanglement or monogamy of quantum correlation.
1:11:55.040 the stronger they are correlated with each other,
1:11:57.040 the less they are correlated with anything else.
1:12:02.040 and see that the two entities are really strongly correlated,
1:12:07.040 but there's a rule of the monogamy of entanglement
1:12:11.040 that there's no correlation with anything else.
1:12:14.040 But therefore, nobody outside those two entities
1:12:18.040 So, one way to do it is to run the bell test,
1:12:25.040 for the local realism, but not necessarily going
1:12:31.040 I just simply use it in a very instrumental way
1:12:33.040 as something that you have correlated particles.
1:13:01.040 but it's all just the question of implementations.
1:13:06.040 All good cryptosystems, fantastic cryptosystems,
1:13:09.040 usually fail because of some lousy implementation.
1:13:12.040 So, can you then somehow deal with the fact
1:13:17.040 that experimental implementations may not be perfect?
1:13:44.040 in the implementations of quantum cryptography.
1:13:57.040 who is probably the most known quantum hacker.
1:14:00.040 So, the guy is basically very clever experiments.
1:14:02.040 This who knows that currently you cannot really implement
1:14:37.040 As long as you can reach the level of implementation
1:14:42.040 which are called sort of the loop-hole-free test.
1:14:46.040 So, if you reach a certain precision level,
1:14:54.040 and with setting up this experiment in a certain way,
1:15:07.040 you can, by measuring the degree of correlations alone,
1:15:11.040 you can say whether something is secure enough.
1:15:16.040 you know that there are no side channels to this game.
1:15:19.040 But we refer to this as a device independent cryptography.
1:15:25.040 Then of course, you know, in order to do this,
1:15:32.040 Alice and Bob, the two people who want to establish
1:15:35.040 this cryptographic key, have access to some truly local
1:15:45.040 So, I'm talking about a scenario where Alice and Bob
1:15:59.040 look, I'm selling you those at some discounted price.
1:16:10.040 But nonetheless, if you take those devices,
1:16:13.040 you can, without knowing really what they are doing.
1:16:24.040 I can use those correlations to generate cryptographic key.
1:16:28.040 So, that's sort of a beauty of this result.
1:16:35.040 you have to also rely that you have a source of
1:16:41.040 And so, that would work as long as you can trust
1:16:45.040 those random number generators that you have
1:16:52.040 So, now, the most dangerous scenario in this case
1:16:55.040 is that you have this device independent system,
1:17:02.040 those devices from someone whom you don't trust.
1:17:06.040 But if, by mistake, you also purchase a random number generator
1:17:09.040 from that person, so that that unfortunately wouldn't work.
1:17:14.040 that your local randomness, your local random number generators
1:17:28.040 So, for example, you can just purchase a quantum random
1:17:35.040 But, you know, those kind of random number generators
1:17:38.040 that you can get today are probably not good,
1:17:42.040 because, you know, even if you get those random number
1:17:52.040 do some kind of run, some kind of a simple test
1:17:55.040 and see whether those random number generators are genuine,
1:18:03.040 So, this brings us to sort of like a question
1:18:09.040 that is basically the question that I want to address here
1:18:14.040 So, given the suppose you want to get the random number generator
1:18:18.040 and you are given someone brings you a black box
1:18:25.040 and use this random generator for cryptographic purposes.
1:18:29.040 Would you be able to check that this random number generator
1:18:37.040 So, what do you request from this random number generator?
1:18:42.040 So, you would like the string of 0's and 1 that is generated.
1:18:47.040 You such that, you know, that's a uniform distribution.
1:18:53.040 The frequency of all pairs and subset of 0's and 1's is the same.
1:18:58.040 So, those are sort of the regular classical well-established
1:19:03.040 test for randomness. But there's more if you want to use it for cryptography
1:19:07.040 that you also like to test that this is truly unpredictable
1:19:11.040 that there's no copy of this device so that, you know,
1:19:14.040 you can easily imagine a situation where someone would just generate
1:19:19.040 two identical random number generators and one would be
1:19:22.040 stored and would generate exactly the same sequence
1:19:26.040 and it will pass, you know, you look at yours
1:19:29.040 and it will just pass all the statistical tests for randomness,
1:19:32.040 but in fact, it's not a private randomness.
1:19:35.040 So, this is not unpredictable because there is a person
1:19:39.040 somewhere who can actually tell exactly what kind of random
1:19:45.040 So, today, when you buy a random number generator
1:19:51.040 and you want to use it say for cryptographic purposes,
1:19:54.040 usually it comes with some kind of certificate.
1:19:57.040 Because, you know, you yourself as the end user.
1:20:00.040 You just, you open this box, you may look inside
1:20:05.040 It's just most of electronics and gadgets there and you don't know
1:20:12.040 So, you basically ask for a certain certifying authority
1:20:16.040 to let you know whether this device is good or not.
1:20:20.040 So, for example, I'm showing you one of quantum random
1:20:23.040 number generators here that is produced by a
1:20:30.040 And usually when you get it, you can get a certification
1:20:33.040 from relevant Swiss agencies saying, you know,
1:20:37.040 we look into this and we can certify that it's done
1:20:40.040 and produced in such and such way that it generates
1:20:45.040 randomness that is kind of a private randomness
1:20:51.040 The question I'm asking now is it, you know,
1:20:56.040 and if you sort of like a bit contrary in a
1:21:03.040 So, you would like to test yourself whether this device
1:21:18.040 computer scientists have all kinds of ideas
1:21:20.040 how to amplify randomness, how to take something
1:21:28.040 So, you can use private simplification, for example.
1:21:35.040 even sort of a source of randomness that is not good.
1:21:40.040 That really, there are really no classical way
1:21:45.040 of improving a certain class of randomness.
1:21:50.040 a popular sources of randomness that computer scientists
1:21:53.040 study, I call it the Santa Vazirani sources,
1:21:55.040 and it's known that there is basically no way
1:22:06.040 There's no classical processing of this randomness
1:22:27.040 in a rating such a way that you can just, you know,
1:22:32.040 get two outputs and you can measure the correlations
1:22:38.040 And then, basically, pretty much by the same argument
1:22:45.040 you can then sample from one of the outputs
1:22:51.040 as long as there's a little bit of true randomness
1:22:59.040 and get a device that gives you not only uniformly distributed
1:23:05.040 but also completely private sources of randomness.
1:23:12.040 that even if you get a lousy random number generator
1:23:14.040 that you don't trust, with a little bit of post processing,
1:23:32.040 And then, you know, there are many ways of doing this,
1:23:36.040 and I think I just wanted to say that, you know,
1:23:40.040 you can use all kinds of belliness qualities,
1:23:44.040 not only the most populous, the adjacent inequality,
1:23:47.040 but, you know, the story, basically, is at the moment,
1:24:06.040 for correlations, for monogamous correlations,
1:24:09.040 you can get devices that you can test for security
1:24:21.040 You can also, you know, test for the sources of the local randomness,
1:24:28.040 so that means that you can push the concept of privacy
1:24:34.040 So, basically, you don't have to know anything
1:24:37.040 about the underlying physics in this device.
1:24:40.040 All you have to do is just to make some statistical test,
1:24:44.040 and no matter what is the underlying physics that you will be able,
1:24:49.040 at least to make statements about privacy of this data,
1:24:55.040 But, you know, so this is actually the story where,
1:24:58.040 if you want to push cryptography or the story of privacy
1:25:02.040 to the limits, this is basically where we can,
1:25:06.040 at least, you know, at the very speculative way.
1:25:08.040 I mean, I'm not saying that this is actually implemented.
1:25:16.040 local free tests of the value in the qualities.
1:25:20.040 What is interesting, though, is that, in my view,
1:25:26.040 and I can develop it into some more coherent,
1:25:28.040 and I can give more technical, more consistent review of this field,
1:25:32.040 quite often when I do this, I feel that, you know,
1:25:35.040 there's a little bit of a superficial approach to this,
1:25:42.040 Because it's, you know, very nice mathematically,
1:25:45.040 it's sort of simplified, but if you go to the bottom of it,
1:25:51.040 There's lots of, you know, lots of interesting questions,
1:25:56.040 For example, you know, those input-output boxes surely,
1:26:01.040 it is not the case that they're just mathematical devices,
1:26:07.040 and if you look at them and they have to be quantum,
1:26:10.040 and the question is, you know, how do you operate this,
1:26:13.040 and how do you understand the whole notion of secrecy
1:26:27.040 then you have to somehow redefine the notion
1:26:30.040 of secrecy in terms of relations between different universes,
1:26:41.040 in one particular part of the multiverse is restricted
1:26:50.040 the access, how the access is sort of restricted
1:26:57.040 And then, you know, there's a whole thing about the random,
1:27:02.040 as the random has always provoked lots of interesting discussions,
1:27:07.040 going back to the past, you know, the question was,
1:27:13.040 Do we have truly random phenomena in nature?
1:27:22.040 point of view taken by, say, a pickers who would say,
1:27:27.040 yeah, atoms, you know, swear for every now and then,
1:27:35.040 perhaps on the other side of this spectrum,
1:27:37.040 was the marketers who was saying, well, you know,
1:27:43.040 and it's just, what is random is due to the lack of your knowledge,
1:28:14.040 In fact, probably I would like to finish with this statement
1:28:18.040 from David, I took it from the new scientist article,
1:28:28.040 it's just, you know, a valid question at this point
1:28:43.040 physics where we don't use the notion of randomism
1:28:52.040 And I think I will probably stop at this point
1:28:59.040 it was sort of like a talk where I was trying probably
1:29:06.040 and the idea of pushing privacy to the limits
1:29:11.040 creates, generates lots of interesting questions
1:29:19.040 is the fact that somehow more and more often
1:29:25.040 in a rather technical and precise language.
1:29:35.040 Charlie David and Peter for helping to create
1:29:39.040 this fantastic field, and this need less to say
1:29:43.040 this field will suddenly thrive for years to come.
1:29:57.040 I have to thank you for the very inspiring presentation.
1:30:07.040 Reminiscence, because I've taken a lot of these
1:30:09.040 group conference pictures, and one of the main
1:30:15.040 are like hurting cats, so you announced there's a
1:30:17.040 group picture and a lot of the people miss it,
1:30:28.040 and a lot of people failed to show up for the group picture,
1:30:33.040 so I took them later on and then just cut their heads
1:30:43.040 OK, so I'm sure there's plenty of things to think about
1:30:49.040 this presentation, but there is coffee outside.
1:30:52.040 We're running very well on time, so there is a 15
1:30:54.040 minutes for coffee, and we come back at for 15.
1:50:13.540 So now we will move to the next part of the event, which is more than the medals and the present
1:50:40.540 Here is the plan mathematics from MIT in 1985.
1:50:51.540 Peter boosted the field of quantum computation by assigning efficient quantum algorithms for
1:50:57.540 factoring large numbers and computing discrete algorithms, each of which can be used to break classical
1:51:12.540 He does prove that a quantum computer could solve a useful hard computational problem exponentially
1:51:11.540 faster than any known classical computer algorithm.
1:51:16.540 Schor also introduced quantum error correcting codes and fault-tolerant quantum computation, which
1:51:22.540 are a scheme for copying with the effects of stray interactions noise is disturbing qubits.
1:51:29.540 The robust quantum error correction large scale quantum computation could be a scheme by the extreme
1:51:40.540 Instead, the theory of quantum error correction is now a well established branch of quantum
1:51:45.540 information science and the difficult path to developing large scale quantum computers appears
1:51:52.540 And Peter will give the presentation and the title will be, I will just read it, the discovery
1:52:02.540 But before that, I will ask Peter to come here to, I can give you the rectangle and everybody
1:53:18.540 Okay, so I want to talk about, you know, the inspiration for discovering the factoring
1:53:25.540 algorithm and some reminiscences about, you know, what, took place when I discovered it
1:53:35.540 I want to give the first few slides of my 1990s factoring talk somewhat updated because,
1:53:42.540 well, they'll show you why the factoring algorithm is such a surprise.
1:53:47.540 And then I want to talk, say, a few words about how I actually discovered the factoring
1:53:53.540 one is saying a few words about what happened after I discovered it.
1:54:02.540 I was saying, what is the difference between a computer running physics experiment?
1:54:06.540 And of course, back then, I was like the joke.
1:54:09.540 What's the difference between an elephant and an egg?
1:54:14.540 So, first answer, of physics experiment is a big custom-built, finicky piece of background.
1:54:21.540 And the computer is a little box that fits in your briefcase.
1:54:25.540 So, for example, and you can see neither of these existed 20 years ago when I discovered
1:54:32.540 Here is a computer, and here is a physics experiment.
1:54:35.540 But if you go back, you know, 50 years before that, here is a computer.
1:54:52.540 And you can even see that the technicians were in the same uniform.
1:55:00.540 This is the Berkeley Particle Accelerator, and this is Iniac.
1:55:04.540 First computer that normally would work on.
1:55:17.540 And if physics experiment answers physical issues.
1:55:20.540 So, for example, if you want to test whether all bodies fall in the same length,
1:55:31.540 And if you want to test whether 15, you want to find 15 equals x times y,
1:55:37.540 you'll probably don't want to use physics experiments.
1:55:40.540 So, this is an ion trap computer, and a Rhino-blots group,
1:55:47.540 and it's an Austria, where it actually did the experiment of factoring 15 using an ion trap.
1:55:55.540 And I'm always afraid when these papers come out that some headline is going to go
1:56:02.540 up here in a newspaper somewhere, physicists spend $2 million,
1:56:15.540 And a third answer is that you don't need to build a new computer
1:56:21.540 for each mathematical question you want to answer to.
1:56:24.540 This is really a very, actually, fundamental about computation.
1:56:33.540 And what that means is that you can master the computer's
1:56:40.540 So, for example, after the cover-tron, it solved all the
1:56:45.540 processes, the questions of this capable of, people built the LHC,
1:56:55.540 and when the LHC solves, when people discover all the physics they can at the LHC,
1:56:59.540 they're going to have to come up with a lot of money to build a new one,
1:57:03.540 or stop running, practical accelerator experiments.
1:57:08.540 So, no one would think of building more than one LHC because that would be really
1:57:16.540 And then there's a lot of physics, condensed matter physics of the LHC is
1:57:22.540 completely useful, whereas if you have one big computer,
1:57:27.540 much one adding mathematical problem you want on it.
1:57:32.540 And this is related to the universality of computation.
1:57:36.540 So, back in the 1930s, there were three people,
1:57:39.540 there were islands of church, Alan Turing, and Kleenie,
1:57:44.540 and they all had completely different looking definitions of computation.
1:57:49.540 What does that mean for a function to be computable?
1:57:52.540 But it turned out they gave the exact same class of computational functions.
1:57:58.540 And what church and Turing proposed was that this was really a very
1:58:08.540 But when people started building wheel computers,
1:58:12.540 this turns out that the definition of computational for a function to be
1:58:19.540 computable really wasn't that useful in practice.
1:58:22.540 For example, if you have a comp function that can be solved,
1:58:26.540 computed, and tend to the 30th years, well for practical purposes
1:58:34.540 So computer scientists made this rather, well,
1:58:44.540 draconian compromise between theory of practice,
1:58:48.540 where they came up with the idea that efficient means it can be
1:58:51.540 computable and polynomial time in the length of its input.
1:58:57.540 So, I mean, it's not really, doesn't really correspond to
1:59:09.540 but it's also something that computer scientists could prove their own
1:59:19.540 once you have the definition of efficient as being computational time,
1:59:24.540 you know, just directed quantitative churches thesis,
1:59:28.540 which was proposed many different times in the 1960s
1:59:35.540 But I think column is actually the first, you know,
1:59:41.540 any computation that any device can perform efficiently.
1:59:46.540 And I don't know how widely recognized was that this is
1:59:51.540 really a statement about physics, rather than about computation,
2:00:00.540 But in fact, if you have different laws of physics,
2:00:03.540 you might be able to compute different things efficiently,
2:00:08.540 It was one of the people to point out, I believe,
2:00:10.540 where several other people were pointed out.
2:00:21.540 The really surprising thing is that this would imply
2:00:43.540 as well, how much faster is a quantum computer than a classical computer?
2:00:51.540 An answerable question, because quantum computers
2:00:54.540 did have some problems by exponential analysis
2:00:58.540 and the speed of other computational problems not at all.
2:01:02.540 So the fact that this misconception is so widespread
2:01:08.540 it really means that the public out of this world
2:01:18.540 where we have convinced the public that quantum computers
2:01:22.540 don't just speed up everything by one number.
2:01:28.540 But that took a long time of planning to do.
2:01:38.540 So my first exposure to quantum computing was when I heard it talk
2:01:44.540 At the last, about quantum key distribution here is,
2:01:48.540 so I'm sure that Charlie is going to mention this in this talk,
2:01:58.540 basically on a tiny budget, a little quantum key distribution device.
2:02:07.540 And this, apparently, is what it took for them to get physicists
2:02:14.540 So I was very intrigued by Charlie Bennett's result,
2:02:21.540 and I went around and looked at papers about quantum computing
2:02:27.540 and the literature, and there really was not very many of them,
2:02:31.540 and most of them were written by David Deutsch.
2:02:39.540 Well, first, neither Charlie nor David Deutsch convinced me
2:02:43.540 that there was a mathematical rigorous description of one computing,
2:02:48.540 not looking back at David's papers in retrospect.
2:02:55.540 but had I also was not convinced at all that it was at all useful,
2:03:07.540 but that was, I don't think David's papers had any really useful algorithms in them.
2:03:20.540 Ummish Vaserami gave a talk, and Bella asked about the paper,
2:03:23.540 quantum complexity theory, wrote with Ethan Bernstein,
2:03:27.540 and this had two really great advances in it.
2:03:32.540 First, it had a problem, which was a problem that no one would actually really ever want to solve,
2:03:39.540 and, but which quantum computers really sped up the computation of a classical computers,
2:03:48.540 and the other thing is, it had a rigorous definition of a quantum Turing machine.
2:03:56.540 I started thinking seriously about quantum computing,
2:04:00.540 whether it would be possible to speed up some real problems with quantum computers.
2:04:08.540 But I didn't get anything where, with this, until I saw time silence paper.
2:04:14.540 So, I was on the conference program committee, and Dan Simon submitted
2:04:18.540 the paper of containing his algorithm through this conference.
2:04:21.540 In fact, it was stopped in 1994, which occurred sometimes in the spring.
2:04:29.540 and I'm very embarrassed to say that the conference program committee rejected it.
2:04:34.540 So, I was not able to persuade the committee that this was a big enough advance over Ummish
2:04:43.540 was around, and he didn't burn Stein's paper, which had appeared in a previous iteration of this conference.
2:04:53.540 So, I mean, in retrospect, clearly I should have been jumping up and down, yelling at them,
2:05:01.540 this was the biggest mistake you could ever make, but I didn't know that at the time,
2:05:06.540 and I didn't jump up and down, and voted to reject it.
2:05:24.540 So, you have hypercube, and you color the point.
2:05:28.540 You color the points, vertices of the hypercube with one of two to the young minus one colors,
2:05:34.540 so there are exactly two colors, are two points labeled with each color.
2:05:40.540 And these points have to be periodic, so to get from a green point, to the other green point,
2:05:48.540 to say what you do is you take a vertical horizontal and right diagonal edge,
2:05:57.540 Vertical horizontal, right diagonal edge, that gets us to the same color,
2:06:01.540 and here, vertical horizontal, right diagonal, it's the same color.
2:06:08.540 So, now you have this hypercube with all these colors on it,
2:06:13.540 and what you're allowed to do is you're allowed to ask,
2:06:20.540 And you want to find this path from one point of the color to another point of the color.
2:06:27.540 Now, classically, the only thing you can do, keep asking,
2:06:34.540 random vertices are maybe nearly random vertices.
2:06:38.540 You can do a little bit better than random until you get two vertices on the same color.
2:06:44.540 And then you're done because you know what the path looks like.
2:06:50.540 One mechanically, so that takes a number of points on the hypercube,
2:06:55.540 which is, you know, two to the D minus one,
2:07:02.540 And one mechanically, you can really solve it in D queries to,
2:07:10.540 you ask D questions of points in superposition,
2:07:16.540 and you get enough information to tell you what D
2:07:32.540 So, silence algorithm really gave me all the hints I need
2:07:37.540 to discover, well, the discrete log algorithm.
2:07:45.540 but it's algorithm, periodicity, it's mod two.
2:07:48.540 The discrete log algorithm uses the Fourier transform,
2:07:51.540 it's mod two to the n, instead of the integers mod z.
2:08:06.540 But, you know, I knew the discrete problem would be solved by using
2:08:10.540 periodicity, silence algorithm used periodicity,
2:08:13.540 and I started thinking about it, and eventually I figured
2:08:20.540 Well, first, how does the faculty algorithm work?
2:08:23.540 You can think of the faculty algorithm as a computational
2:08:27.540 interferometer, maybe a computational diffraction rating.
2:08:31.540 So, what a diffraction grading does is it has a lot of
2:08:35.540 And when you shine colored light, the angle that reflects
2:08:40.540 off our angle, it makes when it goes to the diffraction
2:08:47.540 rating depends on the color, and that's because at certain
2:08:51.540 angles, all the wavelengths add up, so you get constructed
2:08:55.540 in interference, and all the other angles, the wavelengths
2:08:59.540 don't get up, so you get destructive interference.
2:09:02.540 So, the colors are separated by the angle that make coming
2:09:08.540 And the quantum Fourier transform really does the same thing
2:09:13.540 It separates the different possible periods of the periodic
2:09:16.540 function, so each different period results in a different
2:09:20.540 output of the quantum computer, and then from the output
2:09:25.540 And if you know some basic number three, which is well
2:09:31.540 For panelists, you can turn factoring into a
2:09:40.540 Okay, so what happened after the discovery?
2:09:48.540 So this was, I gave a talk at Bellang, so that the algorithm
2:09:53.540 for discrete log on a Tuesday in April of 1994.
2:09:57.540 The next weekend, Uma Shvazirani called me.
2:10:00.540 I was home in bed with a band called, and he asked,
2:10:04.540 said, I hear you can factor in a quantum computer and tell
2:10:09.540 So you can notice that the talk was about the discrete log
2:10:12.540 of the problem, and I had not actually solved the
2:10:17.540 And, well, I don't know if you know the child's
2:10:21.540 good game of telephone, but somehow the result turned
2:10:26.540 to factoring in both telling each other about it.
2:10:35.540 The five days there, and in those five days I had
2:10:48.540 I kept getting, you know, email requests for the paper,
2:10:55.540 So there were lots of different versions of
2:10:59.540 various drafts of the paper spreading around, and people kept
2:11:07.540 asking me questions about outdated drafts, which I had to
2:11:14.540 And in May, which was only a few weeks after I discovered
2:11:19.540 the factory algorithm, I gave a talk at the algorithm,
2:11:25.540 Lechteva talk at a Santa Fe Institute conference on quantum
2:11:29.540 information, and August, I gave a talk at a conference
2:11:33.540 in this, and I guess Arthur Eckert gave a talk in Colorado on
2:11:38.540 a comic optics conference, and in October I gave
2:11:48.540 And by that time, the paper was actually written.
2:11:52.540 I presented it at the Fox conference that November,
2:11:55.540 which Dan Sirens paper also added to that conference.
2:11:59.540 And one interesting thing is that I started describing quantum
2:12:12.540 computers as quantum Turing machines, which was what
2:12:18.540 But after I discovered the result, I started talking with
2:12:22.540 It's absolutely impossible to explain the quantum Turing machine
2:12:25.540 to a physicist that can't understand it because it's not
2:12:29.540 It doesn't really correspond to any actual experiment.
2:12:34.540 So I started using the quantum circuit model instead,
2:12:38.540 which I think was first described by David Deutsch.
2:12:43.540 And really, how the quantum circuit model got to be the
2:12:54.540 And let's see, I'm probably out of time, is that right?
2:13:02.540 So one objection to the doctrine result was if you needed to
2:13:05.540 do 10 to the night steps on a quantum computer, each gate had
2:13:08.540 to be out here to one part in 10 to the night.
2:13:11.540 Of course, this is completely out of the question experimentally.
2:13:15.540 And one of the biggest detractors of quantum computation was
2:13:23.540 Will Flandauer, who worked at the same place that Charlie
2:13:26.540 Bennett and David Deutsch and some other people working on
2:13:31.540 And I think Will Flandauer described the situation there as,
2:13:36.540 well, we have four people working on quantum computation and
2:13:39.540 one person working against quantum computation.
2:13:43.540 So there are, you know, so what's the argument?
2:13:48.540 Well, quantum computers can't be made full power.
2:13:52.540 You can't use, we don't see, because of the no cloning
2:13:55.540 theorem, which says if you start with a quantum state,
2:14:01.540 Can't measure to see if there's an error, because the
2:14:06.540 If it means that if you measure the quantum computation,
2:14:11.540 And then, of course, if the computation is disturbed,
2:14:20.540 though the quantum error-prepping codes exist,
2:14:24.540 and quantum computers can be made full-powering by using them.
2:14:30.540 Well, you'll arrange the codes so that likely errors are
2:14:35.540 And what that means is you can measure the errors without
2:14:47.540 there are fault-powered specials, the realms,
2:14:50.540 which say you only need gates accurate to maybe one part
2:14:56.540 This number really depends on the exact quantum fault-powering
2:15:03.540 And it's still unresolved as to what this number should be
2:15:14.540 there is fault-powered without using too much overhead.
2:15:19.540 So this is still very difficult experimentally,
2:15:25.540 various groups are coming really close to this number,
2:16:04.540 Very nice piece of history as a beautiful way to see how things
2:16:22.540 So there's a question from a YouTube viewer for Peter.
2:16:28.540 So what are the most significant reasons to think that factoring cannot be
2:16:32.540 following polynomial time on a classical computer,
2:16:35.540 apart from the fact that many people have failed to do so?
2:16:40.540 Well, actually, I don't think there are that many reasons.
2:16:50.540 one of the most famous and best number theorists around,
2:16:54.540 he thinks it's entirely possible there's a polynomial time
2:16:57.540 algorithm for factoring on a classical computer.
2:17:01.540 So the only real reason we don't think there is one is that nobody
2:17:08.540 And we think that we're smart enough that it existed.
2:17:11.540 It would have been discovered, which is, of course,
2:17:38.540 I will continue with our D, which is Charles Bennett.
2:17:46.540 Charles Bennett is an intellectual leader in quantum information science
2:17:54.540 He earned a BS in chemistry from Brandage University in 1964
2:18:02.540 for molecular dynamic studies, computer simulations of molecular motion.
2:18:09.540 one year as a teaching assistant about a genetic code
2:18:17.540 He continued his research under Anisur Raman at Argonne Laboratory.
2:18:28.540 to show that general purpose computation can be performed
2:18:32.540 by logically and thermodynamically reversible apparatus.
2:18:36.540 It's a little bit at a small company here that just...
2:19:01.540 of Maxwell's demo attributing its inability
2:19:08.540 So, to the top of the dynamic coast of this poison
2:19:39.540 Yes, with James Brasser from the University of Montreal,
2:19:49.540 a secret encryption key with security from Evers,
2:19:54.540 by the basic quantum limitations of measurements
2:19:59.540 Menet and collaborative resource introduced quantum teleportation,
2:20:03.540 whereby entanglement and classical singers are used
2:20:08.540 He and co-workers proved that a quantity called
2:20:11.540 the bi-moment entropy is the proper measure of entanglement
2:20:15.540 a nearly result in the quantification of entanglement,
2:20:18.540 which continues to be an active area of research.
2:21:25.540 Okay, and then Charles will give us a presentation building
2:22:04.540 I was here in the 1980s with Ralph Landauer,
2:22:08.540 and it's a place where a serious physics has been done
2:22:13.540 I'm going to talk about the culture of really the culture
2:22:28.540 information science was an abstraction from practical experience,
2:22:32.540 but the information revolution that we're still in the middle of
2:22:39.540 is from these two brilliant, I mean, almost brutal abstractions
2:22:45.540 by touring the idea of a hardware independent notion of computing,
2:22:51.540 And even more brutal idea that the theory of communication
2:22:57.540 is best developed by ignoring the meaning of messages.
2:23:01.540 So they did a tremendous service to humanity
2:23:11.540 They left out a couple of essentially mathematical properties,
2:23:17.540 which they thought were just physical stuff that wasn't really necessary to think about.
2:23:28.540 they thought were thermodynamic questions of not really much importance,
2:23:33.540 and superposition, which was the idea that was left out of Turing's theory
2:23:38.540 when he thought of it as a theory of computation.
2:23:42.540 I mean, in all of the 20th century scientists,
2:23:49.540 and they certainly knew about thermodynamics
2:23:53.540 but they just thought that wasn't so important.
2:23:56.540 Well, conventionally, the information carriers
2:24:00.540 are what a physicist would call a classical system.
2:24:05.540 and you can measure it without disturbing them,
2:24:07.540 and then to specify the joint state of two objects,
2:24:13.540 and what's in my right pocket, it's sufficient,
2:24:15.540 and sometimes necessary to describe the states of both,
2:24:21.540 But of course, quantum systems don't behave that way.
2:24:31.540 because people focused on the uncertainty principle
2:24:33.540 causing quantum systems to behave less reliably
2:24:38.540 And now, as we've heard from several of the speakers today,
2:24:44.540 there are positive consequences of quantum mechanics
2:24:52.540 is by my conversation with Stephen Wiesner,
2:24:58.540 And he had some ideas that things you could do with information
2:25:10.540 into a form where if you transmitted that message,
2:25:14.540 nowadays we would say multiplex them together,
2:25:17.540 so that the receiver can receive either one of them,
2:25:23.540 Now, that's impossible in Shannon's theory,
2:25:25.540 because you just make a copy and you decrypt it one way
2:25:29.540 So this, the idea that the uncompiability of quantum information
2:25:35.540 The other one was even more direct application of that idea
2:25:39.540 of the quantum bank note that cannot be copied.
2:25:42.540 Now, I guess I don't think the Euro notes have this,
2:25:45.540 but French and German bank notes used to have
2:25:49.540 a print explaining how many years in prison you would spend
2:25:52.540 if you had copied the duplicated the notes.
2:25:55.540 Well, anyway, I think he wrote a manuscript
2:26:02.540 which didn't get published until 15 years later
2:26:12.540 because he became interested in sort of political activism
2:26:18.540 So, but I think this notes that I took on in 1970
2:26:26.540 where the notion of quantum information theory
2:26:32.540 So then I went around talking to other people,
2:26:34.540 including David, and we've heard a lot of the rest of the history.
2:26:53.540 Like Peter just said, oh, well, I was only working on it part time.
2:26:58.540 So what's the difference between ordinary information
2:27:14.540 you can explain the notion of an entangled state.
2:27:16.540 But this doesn't work very well at the dinner party.
2:27:22.540 The quantum information is like the information in a dream.
2:27:26.540 If you try to explain what you're dreamed to somebody else,
2:27:30.540 you forget the dream and only remember what you said about it.
2:27:34.540 And of course, this means you can lie about your dream
2:27:37.540 and not get caught unless you're trying to lie to your spouse.
2:27:45.540 a well-understood theory of how the quantum information behaves.
2:27:51.540 have been developing for the last several decades.
2:27:54.540 And it's really exciting because it's the right.
2:28:00.540 It's the right basis for the theory of communication and computation.
2:28:04.540 Well, it's a better basis than what we had before,
2:28:07.540 thanking Turing and Shannon for what they did.
2:28:14.540 which may not be important yet in a technological sense,
2:28:20.540 but in a conceptual sense, it's really an improvement.
2:28:25.540 Oh, so one of the things that came out of this
2:28:29.540 is that physicists and chemists used to think of quantum mechanics
2:28:39.540 that I'm not sure exactly what you'd call them,
2:28:48.540 Just as all classical information can be reduced to bits,
2:28:52.540 all quantum information can be reduced to qubits.
2:28:54.540 And you only have to work on them one and two at a time
2:28:59.540 So this idea of a universal, I think that's David's idea,
2:29:02.540 a universal quantum computer as an idea that's
2:29:06.540 as crisp and fruitful as the universal classical computer
2:29:32.540 and horizontal photon as zero, and I have different colors
2:29:36.540 This is a conditional, not operation, or an exclusive bar.
2:29:50.540 And then you put the first qubit in in the intermediate quantum state
2:29:54.540 you get an intermediate state between both of them
2:29:59.540 And that's an entangled state that has no analog
2:30:05.540 So you can say it's a state of sameness of polarization
2:30:09.540 even though neither photon has a polarization itself.
2:30:12.540 Well that's an idea that would bother a typical computer
2:30:23.540 this is a stone-even proof theorem, so how can I take what you're saying?
2:30:28.540 But actually in an earlier time in my life,
2:30:32.540 I was in the Hay-Ashbury district of San Francisco in 1967
2:30:37.540 and there was easy to find people who thought they were perfectly in tune with you
2:30:41.540 even though they had no opinion about anything.
2:30:44.540 Now the hippies believed that with enough LSD,
2:30:48.540 everybody could be perfectly in tune with everybody else.
2:30:52.540 But they were, they were not really especially good at mathematics.
2:30:56.540 And now we have a quantitative theory of quantum information.
2:31:00.540 We know that entanglement is monogamous and the more entangled two systems
2:31:06.540 Of course the hippies weren't very good at monogamy either.
2:31:16.540 We go through a very simple quantum operation
2:31:21.540 And then suppose Bob likes the fact that he's entangled with Alice
2:31:25.540 and he decides, well let's have a little bit more of this.
2:31:31.540 Well the trouble with that is that that degrades his entangled with Alice
2:31:37.540 So he's only classically correlated with each of them.
2:31:40.540 But, and so that means if either of them leaves town,
2:31:44.540 he just has a classical correlation that could be cloned or copied or you know,
2:31:49.540 But, and more interesting thing happens if they both stay in town.
2:31:53.540 And that is that he becomes entangled with the now non-trivial relationship
2:31:59.540 between the two of them that he's brought about,
2:32:02.540 which I would say is an appropriate punishment.
2:32:07.540 And so now we've developed the quantum theory of information and information processing.
2:32:11.540 We have to explain what we mean by classical bits.
2:32:14.540 And a classical bit is just a bit with one of two arbitrary
2:32:20.540 The classical wire is something that conducts classical information reliably,
2:32:27.540 In other words, it's a quantum wire with an eavesdropper.
2:32:30.540 And that classical computer is just a quantum computer that's handicapped
2:32:34.540 by having eavesdroppers on a whole its wires.
2:32:37.540 So instead of saying, why do it as a quantum computer speed up computations?
2:32:41.540 A more sensible way of asking that question is why do some computations
2:32:47.540 get horribly slowed down by having eavesdropping on every step of the way?
2:32:56.540 Why almost every interaction between two systems produces entanglement?
2:33:01.540 Why wasn't it discovered till the 20th century?
2:33:04.540 Well, because of monogamy, most systems of nature,
2:33:07.540 other than little ones like photons, interact so strongly with their environment
2:33:12.540 as to become entangled with them almost immediately, and that means that the relation
2:33:17.540 between the parts of the system is degraded to mere classical correlation.
2:33:21.540 It's a little bit like a life of celebrities where if you read the people magazine,
2:33:29.540 then you read the next issue of people magazine and you find out what they had for lunch.
2:33:33.540 And so they had no private life because they're being eavesdropped on continuously.
2:33:42.540 This is sort of a quick version of decoherence theory in the version,
2:33:50.540 Most systems in the kind of world we inhabit are continually eavesdropped on by multiple different eavesdroppers.
2:33:58.540 For example, the photons of light are bouncing off all of us,
2:34:02.540 and some of them are going out the window and never coming back,
2:34:05.540 and they certainly don't interact with each other afterwards.
2:34:07.540 So what happens is, for a typical thing in our world, other than this microscopic thing,
2:34:13.540 the environment eavesdrops on it and creates multiple redundant copies of some properties
2:34:22.540 No, this is, I think Peter already talked about this.
2:34:26.540 In classical computation, you can break all computations down into ants and oars and knots,
2:34:33.540 but you may need a lot of them to do a problem like this factoring problem,
2:34:37.540 and if you had a quantum computer, you could do it much faster.
2:34:43.540 And we have now a well-developed theory of quantum computational complexity,
2:34:48.540 where we have your origin, our earlier theory of classical complexity classes,
2:34:53.540 like P and NP, and we've got the new quantum ones that sort of interpolate
2:34:58.540 between them in an interesting way that's still being explored.
2:35:02.540 Now I'm going to go back and talk a little bit about the way ideas develop
2:35:07.540 in a way that's not in a straightforward way.
2:35:10.540 In fact, bad ideas are sometimes extremely good for advancing scientific progress
2:35:19.540 So, and one of the biggest sorts of bad ideas was Einstein.
2:35:24.540 So Einstein really didn't like quantum mechanics,
2:35:28.540 and because he's the only 20th century scientist,
2:35:33.540 most people can name, they'd have the attitude that,
2:35:37.540 if Einstein didn't like and it didn't understand it, what was it for me?
2:35:46.540 and I would say, although I'm not really a historian of science at all,
2:35:51.540 I think his mistake was viewing entanglement as action at a distance.
2:35:55.540 It's some kind of influence of one particle on another,
2:36:00.540 and the right way is to think about it as an entangled state
2:36:04.540 is that you have to give up the common sense idea
2:36:07.540 that if the whole is in a definite state, then each part must be in it.
2:36:11.540 And then once you've given up that idea, it's quite possible to understand
2:36:15.540 how you can have this strong correlation, which doesn't mean
2:36:21.540 that either particle is influencing the other.
2:36:24.540 Now, but many people continue to follow this bad path,
2:36:34.540 Well, actually he submitted it, and I forget if this was Ash or Paris
2:36:40.540 this paper is so wrong that we must publish it immediately.
2:36:45.540 And it turned out to be the right thing to do,
2:36:47.540 because it stimulated the refutation of the idea
2:36:50.540 that entanglement can be used for a long distance communication.
2:36:53.540 So this gives you the idea that wrong ideas are very good for scientific progress.
2:37:04.540 Conversely, and I'm going to be talking about this
2:37:06.540 in the context of the reversibility in Maxwell's demon,
2:37:10.540 good ideas, indeed quantum mechanics itself,
2:37:16.540 So we think about the idea between mathematics and physics,
2:37:21.540 between dynamical emotion, and computation.
2:37:24.540 And this is very nicely stated by Laplace in 1814,
2:37:35.540 that if the universe has deterministic laws,
2:37:38.540 if we know the present state that we know the entire future passed.
2:37:43.540 Well, the next problem came up in connection with Maxwell's demon.
2:37:56.540 really, of the mathematics of random motion of atoms in the gas.
2:38:03.540 And he said, if you had somebody who is able to look at the gas molecules,
2:38:14.540 and you could violate the second law of thermodynamics.
2:38:28.540 He just gave it as a homework assignment to visit after that.
2:38:31.540 Now, actually, the time was right right at the beginning of the 20th century
2:38:37.540 for someone to solve this problem, and it was Smokovsky.
2:38:40.540 And he considered a version of the Maxwell's demon problem,
2:38:44.540 which was just a trap door so that the molecules coming from one side
2:38:51.540 But if they hit the door from the other side,
2:38:54.540 And eventually, all the gas would collect on the right,
2:38:58.540 and make holes in the street with it for just using the energy of heat.
2:39:04.540 And then he argued that if the door was light enough
2:39:11.540 that it could be pushed open by molecule, it would have its own red emotion
2:39:15.540 and it would work and reverse exactly as often as it worked forward.
2:39:18.540 So he really solved the problem back in 1912.
2:39:25.540 And people realized that measurement was a problematical thing,
2:39:28.540 which they thought was a straightforward thing.
2:39:30.540 And then somehow they got timid in a way that I don't understand,
2:39:34.540 which is the plus already imagined that everything in the universe,
2:39:38.540 including all of our thoughts, are mechanistic.
2:39:45.540 people started worrying if the intelligent being
2:39:48.540 could somehow do something that a trap door couldn't do.
2:39:56.540 it was actually mathematically and physically correct,
2:39:59.540 but it gave people the wrong ideas because of its title,
2:40:02.540 and because it didn't quite clearly stay in words
2:40:05.540 as well as in the equations why the demon doesn't work.
2:40:09.540 And finally, it was felt a raw flandauer to say
2:40:14.540 and it was the irreversible act of erasing information
2:40:19.540 So here's my sermon, the sermon part of this history thing.
2:40:24.540 Basic science in the future, haste makes waste.
2:40:27.540 Scientific progress, I think, is mostly incremental
2:40:34.540 It was a guy who came from other bar to buy BMs
2:40:52.540 that's like making a firm decision to be spontaneous.
2:41:01.540 for years, people didn't take this subject seriously
2:41:14.540 And my favorite example of this was about 20 years ago.
2:41:18.540 I met a scientist at Jet Propulsion Laboratory
2:41:21.540 and he was saying the most proud accomplishment
2:41:27.540 and they had applied to make it go to all of outer planets.
2:41:34.540 Because people don't know anything besides Jupiter and Saturn
2:41:39.540 And they said, but the planets won't be lined up
2:41:47.540 not about 200 years, just due to Jupiter and Saturn.
2:41:50.540 So he says he and all of the other scientists working on it
2:41:53.540 and engineers conspired to make everything last twice as long
2:42:02.540 well, you wouldn't want the thing to fail just because this part
2:42:07.540 And he was working on the thermoelectric power supply for it.
2:42:15.540 they could repurpose it and set go to all of them.
2:42:18.540 So the moral of the story is sometimes you have to lie
2:42:21.540 to the politicians, but if you do it in the right way
2:42:24.540 and you don't do it too often, that may be the best thing for science.
2:42:59.540 Way to behave with politicians or something.
2:43:27.540 So do you think in the quantum computational speed up,
2:43:34.540 is there any clear sign that entanglement plays a role
2:43:41.540 Well, it's hard to separate the two because from the superposition
2:43:48.540 But it's an important question because people have asked
2:43:55.540 is it does every useful quantum computation
2:44:00.540 that where there's some advantage over classical,
2:44:04.540 And I think actually Peter would know the answer that better.
2:44:15.540 Grover's algorithm involves entangled states, but it's not really,
2:44:23.540 Our central to Grover's algorithm, but I don't think
2:44:26.540 I don't think it will work without entanglement.
2:44:29.540 Well, one argument you make is if you don't have entangled states,
2:44:32.540 there's a efficient way of simulating a quantum computation.
2:44:44.540 The only problem that I wanted, it's just a stupid remark
2:44:53.540 I would like to call your attention that everybody now
2:44:56.540 knows after tomorrow, again, that their papers speak,
2:44:59.540 and I have it that they're not cloning theorems two years
2:45:03.540 You were two years before, Wooters and Zurich,
2:45:07.540 Oh, and there was also before that there was two years before.
2:45:17.540 I think it was discovered in a paper that was cited by Wooters
2:45:24.540 that had been written for like 10 years before,
2:45:37.540 Yeah, so you got there almost at the right time
2:45:44.540 Yeah, so this is almost most scientific discovery
2:45:50.540 sometimes very well, and it's not the part of the discover
2:46:18.540 David was born in high-fying Israel in 1953.
2:46:26.540 and if I get North London, before reading National Sciences
2:46:32.540 and taking part three of the mathematical drivers,
2:46:41.540 and I have to say that his supervisor was David Shama,
2:46:51.540 including Stephen Hawking and Martin Reese.
2:46:55.540 And he wrote his thesis on quantitative theory in course,
2:47:02.540 David is one of the founding fathers of quantum computing.
2:47:04.540 He introduced the notion of a quantum Turing machine
2:47:06.540 that will operate on arbitrary superposition of states
2:47:11.540 The concept of the quantum logic gate and quantum circuit,
2:47:14.540 as well as the network model of quantum computation.
2:47:18.540 He showed that all possible operations on a quantum computer
2:47:22.540 could be generated by combining sequences of a single kind
2:47:34.540 and one simple type of reverse world classical,
2:47:44.540 though it proposed the first quantum algorithms,
2:47:46.540 known as a Doge and Doge and Johnson algorithms,
2:47:49.540 showing that quantum computation could solve
2:47:52.540 certain problems faster than any known classical computer.
2:47:55.540 So please, let's all congratulate David for the world.
2:50:02.540 A couple of years ago, the mathematician Hannah Fry
2:50:15.540 It was about an episode in the history of ideas,
2:50:27.540 or in other words, if Lovelace hadn't died young.
2:50:32.540 Because, well, from the evidence in that documentary,
2:50:36.540 I suspect that the first person to get the universality
2:50:53.540 that she was theorizing about the Babidge's analytical engine.
2:51:02.540 the significance was in the design and the theory
2:51:24.540 to understand what one could call arithmetic
2:51:33.540 This previous design, the different engine,
2:51:36.540 could compute polynomials in one fixed point variable.
2:51:40.540 So, very limited kind of universality as universal for those.
2:51:43.540 But Babidge realized that if he added just a few more features,
2:51:51.540 the machine would make the jump to universality
2:51:54.540 becoming the analytical engine universal for any arithmetic
2:51:59.540 function of any number of variables of any finite precision,
2:52:04.540 basically what we would today call computable functions.
2:52:15.540 was the significance of the analytical engine's ability
2:52:23.540 but anything in the world, in the physical world.
2:52:31.540 like computer music, and art, and chess, and so on.
2:52:35.540 But this wasn't just a matter of usefulness.
2:52:44.540 as a physical object depend on a momentous property
2:52:49.540 of the laws of physics themselves, all of them.
2:53:02.540 an infinitesimal fraction of all mathematical objects
2:53:05.540 and relationships, it could also, apparently,
2:53:11.540 instantiate or simulate or emulate all possible motions
2:53:20.540 of all possible physical objects and their laws,
2:53:24.540 This physical universality is an intrinsic property
2:53:36.540 It doesn't follow from mathematical universality.
2:53:50.540 Yet, it seemed that both of them were exhibited
2:53:58.540 Well, whatever the reason, it's in the laws of physics.
2:54:02.540 It would make no sense to try to prove this
2:54:39.540 Well, Turing's great paper presenting his conjecture
2:54:48.540 To a fundamental puzzle posed by the mathematician David Hilbert,
2:54:53.540 basically, what is the relationship between
2:54:56.540 a true mathematical statement and a provable one?
2:55:00.540 Hilbert had hoped that one could define a system of proof,
2:55:04.540 such that a mathematical statement was true
2:55:08.540 if an only if it could be proved under that system.
2:55:20.540 Notably, could Google prove that there can be
2:55:24.540 no method of proof that identifies all true mathematical
2:55:31.540 Now, Turing's approach did exactly the same in that respect,
2:55:38.540 but it had wider implications, as we now know,
2:55:41.540 because of these physical objects, computers.
2:55:46.540 The reason Turing's approach had this additional reach
2:55:51.540 was that Goethe's model of proof was a model inside the arithmetic
2:56:03.540 He simply defined proofs as finite sequences
2:56:08.540 of symbols drawn from a finite set and all that stuff.
2:56:16.540 Turing, who realized that that notion of what proving something
2:56:24.540 So he acknowledged it as a substantive conjecture,
2:56:30.540 The model of proof that he used was computation.
2:56:36.540 And the model of computation that he used was physical.
2:56:44.540 with symbols in a finite set of discrete operations on them,
2:56:51.540 And when he conjectured that this machine was universal for proofs,
2:56:58.540 the phrase he used was that it could compute anything which
2:57:09.540 At the time, the word computer meant a human being.
2:57:15.540 A person whose job was to manipulate symbols
2:57:29.540 So by anything that would naturally be regarded as
2:57:33.540 computable, he meant computable in nature by physical objects.
2:57:39.540 And by provable, he meant provable by physical objects.
2:57:44.540 Now that conjecture, unlike Girdle's proofs,
2:58:05.540 And when I proved Turing's conjecture from quantum
2:58:12.540 theory in 1985, it was with the slight correction
2:58:16.540 that the universal machine is not Turing's paper machine,
2:58:26.540 But I soon found out that not everyone saw it that way.
2:58:35.540 The referee of the paper in which I presented that proof
2:58:39.540 insisted that Turing's phrase would naturally
2:58:43.540 be regarded as computable referred to mathematical
2:58:54.540 And so what I had proved wasn't Turing's conjecture.
2:59:01.540 So I asked some mathematicians what mathematical intuition is.
2:59:07.540 Turned out, it was as much of a mystery to them as to me.
2:59:11.540 So some of them said it was met a mathematical intuition.
2:59:16.540 Fair enough, but they couldn't tell me what that was either.
2:59:20.540 Some kind of mathematical mysticism, I think.
2:59:29.540 about whether his mathematical model of proof
2:59:37.540 but something else, like mathematical intuition or something.
2:59:43.540 Now, Turing's basic insight was that proof is computation.
2:59:54.540 That it isn't physical, seemed to me a philosophical absurdity.
2:59:59.540 But it was an absurdity that all the mathematicians
3:00:15.540 So I called it the mathematicians misconception,
3:00:18.540 the denial that proof is physical is one way of putting it.
3:00:23.540 By the way, Rolfandar, Charles Bennett's old boss
3:00:28.540 had been campaigning for years with the slogan of computation
3:00:38.540 like Fermat's last theorem, aren't physical.
3:00:43.540 But there is a difference between truth and probability
3:00:47.540 was the main point of all those 1930s discoveries.
3:00:53.540 Still, in my paper, I had to defer to prevailing usage.
3:00:59.540 So I changed it to define Turing's conjecture
3:01:07.540 And the referee at least agreed to let me call my result
3:01:11.540 a proof of the Turing principle to distinguish it
3:01:18.540 The principle that can be a physical object
3:01:20.540 whose motions contain those of all other objects.
3:01:25.540 Nevertheless, now people sometimes call that
3:01:32.540 And that's how the mathematician's conception
3:01:36.540 ended up giving me credit for something Alan Turing did
3:01:54.540 as something one might hope to prove one day
3:02:00.540 but that it could be proved to be a property of quantum mechanics.
3:02:11.540 And he got a bit agitated and at the end he stood up
3:02:16.540 and declared, with good humor, but very emphatically,
3:02:21.540 I've never heard such a load of rubbish in my life.
3:02:27.540 I tried to explain further, but he seemed implacable.
3:02:35.540 and at the dinner afterwards, he came over to where I was sitting
3:02:39.540 and he said, you know, I think there might have been
3:02:46.540 And we did discuss it later, but unfortunately,
3:03:01.540 the mathematician's misconception is done more
3:03:07.540 It expresses the idea, acknowledged or not,
3:03:12.540 that somewhere out there in the world of mathematical abstractions
3:03:17.540 or in some supernatural world of mathematical intuition,
3:03:21.540 there is the authentic, official, though ineffable.
3:03:32.540 And if some physical process that doesn't conform
3:03:36.540 to that definition turns out to allow us to know some new necessary truth,
3:03:44.540 that process wouldn't constitute a proof of that truth.
3:03:52.540 It so happens that a quantum computer's repertoire
3:03:57.540 of integer functions is the same as the Turing machines.
3:04:09.540 First of all, we only know that they only differ in speed
3:04:16.540 And second, quantum theory won't be the final theory of physics.
3:04:22.540 And even if it is, you can't prove that either from mathematical intuition.
3:04:28.540 In reality, we only have physical intuition.
3:04:32.540 Never provable, always incomplete, always full of errors.
3:04:39.540 The misconception also affects thinking about information.
3:04:44.540 For example, a quantum cryptographic device
3:04:48.540 may perform a classical information processing task
3:05:01.540 well, quantum cryptography isn't an information processing task.
3:05:05.540 It's just an engineering task like building a washing machine.
3:05:09.540 Why? Because Turing machines couldn't perform it.
3:05:15.540 Again, they think that there's a mathematical definition of information
3:05:19.540 out there somewhere independent of physics.
3:05:24.540 The same holds for probability, by the way.
3:05:28.540 Similarly, again, the answer to Eugene Wigner's famous question
3:05:33.540 about why mathematics is unreasonably effective
3:05:37.540 as he put it in science is not that the physical world
3:05:42.540 is actually being computed on a vast computer belonging to God
3:05:53.540 Because there's no reason other than the misconception
3:05:59.540 why the snailions computer should itself generate
3:06:03.540 that particular tiny piece of mathematics that we call computable.
3:06:09.540 Purely mathematical intuition will never reveal anything about proof
3:06:15.540 or computation or probability or information.
3:06:21.540 If you want to understand any of those things fundamentally,
3:06:28.540 And in particular, with what is currently the most fundamental theory
3:06:34.540 in physics of quantum theory, it won't always be the most fundamental,
3:06:39.540 but its replacement will not come from mathematics
3:07:14.540 I have a very simple question. What is physical?
3:07:34.540 There seem to be various, I don't know, it's the answer,
3:07:38.540 but there seem to be various levels of reality.
3:07:42.540 And there's the level that's only accessible by experiment.
3:07:47.540 And then there's the level to find out what laws the laws are.
3:07:51.540 And then there's the level that is independent of the laws.
3:07:54.540 So we know that Fermat's last theorem is true.
3:07:57.540 And if somebody comes and finds that general relativity has a flaw
3:08:02.540 or quantum theory has a flaw, nobody will worry that maybe Fermat's last theorem isn't true.
3:08:12.540 They are things that could be overturned at any moment.
3:08:17.540 So I can't provide an answer better than that.
3:08:46.540 I am confused. Can you explain the difference between what is mathematical?
3:08:58.540 Which is like in the top, a mathematical proof of physics proof for one understood is the physics point, I think.
3:09:05.540 Well, you have to draw a distinction between what issues of what we can know, how do we know things?
3:09:24.540 We then develop mathematical intuitions from there.
3:09:30.540 However, there are necessary truths which are independent of the laws of physics.
3:09:36.540 And they don't become any less necessary if we don't know them.
3:09:40.540 So as far as the necessity of terms goes, mathematics is at the top.
3:09:58.540 We still have a couple of minutes to let me ask a question myself.
3:10:03.540 I know that you are the great advocate of the multiverse space of quantum mechanics.
3:10:08.540 But now you also say the quantum mechanics most probably is not the last work.
3:10:16.540 Well, I think that the multiverse interpretation is on the same level of the existence of the multiverse.
3:10:29.540 It's on the same level as the existence of the dinosaurs.
3:10:36.540 What is going to be proved false is what the multiverse consists of.
3:10:42.540 We don't actually have a very good idea of what the structure of it is at the moment.
3:10:47.540 Within quantum theory we kind of know how to do calculations.
3:10:54.540 And we know that as we sit here in the lecture room there are other copies of us
3:11:00.540 watching a different lecture and listening to different people on the prize and so on.
3:11:09.540 But the details are going to change because quantum theory is in many ways totally unsatisfactory.
3:11:18.540 Some people do not support this multiverse interpretation.
3:11:23.540 So you said they are simply wrong or they are wrong in different ways, but yes.
3:11:32.540 Well, I am going to ask David about something that I think he thinks.
3:11:44.540 Would you describe yourself as a technological optimist?
3:11:51.540 Well, I used to be a technological optimist, but I then started studying a little bit cosmology
3:11:59.540 and maybe thinking too hard about the current principle.
3:12:03.540 And it occurred to me that perhaps the universe is infinite, but the self-destructive tendencies of the civilization
3:12:16.540 that we are in, our particular bubble, suggest that it may not last more than a few thousand years.
3:12:21.540 And that is okay because there are infinitely many other bubbles where they do better.
3:12:31.540 But I think you think maybe one of those bubbles will get it right well enough so that it can spread its beneficent influence
3:12:40.540 throughout everywhere, whatever that means.
3:12:45.540 I think the mistake there is when you said the evidence of our self-destructive nature.
3:12:53.540 By our human, our civilization or our species or whatever.
3:12:57.540 Really, basically what Schopenhauer said, that the argument that some of us suggest that we are all possible words.
3:13:07.540 Yes. Well, it is obvious that all of our past was worse than the present.
3:13:16.540 And the evidence that we are self-destructive is all what you might call extrapolation.
3:13:25.540 And in order to reach that conclusion, you have got to extrapolate selectively.
3:13:39.540 But it is not very convincing because it could always be made no matter how good things are.
3:13:44.540 If you look at the actual details, we have time and again solve problems.
3:13:51.540 And our particular civilization is different from all other ones in previous ones in that respect.
3:13:57.540 So you cannot extrapolate from them either.
3:14:00.540 All civilizations, basically other than our scientific, technological, whatever you call it, civilization, have in fact been destroyed.
3:14:10.540 And another interesting thing is that none of them were destroyed by the ways that pessimists suggest ours will be destroyed.
3:14:19.540 So there is again a disconnect, so it does not work.
3:14:30.540 How you set the probability as well as the validity, which is true in all interpretation, both are physical.
3:14:38.540 How you make the distinction, because one in semantics essentially prove the validity.
3:14:44.540 And the other part is the purely syntactical, which is the probability.
3:14:48.540 I don't think mathematical truth is syntactical.
3:14:51.540 Well, in that respect, I am a Platonist of something.
3:14:55.540 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.
3:15:02.540 But you have to distinguish between the necessary features of the things that are out there.
3:15:08.540 And the myth by which we find out about them.
3:15:11.540 In the case of the mathematical truths, we definitely only have access to an infinitesimal proportion of them.
3:15:18.540 But with physical truths, we seem to have access.
3:15:22.540 There is nothing that seems fundamentally hidden from us.
3:15:29.540 So let's find David again for this one, I wonder from that.
3:15:33.540 Just to finish the event, so let me remind you that this is not yet over,
3:15:48.540 There was a post ceremony public event this afternoon.
3:15:52.540 It started in the sixth series, it was a few minutes from now.
3:15:55.540 And the Savoya accessor palace, interesting.
3:15:59.540 And it's a moderate roundtable discussion with a hardbot Nevin,
3:16:03.540 who is a Google's director of engineering here.
3:16:06.540 And a central kurioni, who is the vice-president of IBM, Europe,
3:16:10.540 and director of IBM, research lab, and Zurich.
3:16:13.540 And Thomas of Kalarco, the director of Institute for Commerce Control Systems,
3:16:17.540 and the University of Uhm, and I did a figure for this European commission,
3:16:28.540 And there is a boss that we hire that will take 50 people.
3:16:37.540 This is the first conference, and then we will see you there.
3:16:42.540 So it will be an interesting discussion about the importance of quantum technologies.
3:16:47.540 Okay, well, thank you very much and congratulations again to all the awardees.
