00:07:45.000 to top scientists also that will give presentations for us.

00:07:49.720 But let me start with the South Park.

00:07:52.480 As you may all know, today, Stephen Hawking passed away.

00:07:57.080 He's hard to emphasize, or to ever emphasize,

00:08:01.640 the impact he has had in many generations of physicists.

00:08:05.360 I personally consider him a very good friend,

00:08:08.120 a colleague in Cambridge for many years.

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

00:08:27.880 like him in the history of the humankind,

00:08:31.240 and there will never be anybody like him in the future,

00:08:33.720 because the condition he had,

00:08:35.640 it was such a way that the way he survived

00:08:40.000 in a way that nobody else has survived,

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.

00:08:51.760 And so in that sense, even in that regard,

00:08:53.720 he was also a pioneer.

00:08:55.720 We know all his many contributions to physics,

00:08:59.000 in particular to black holes, to gravity, and cosmology in general.

00:09:04.200 So his impact in science will be remembered

00:09:09.320 for many, many years to come.

00:09:12.080 I would say many generations of hundreds of years

00:09:15.080 because his discoveries, first of all,

00:09:17.800 from the results were painters about the general existence

00:09:22.160 of singularities and general relativity,

00:09:24.400 then the thermodynamics of black holes, the hockey

00:09:26.800 and radiation, the waveforms of the universe

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

00:09:35.920 to solve the problem that he pointed out

00:09:40.640 for the whole community, which is the information,

00:09:42.960 lost paradox, that he has more than 40 years

00:09:47.000 of several generations of physicists trying to solve.

00:09:52.640 And he would also be remembered.

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

00:10:02.200 of science, he's no doubt was the main figure

00:10:06.640 for promotion of science, physics, but in general,

00:10:10.280 science worldwide.

00:10:11.720 So probably he's not a suggestion,

00:10:13.680 the best known scientist in the world.

00:10:17.320 And so he has many legacies that for us,

00:10:23.520 it would be available to measure the impact

00:10:25.960 he has had in our lives in the community

00:10:28.600 in physics in general.

00:10:30.040 So I will ask all of you who do the mind

00:10:32.800 to stand up and join with me for a minute of silence.

00:12:16.840 So let me start.

00:12:20.320 So SDP, the Rex Meidel, is giving you

00:12:22.200 an old friend Maurice Dirac.

00:12:24.080 He's distinguished theoretical physicist,

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.

00:12:42.760 And he was a regular visitor to my CTP,

00:12:46.400 and Salan used to recognize that one of the motivations

00:12:49.600 he decided to do, the particle physics was,

00:12:53.080 who's worked with Salan, with the Dirac, sorry.

00:12:58.040 So the rectangle recognizes scientists

00:12:59.920 who have made significant contributions to theoretical physics.

00:13:03.120 And you have seen at least very prestigious,

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,

00:13:19.040 David Deutsch, of Oxford University,

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,

00:13:37.520 computer sciences, and information theory.

00:13:41.560 The committee this year for this election

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

00:13:57.040 at some point during mass of mathematician

00:13:59.080 and the third one is a theoretical physicist.

00:14:01.560 And the committee had a very difficult job

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

00:14:18.120 is usually more into theoretical physics,

00:14:19.800 and these cover many areas.

00:14:22.000 And I can mention the members 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,

00:14:34.320 Professor Bert Halperin from Harvard,

00:14:36.640 or some Martin Reese from Cambridge.

00:14:39.520 Professor Ashut Sen from Alahabad in Asia-Rang, in India,

00:14:44.640 and Professor George O'Paddisi from Rome.

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

00:14:59.160 with the end result.

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.

00:15:18.920 And then after that, we have a coffee break,

00:15:21.080 and we start with the award.

00:15:22.440 So the ceremony, which each of the award

00:15:25.120 is with the representation.

00:15:27.000 So let's, as Peter Zoller, to start his presentation,

00:15:33.200 and please join me in welcoming Peter.

00:15:35.880 Thank you.

00:16:14.840 OK, so let me start out by congratulating

00:16:17.400 the winners of this actually last year's Dirac Merelle.

00:16:22.000 And I just want to put down the citation,

00:16:25.560 you know, that was given for the prize.

00:16:27.480 It's easier for pioneering work in applying

00:16:30.240 for the mental concepts of quantum mechanics,

00:16:32.880 to solving basic problems in computation, communication,

00:16:36.120 and therefore bringing together the fields

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

00:16:44.720 with these prizes to these people here

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

00:17:00.480 talk going back 25 years, or maybe 30 years,

00:17:03.800 where many of these things started, or where

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.

00:17:20.320 So I was interested or became interested

00:17:23.240 how do we actually build quantum computers

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.

00:17:38.680 And time is progressing.

00:17:40.440 And all of these realities were becoming

00:17:42.280 also quantum technologies.

00:17:43.840 And might have actually quite an important impact

00:17:46.720 on our life, even in the future.

00:17:49.080 So I think that this is one of the prime examples

00:17:51.760 of basic science.

00:17:52.920 If the disciplinary science at the end

00:17:55.360 is becoming something that's even sort of

00:17:57.560 useful from the perspective of society.

00:18:01.720 I could not, you know, refuse to sort of show

00:18:07.880 very old photo.

00:18:09.120 This is like political party meetings of quantum information

00:18:12.160 25 years ago.

00:18:14.120 And I've to say that two of the prize winners are here,

00:18:16.600 this photo.

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

00:18:22.480 the one that took these pictures.

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.

00:18:30.720 And Peter Shaw is over here.

00:18:34.240 And I'm sure exactly why these meetings

00:18:36.320 happened in Toronto.

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

00:18:42.880 and talked for quite a while.

00:18:45.000 And you know, just because you're out to Eckhart,

00:18:48.200 he's hiding a little bit here.

00:18:50.560 David, David Jenssel.

00:18:52.240 And you can also see that I'm over here.

00:18:55.240 And Ignacio Ciroc is hiding over here.

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

00:19:04.480 of iron trap quantum computing that I

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

00:19:21.640 I guess at all, you know?

00:19:24.240 So this is Ignacio, how we really look at this stage.

00:19:28.040 There is one strange look that there are

00:19:29.800 in this, of course, you know, this is from David Jenssel block,

00:19:34.000 all of the names here, and many famous people,

00:19:36.200 and also people that are in the audience

00:19:37.920 and over a sort of present that is meeting.

00:19:40.240 So these were historical meetings where

00:19:42.880 these things were sort of starting.

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,

00:19:52.160 I learned about quantum computing

00:19:54.200 and the way that I will summarize now.

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.

00:20:08.880 And you might ask yourself, you know,

00:20:10.920 what's this thing at the background over here?

00:20:12.880 This thing at the background here is actually

00:20:14.520 an iron trap quantum computer, as we have at the moment

00:20:17.120 in this book, and over the few qubits.

00:20:19.800 This is the book by Rhina Blackness,

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.

00:20:27.400 But even also know what the perspective is

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.

00:20:52.520 As I said, for me, actually, the moment

00:20:55.400 where you learn these things, that somehow

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.

00:21:06.240 It will be the second speaker, to me,

00:21:08.920 at the ICAP conference in Boulder.

00:21:10.920 ICAP is a very prestigious international conference

00:21:13.720 and atomic physics, usually very experimentally dominated.

00:21:17.120 So it was entirely sort of my own conference.

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,

00:21:28.040 that were sort of a little bit outside,

00:21:29.680 that would somehow bring new things

00:21:31.360 into atomic physics and stimulate the field.

00:21:33.480 And this is, I have no idea who I've seen,

00:21:35.880 why did you have to do this conference?

00:21:37.720 It was some clever guy, the program committee must be.

00:21:40.440 So, but outdoor came and gave a talk

00:21:42.920 that I would really say changed a lot of these things

00:21:46.120 that were around, because really diverted,

00:21:47.880 I would say, the interest in atomic physics,

00:21:51.280 two quantum information processing.

00:21:53.600 And I've sort of, a few old slides,

00:21:55.600 that they're not precisely the presentation

00:21:58.400 that outdoor gave, but it gets very close.

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,

00:22:04.720 because they're a little bit historical slides

00:22:07.000 that show you what the kind of things

00:22:08.960 were that around the questions being asked

00:22:11.280 what the challenges were.

00:22:13.080 They're sort of starting out by making this remark,

00:22:15.360 computing is a physical process,

00:22:17.160 you know, here's sort of a classical physical process,

00:22:19.720 we are just moving beats around and so on.

00:22:22.160 And of course, our press and computers,

00:22:25.400 you know, process information according

00:22:27.320 to laws of classical physics.

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,

00:22:35.560 nature based a lot of quantum physics

00:22:37.560 and at the fundamental level of that for information science

00:22:40.360 must also be a quantum information science.

00:22:42.280 I think this is sort of the starting point

00:22:44.440 and all of these things were happening

00:22:46.600 and the question is that at the end,

00:22:48.320 more powerful and we believe that the answer is yes.

00:22:51.800 In particular, since the note outdoor echo,

00:22:54.200 the historical behavior reported that the show algorithm

00:22:56.840 was just invented in a few months ago

00:22:59.320 before this thing, and this was sort of,

00:23:01.240 we finally had the killer application,

00:23:03.040 you know, that was a very true and deep motivation

00:23:05.640 for pursuing these kind of things.

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,

00:23:13.680 a set of qubits and all of these things

00:23:15.400 that I will explain now here briefly,

00:23:16.960 but sort of why do we want to do these things?

00:23:19.800 And again, this is from outer star,

00:23:21.560 it says technology to be more slow,

00:23:24.600 we would still some extent agree with that there.

00:23:27.280 Computer science, new complexity classes,

00:23:29.480 we still hope for that physics to learn more

00:23:32.920 about quantum theory, this is always true

00:23:34.720 by definition.

00:23:35.560 So it's kind of a win-win situation over here.

00:23:38.600 And of course, what we learned from outer stock

00:23:41.040 that is that the basic element,

00:23:42.960 instead of the classical bit,

00:23:44.400 that all it takes on value of series and one,

00:23:46.800 is now the quantum bit, which is a superposition

00:23:49.360 of two quantum states here and one,

00:23:51.120 so we can have things like zero plus one over here,

00:23:54.040 we've presented here on the blocks here,

00:23:56.160 and these classical versions of the quantum bit

00:23:58.720 that can't be in the superposition.

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,

00:24:05.520 there's an old woman and there's a young girl

00:24:07.920 at the same time sort of symbolizing this thing

00:24:10.240 or peculiar being in a superposition state,

00:24:14.280 don't take this thing too literally, of course.

00:24:18.440 And of course, we have quantum registers

00:24:20.200 and this is where entanglement comes in,

00:24:22.200 that we can store, of course, in a sense,

00:24:24.640 of superposition states,

00:24:25.800 and our quantum register superposition

00:24:28.240 of all these different numbers at the same time,

00:24:30.440 this is not the guess entanglement,

00:24:33.240 and of course, what we're doing with our quantum computers

00:24:35.880 sort of in the laboratory,

00:24:37.080 are trying to breed little Schrodinger cats

00:24:39.600 that are doing this computation for us.

00:24:41.680 So entanglements, superposition of them,

00:24:45.000 avoiding decoherence as the coupling to the environment

00:24:47.720 is sort of essentially all of these things.

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,

00:24:55.360 say 300 qubits, you know,

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,

00:25:11.280 it is six, you know, make a statement,

00:25:13.680 well, if you're a quantum mechanical person,

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

00:25:23.280 that can actually simulate quantum devices

00:25:26.480 as a programmable system.

00:25:27.920 This was sort of the second leg

00:25:30.880 in which all of these things built

00:25:32.240 and this is sort of the starting point

00:25:33.880 of what would be today called quantum simulators.

00:25:37.440 So, but one of the things that Otto mentioned

00:25:40.120 in his talk was, of course, that the big challenges,

00:25:42.320 how do we actually build the quantum computer

00:25:44.160 because at that point, not in you.

00:25:46.000 And what are the challenges to do so?

00:25:48.920 Well, if you want to build a quantum process,

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,

00:26:03.160 that you can see that there's sort of,

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,

00:26:09.720 that there's two kinds of gates, you know,

00:26:11.680 the single qubit gates that make certain rotations

00:26:14.320 of your qubit on the block sphere.

00:26:16.240 And if you combine these things with two qubit gates,

00:26:18.840 like a C-NARC gate that's indicated over here,

00:26:21.960 then if you control qubit and then target qubit

00:26:24.280 and then some unitary operation

00:26:26.000 and then conditional to the state of the first one,

00:26:28.400 you operate on the second one.

00:26:30.120 If you can build these kind of gates,

00:26:31.840 the second one being the antagonist gates,

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

00:26:38.680 provided you have the way at the end

00:26:40.040 to read these things out.

00:26:40.960 So the historical challenge was to come up

00:26:43.920 in different implementations, you know,

00:26:45.560 with ways of implementing these kind of gates

00:26:48.080 and what we talk about is, of course,

00:26:49.880 an network model.

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,

00:26:57.520 what we now call quantum parallel processing,

00:27:00.200 sort of this was the envisioning part,

00:27:02.720 you know, in this original idea

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

00:27:09.560 was given by the shore algorithm

00:27:11.600 and the source of the doge troso algorithm

00:27:13.920 is an example where we have a certain quantum advantage.

00:27:18.880 And it's always based on the fact

00:27:20.360 that what the quantum computer does is,

00:27:22.560 it's like a picket from it,

00:27:24.080 but it is, you know, big hillman space

00:27:26.040 that we take different computational paths,

00:27:28.040 but we can let them interfere.

00:27:29.840 And something like the shore algorithm, for example,

00:27:32.000 just really uses this thing in order

00:27:34.080 to get the corresponding advantage out.

00:27:37.040 So with this, sort of at the end of this introduction,

00:27:40.360 what sort of, you know, we walked out

00:27:42.280 and the analysis Iraq over here

00:27:44.040 and I was sitting at his talk about how to echo

00:27:46.360 and we looked at the gson and said,

00:27:48.160 I guess we know how to actually beat something like this

00:27:50.280 because we were just working on trapped ions,

00:27:52.480 you know, that were developed for atomic clocks.

00:27:55.720 And we had some ideas how to build this case.

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

00:28:03.640 in the laboratory in our collaboration

00:28:05.760 with experimentalists where we are.

00:28:07.720 What was the idea?

00:28:08.560 So, you know, people were building for atomic clocks,

00:28:11.480 iron traps and this is a single atom,

00:28:13.840 that's a single atom over here.

00:28:15.600 These are iron, so they repel each other

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?

00:28:28.080 So we cool away all of the phonons.

00:28:30.280 This can be done by laser cooling.

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

00:28:41.880 and this is the qubit, you know,

00:28:43.320 the quantum ratchers that we would like to manipulate

00:28:46.000 and how do we manipulate it?

00:28:47.760 Well, if you would like to do single qubit rotations

00:28:50.240 on the block sphere, you can do these things

00:28:52.240 by just shining lasers on one of them

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

00:28:59.160 and then experiment.

00:29:00.520 But there's also phonons and you can try to quantum control

00:29:03.960 the motion of these phonons.

00:29:05.520 And this is part of the building blocks

00:29:07.120 and sort of, you know, of building the corresponding set

00:29:10.520 of gates that constitute the quantum computer.

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,

00:29:22.280 which is here on the right-hand side.

00:29:24.240 And there's many groups out there that are pursuing these things.

00:29:27.520 Where are we at the moment in the lab?

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

00:29:39.520 that are shining or these things,

00:29:40.960 but just based on this original idea.

00:29:43.640 And what's kind of interesting is that we have now

00:29:46.840 like a little quantum compiler.

00:29:48.400 So if you have some unitaries, some quantum algorithm

00:29:51.200 that you have, you can decompose it, you know,

00:29:53.160 in the different bits and pieces.

00:29:54.840 And we have quantum compilers that tell us, you know,

00:29:57.120 what sequence of laserhouses you have to shine

00:29:59.720 on these ions to represent the certain quantum computation.

00:30:04.320 Of course, the short algorithm was one

00:30:06.720 of the killer applications, initially, and they still

00:30:09.160 used, but it would say the point, of course,

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

00:30:16.800 at the moment, it's just horrendous.

00:30:18.520 So we have to wait a little bit, except we

00:30:20.520 want to factorize 21 hours over some people

00:30:23.440 might even know the answer.

00:30:25.800 So I would say that a lot of interest

00:30:27.600 has focused in recent years on quantum simulation.

00:30:30.480 And this is like taking a many-body system

00:30:32.640 that we have out there called the many-body system,

00:30:36.000 like a spin system.

00:30:38.040 And you would like to, for example,

00:30:40.520 calculate on the universal quantum computer

00:30:42.960 here the time evolution of a many-body system

00:30:46.880 that's represented as a set of spins.

00:30:48.760 And there is sort of a point out this

00:30:50.640 is what we call digital quantum simulation

00:30:52.840 that would also be analog quantum simulation at the end.

00:30:56.120 Think of this like having a many-body system,

00:30:58.320 which is available of spin-up and spin-down.

00:31:00.920 And you specify a certain Hamiltonian,

00:31:03.040 and by shining laser pulses, you can hear

00:31:05.280 it's a function of time.

00:31:06.640 It uses a certain time evolution, which

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,

00:31:22.760 these operators cannot commute here.

00:31:26.280 You can always decompose the unitary time evolution

00:31:28.920 in little steps, and we can factorize them

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

00:31:43.360 of a quantum many-body system.

00:31:45.560 And a few years ago, this were the kind of themes

00:31:48.760 that the experimentalists were playing with.

00:31:50.880 They were right down the Hamiltonian,

00:31:52.600 like a familiar, say, an easing Hamiltonian over here.

00:31:56.040 And this was comparison theory and experiment

00:31:58.680 with only up to about six spins.

00:32:00.800 And the meantime, as I said before, they

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

00:32:14.240 to mimic the corresponding time evolution.

00:32:17.240 So this was a few years ago.

00:32:19.440 More recent work, and I'm not going

00:32:21.520 to explain all of the details here,

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

00:32:37.160 in two dimensions.

00:32:38.120 But this is, I can't tell you a little bit in the future.

00:32:41.400 And we can sort of take a model like this,

00:32:43.600 and we can map it to a certain number of qubits over here.

00:32:46.800 And, you know, this nature paper here,

00:32:49.000 and the people who should get the credit

00:32:51.120 these things might be listed here,

00:32:53.360 and just in the more shakers is the theorist.

00:32:56.640 You can sort of, you know, mimic these things.

00:32:58.400 And here's a comparison theory and experiment

00:33:01.320 to be honest, it's only a few proper steps.

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,

00:33:10.160 are at the point where, at one point,

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.

00:33:18.680 What's really impressive in this experiment

00:33:20.480 was the fact that there was only four qubits,

00:33:23.320 but 220 quantum gates were possible.

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.

00:33:33.720 And that's quite an amazing development.

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,

00:33:41.920 now we talk about 220.

00:33:43.400 So things are becoming sort of a certain maturity

00:33:46.680 in this context.

00:33:49.480 There's also another way of doing quantum simulation,

00:33:52.560 and I just want to mention this,

00:33:53.880 because I will afterwards refer to this,

00:33:56.280 which is what we call analog quantum simulation.

00:33:58.840 So far, I've talked about quantum computing

00:34:00.960 about gates, you know, single to cubic gates

00:34:03.360 and all of these things.

00:34:04.920 You can also try to sort of, you know,

00:34:06.800 imitate, it's called the many body dynamics.

00:34:09.880 By simply designing your system is such a way

00:34:12.440 that you mimic directly the corresponding Hamiltonians,

00:34:15.960 not this, you know, this digitized version

00:34:18.040 that we had before.

00:34:19.520 And you can also do that with ions,

00:34:21.040 and the way that you do with this,

00:34:22.360 that you can sort of shine in lasers,

00:34:24.640 and these lasers will distort these ion crystals,

00:34:27.080 and if you eliminate this thing,

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.

00:34:36.200 And here's an example of, you know,

00:34:38.360 if I take all spin downs, I take a model,

00:34:40.520 like an x, y model, sigma plus sigma minus,

00:34:43.560 if I flip one spin over here,

00:34:45.440 you can see now that the spin oxidation

00:34:47.440 moves here to the left and moves also here to the right,

00:34:50.240 and you can try to see the entanglement,

00:34:52.040 because if I give you one spin over here,

00:34:54.560 which is at the same time moving 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

00:35:07.120 are able to demonstrate.

00:35:08.040 So we have the possibilities to build all of these very

00:35:11.600 exotic spin models, for example,

00:35:14.400 and of course that's here, in the case of one D,

00:35:17.360 but we can also do more generally.

00:35:18.800 So let me sort of try to summarize, you know,

00:35:21.920 what, after all of these years,

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.

00:35:31.040 The ions are just one example,

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,

00:35:56.720 and whenever you have a favorite Hamiltonian

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

00:36:15.120 to the individual cube it separately,

00:36:17.000 so we have single-side control.

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

00:36:25.760 than something like that.

00:36:27.520 And of course, it comes with the fact

00:36:29.000 that if you take new tools like the quantum gas microscope,

00:36:32.360 that these new tools allow you also

00:36:34.120 to do weedouts on the level of single atoms

00:36:37.080 or on the level of single spins.

00:36:39.240 So I would say this is sort of achieving

00:36:41.200 in the quantum, many body system complete control

00:36:43.800 of these systems, and of course, we

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,

00:36:51.040 and so on, build on theoretical ideas

00:36:53.640 that we developed in this book some time ago

00:36:57.120 in collaboration, of course, with many people.

00:37:00.640 And this sort of now takes me to the little bit new part

00:37:04.400 of my talk where you might ask yourself,

00:37:07.080 what do we want to do now?

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,

00:37:14.920 experimentalists have single-side control

00:37:16.960 in these many body systems.

00:37:18.800 And what's also coming in is that they

00:37:21.040 could do these experiments with very high repetition rates.

00:37:24.480 And then, of course, you as a theorist

00:37:26.160 start to think about these things.

00:37:27.520 What should we do with that?

00:37:28.800 We have new tools available.

00:37:30.480 What should we do?

00:37:31.200 And I will give you now one example

00:37:33.400 that we are working on at the moment, again,

00:37:35.760 in collaboration with the experimentalists,

00:37:37.480 the new theoretical ideas.

00:37:39.560 And at the end, these leads that do a whole new generation

00:37:43.280 of experimental realizations.

00:37:46.160 And I will talk a particular about measuring

00:37:48.360 entanglement as rainy entropy.

00:37:49.960 And, of course, I have to explain to you

00:37:51.480 in detail what it means.

00:37:53.320 But before I do that, I want to sort of highlight

00:37:56.400 one very recent development that I find

00:37:59.280 is very exciting related to rigbreak atoms in these systems.

00:38:04.640 I've talked about ions that match

00:38:06.280 in the habit models a little bit.

00:38:07.960 This is sort of a new toy in this context.

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

00:38:19.000 single systems of humans.

00:38:21.720 I guess all of you know what the tweezers

00:38:23.720 from biology, where you focus a laser

00:38:26.000 and they're able to trap a particle.

00:38:27.440 But you can do the same thing also with atoms.

00:38:29.840 So you can trap atoms.

00:38:31.080 You can cool laser coordinate down.

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.

00:38:39.440 What you do now is this that you can actually

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,

00:38:57.240 this is film, this empty empty empty.

00:38:59.480 You can simply rearrange all of these things you together.

00:39:02.520 And if you, for example, you know,

00:39:05.480 play the experimentalist appear, you can even, you know,

00:39:09.080 have your name written or so, this context,

00:39:12.720 and you can do these things also in 2D.

00:39:15.440 So these are really sort of bottom-up design, you know.

00:39:18.440 You want an atom there, though,

00:39:19.960 with this kind of interaction, you can do these things

00:39:22.320 now in the lab, OK?

00:39:24.760 What's really promising is the fact

00:39:26.440 that the next generation will have, you know,

00:39:29.080 about 1,000 of these atoms in 1D, 2D, and 3D.

00:39:32.560 So we're getting at the point where we can really, really

00:39:35.040 make these things useful, you know,

00:39:37.000 in a completely new context.

00:39:38.400 Here's an example.

00:39:42.200 So if I take now the system over here,

00:39:44.240 I can't excite atom to Ritberg states,

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

00:39:53.280 that built, you know, on basic interactions

00:39:55.440 that you can engineer in this atomic system.

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,

00:40:06.400 down to the point where I can engineer quantum

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

00:40:20.880 of design toolbox here of this quantum,

00:40:26.720 of general quantum many body systems.

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

00:40:45.840 that we're working on at the moment,

00:40:47.280 that started some time ago, it's purely theoretical ideas,

00:40:50.480 but I will show you at the end of my talk now

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

00:41:04.800 at the end, and also leads to, you know,

00:41:06.800 experimental realization, and all of these things

00:41:08.880 happen just within one year.

00:41:12.080 And I would like to ask now a question,

00:41:14.000 which is very important,

00:41:14.880 that whenever we talk about quantum simulation

00:41:17.280 and all of these things, we talk about entanglement

00:41:19.560 in these systems, and the question is this,

00:41:22.160 can be actually measured as a protocol

00:41:24.800 entanglement in systems, like, for example,

00:41:28.440 if I give you a quantum antibody system

00:41:30.520 and it's in a pure state, then, of course,

00:41:33.080 the phenomenon entropy will have entropy zero,

00:41:35.360 but if I partition it, the partitioning

00:41:37.760 and the entropy will then be a mixed state,

00:41:39.760 and this mixed state will have an entropy,

00:41:42.040 which is not equal to zero.

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,

00:41:57.080 but we trace it over the second part,

00:41:58.960 defining this row A here.

00:42:00.600 For example, it's a ground state of a certain system,

00:42:03.160 and then we have, you know, an entropy,

00:42:05.920 this either is a phenomenon entropy,

00:42:07.560 it will be intercede actually the following,

00:42:09.400 you know, in this rainy entropy,

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,

00:42:17.160 then you will try this interesting,

00:42:18.440 because we might characterize here,

00:42:21.200 set the biological or strongly correlated quantum crazy.

00:42:24.120 So you would like to build new tools,

00:42:26.360 you know, that are available in these experiments

00:42:29.520 that answer interesting quantum many bodies.

00:42:31.840 Questions that so far could not be answered.

00:42:34.360 So the question is, can we actually measure things

00:42:36.720 like these things over here?

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

00:42:44.520 get credit for some of the earliest ideas

00:42:46.680 in this context, but we thought

00:42:48.040 much more in a quantum computing context.

00:42:50.760 Can we measure rainy entropy with copies?

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

00:43:02.920 of row is cleared.

00:43:05.760 And we wrote some theory papers over here,

00:43:08.640 which then Mark was kind of picked up,

00:43:11.440 and we found certain protocols,

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,

00:43:18.240 you know, one over here and one over here.

00:43:20.200 These are Harvard models that are being implemented,

00:43:22.480 and I would like to tell you now a little bit

00:43:24.440 what the underlying ideas are,

00:43:26.080 but then we placed this protocol by Sunday,

00:43:28.080 which is now maybe much easier,

00:43:30.240 and for the experimentalists,

00:43:31.400 so so much more friendly to implement,

00:43:33.680 so that I need this thing as a warm up here.

00:43:37.280 So the story that Otto Ecker told us,

00:43:39.640 you know, quite some time ago, was the following one,

00:43:42.400 well, we mentioned that you're interested

00:43:43.920 in trace of row to the power n,

00:43:46.320 but you have the ability to make any copies

00:43:48.800 of a quantum system like this thing over here.

00:43:52.000 How do you get from this thing here,

00:43:53.760 this trace of row to the power n,

00:43:55.440 and the answer was that, well,

00:43:57.600 if you introduce an operator, Bn,

00:44:00.120 this is essentially a swap operator,

00:44:02.440 then it simply we orders all of these indices

00:44:04.840 that we have for we in such a way,

00:44:06.840 that the trace of row to the power n, you know,

00:44:09.560 is acting with this swap operator

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.

00:44:17.560 So if you can measure this expectation value,

00:44:20.320 and so the implement this swap operator,

00:44:22.640 you have here the trace of row to the power n,

00:44:25.400 which are these many entropy that one is interested in.

00:44:28.640 Here's sort of a simple example,

00:44:30.000 that illustrates what we mean by that.

00:44:31.600 If I take two copies here,

00:44:33.600 below that introduces swap operator,

00:44:35.680 we simply interchange these two indices,

00:44:38.080 as you can see over here.

00:44:39.480 Well, if you go through the map down here,

00:44:41.240 trace of, you know, the swap operator,

00:44:43.280 row one tensor, row two,

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,

00:44:55.520 originally, was the whole quantum circuit,

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

00:45:02.080 for doing these things.

00:45:03.680 Now, we came up with ideas how you can actually avoid

00:45:06.960 all of these complications,

00:45:08.280 at least at the case of Harvard models.

00:45:10.360 And this led to, without telling you the details of this,

00:45:13.640 that these papers here,

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,

00:45:20.480 which by building two copies over here,

00:45:22.800 allowed one to measure our rainy entropies,

00:45:25.200 and the wind principle that exists,

00:45:27.840 but let me now give you a version,

00:45:29.760 which is actually very cute physically.

00:45:32.160 But at the same time, I think it is also something

00:45:34.840 that's experimentally much simpler.

00:45:37.320 And this is, I would like to measure rainy entropies

00:45:40.040 via random measurements,

00:45:42.280 and it works for a single system.

00:45:45.200 So these were theoretical ideas that are not even one year old,

00:45:49.120 sort of published in these papers over here,

00:45:51.280 that want to give, particularly credit

00:45:53.080 to our previous evidence, Benoit Vermez for all of that.

00:45:57.000 And you can see my old collaboration

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.

00:46:13.080 And as I said, also useful,

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,

00:46:24.240 then they are able to measure rainy entropies.

00:46:26.760 So let's try to make a virtual copy.

00:46:29.280 You will ask me, what to mean by virtual copy?

00:46:31.920 They'll say that the virtual copy is exactly

00:46:34.440 their replica tricks that we know so well

00:46:36.960 from the work of Parisi, for example.

00:46:39.840 You know, there's usually more mathematical trick,

00:46:41.960 but out of this mathematical trick,

00:46:43.520 we make something over here,

00:46:44.960 which at the end becomes a real measurement protocol.

00:46:48.920 And so how does it work?

00:46:50.400 Well, I go back to note paper by Stephen Fanank,

00:46:53.320 and he pointed out the following thing,

00:46:55.880 that suppose that you got a spin system over here,

00:46:59.240 and you're interested in the set of subsystem

00:47:01.880 that we call A over here.

00:47:03.720 And let's apply now over here some U-A,

00:47:06.640 which is some random unitary operations

00:47:09.160 on the spins that we have here of interest.

00:47:12.680 If you make measurements after that,

00:47:14.520 then you can see that the probabilities

00:47:16.280 that we find over here are just given by this formula.

00:47:19.120 You know, rho, then you scramble it up

00:47:21.160 by this random unitaries,

00:47:22.840 and then you do your measurement,

00:47:24.040 this gives you the probability.

00:47:27.240 But now let's do the following.

00:47:28.280 Suppose that I average now,

00:47:30.200 this thing over all possible unitaries,

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,

00:47:37.040 if I've done a very good scrambling,

00:47:38.720 all of them will be the same,

00:47:40.120 which is equal to a constant.

00:47:41.960 But what's very interesting is that if you look at the square

00:47:44.480 of this probability and then you average,

00:47:47.040 then you find that indeed here is your rainy entropy appearing.

00:47:50.760 So there's a way of measuring rainy entropies

00:47:54.200 by looking fluctuations in the systems

00:47:56.400 in with random measurements.

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,

00:48:07.480 but I write it under one trace.

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

00:48:20.320 belongs to a circular unitary ensemble,

00:48:22.800 you get light, if you have Gaussians,

00:48:24.920 for example cross correlations.

00:48:26.440 This u will be correlated with that here,

00:48:28.520 but there will also be cross correlation

00:48:30.320 between these two different virtual copies.

00:48:32.440 And this is the one that makes the magic of it,

00:48:35.520 the end to allowing us sort of here

00:48:38.040 to extract the rainy entropies from that.

00:48:40.840 In quantum information, this is called two-design

00:48:43.400 or T-design in a more general context.

00:48:46.480 And so you can see that if in a system like that,

00:48:49.280 we're able to perform random measurements,

00:48:51.680 there will be possibilities for extracting

00:48:54.680 interesting stuff like some example rainy entropies,

00:48:57.600 a scientist, an indicator, a quantifier of entanglement

00:49:02.040 measurements.

00:49:03.080 The questions, of course, how to realize

00:49:04.800 and how many measurements the unitary is we need.

00:49:08.120 This is getting a more technical discussion

00:49:10.240 and I've just had a few slides

00:49:11.640 that should sort of indicate you

00:49:12.920 and then I'll show you some experimental results for that.

00:49:16.960 So the measurement protocol sort of, you know,

00:49:19.000 at the end, it will be something like this

00:49:20.680 where we have time.

00:49:21.960 And the next one, mentally, it has done

00:49:23.360 an interesting quantum dynamics over here,

00:49:25.640 preparing a certain interesting quantum state,

00:49:27.880 maybe on the quantum computer or the quantum simulator.

00:49:31.600 And then we would like to ask,

00:49:32.960 can we measure trace role to this power n

00:49:35.440 of a subsystem over here?

00:49:38.240 And the way that we do it is that the random unitaries

00:49:41.160 we simply build up by using the fact

00:49:43.560 that I've pointed out before,

00:49:45.440 we have available in the laboratory

00:49:47.880 called the many body systems

00:49:49.840 that we have single-site addressing.

00:49:51.680 So I can go in, for example, and make a random disorder

00:49:56.200 and it becomes a programmable random disorder

00:49:59.800 that we can add to our systems.

00:50:02.880 And what we have at the very end is that

00:50:05.120 if I do sort of a series of mini-cranches,

00:50:07.560 you know, with different disorder systems over here,

00:50:10.320 the question is, how does this thing here

00:50:12.280 converge to a circular unitary ensemble?

00:50:15.480 How many of these order patterns do we need

00:50:18.400 that we have to program in an experiment like that?

00:50:22.200 And these answers are answered over here

00:50:24.240 by having, for example, an easing model

00:50:26.080 in over the certain number of left side

00:50:27.800 and the certain disorder, all of these things

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,

00:50:35.120 then these things have converged down here,

00:50:37.240 essentially, to the value that we want.

00:50:39.520 So it takes about, you know, say in this case,

00:50:41.960 you tend to know, these order-realizations

00:50:44.760 in order to converge down to the fact

00:50:47.360 that they have unitaries,

00:50:48.360 that approximate values at least

00:50:49.760 on the second order correlation function,

00:50:51.680 the circular unitary ensemble.

00:50:54.240 All of these things are available in the lab.

00:50:56.560 And if you ask yourself how fast as it converged,

00:50:59.640 then the answer is simply that the number

00:51:01.720 of necessary trenches of also scales

00:51:04.280 with the system size, which is your subsystem size

00:51:07.280 that you want.

00:51:08.280 And this works in one D and two Ds.

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

00:51:15.960 of random unitaries for period measurements.

00:51:19.680 So all of these things that we do here,

00:51:21.600 essentially, is that in our controlled,

00:51:23.520 called the main body system,

00:51:24.840 we can sort of do chaos by design

00:51:27.360 and by these chaos by design,

00:51:29.280 construct a measurement protocol out of these things

00:51:32.320 so that p to the power n gives us

00:51:34.360 these rainy entropies to the nth power.

00:51:36.560 And in space of the fact that we have

00:51:38.240 these correlation functions over here,

00:51:40.240 that we imitate with our random disorder

00:51:42.760 that should approximate as well as possible

00:51:44.840 the circular unitary ensemble here.

00:51:47.840 Well, these results are sort of consistent

00:51:49.800 with random gates that people are trying to do,

00:51:53.920 for example, with superconducting circuits

00:51:56.920 at the moment.

00:51:58.280 But in our case, I would say we get these things,

00:52:00.800 essentially, here, for free in our systems.

00:52:05.040 So the measurement protocol,

00:52:06.480 then sort of works like this,

00:52:07.720 that we have here a sequence of random unitaries

00:52:11.080 that we have to implement,

00:52:12.080 and then we do our standard measurement

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.

00:52:19.720 And we have to repeat these things.

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

00:52:28.440 over here and I will not enter the details

00:52:30.560 behind it.

00:52:31.880 What it simply means is that in these experiments,

00:52:34.200 if you do about 100 measurements

00:52:35.720 and if you do about 100 unitaries,

00:52:37.520 then this is essentially for sufficient,

00:52:39.800 no, for the system sizes that we can do in our context.

00:52:45.240 What's this thing now enabling?

00:52:47.320 Well, maybe you would like to see something like an aerial

00:52:50.120 or all of you, I guess,

00:52:51.240 know that if you have a quantum system

00:52:52.960 that take a certain subsystem out of over here,

00:52:56.360 in a system of being the aerial or,

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,

00:53:09.040 this is sort of what you see ideally

00:53:11.360 if you apply our protocol in this context

00:53:13.720 that you can see that with a sufficient number

00:53:16.000 of these orders, we are right on top.

00:53:18.080 So this is would be a way of experimentally measuring

00:53:20.480 aerial, as never done before.

00:53:22.720 And I think this is now sort of constructing tools

00:53:25.600 that will allow us to do so.

00:53:27.600 Or if you're interested in, say,

00:53:29.120 many body localization,

00:53:30.480 and you would like to see that you have entropy growth,

00:53:33.880 you know, entropy growth,

00:53:35.760 which is logarithmic hidden systems.

00:53:38.000 And you would like to see that, again,

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

00:53:50.920 that we have available will allow to see

00:53:54.280 completely new physics, it is context.

00:53:58.440 You know, a few weeks ago, I got from,

00:54:01.080 from testing roles in the right-of-law school,

00:54:03.320 you know, this email over here,

00:54:05.240 they have implemented these ideas.

00:54:07.040 And what you can see here is results

00:54:09.760 for linear entropy to the system,

00:54:11.400 first of all, for 10 ions.

00:54:13.520 And this is supposed to be a product, say,

00:54:16.520 initially, so down here,

00:54:17.880 they are doing some trench dynamics.

00:54:19.880 You know, the total system should be pure,

00:54:21.840 so this thing should go down to zero on the right-hand side

00:54:24.880 over here.

00:54:25.880 This is exactly what you expect, you know,

00:54:28.080 for this entanglement entropy is to be

00:54:30.880 in these crunch dynamics that we have for, you know,

00:54:33.240 in trenches.

00:54:33.920 And they can even do it for 20 ions,

00:54:37.280 sort of a result over here.

00:54:39.680 And I would say that we have the tools now available,

00:54:42.480 if you can do this thing for larger system,

00:54:44.320 to it's testing what we call this quantum supremacy.

00:54:47.840 And the nice thing is that these protocols

00:54:50.280 that we have here, of course, are available for many systems.

00:54:53.600 And a few more slides and quantum networks

00:54:55.680 and quantum computers, so they'll be doing networking

00:54:58.560 and protocols and all of that.

00:54:59.880 But out to us, so we'll give a talk afterwards

00:55:02.320 at more quantum communication.

00:55:04.240 So we'll basically skip these things,

00:55:06.480 so instead of satellite links,

00:55:08.680 we would like to talk about, say,

00:55:10.600 networking of quantum computers with these things here.

00:55:13.880 So this would be an extra talk.

00:55:16.720 But I guess you sort of got the idea here

00:55:19.640 of the snapshot of these demands triggered 25 years ago

00:55:25.960 that led now to experimental programs

00:55:28.720 that are now at the point.

00:55:30.200 I guess we've got new and interesting physics out

00:55:33.800 and at the same time, you know,

00:55:35.680 you're sort of opening the door,

00:55:37.040 also to quantum technologies.

00:55:38.640 And let me conclude by congratulating

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.

00:55:51.160 And I just want to make a last remark here,

00:55:54.360 the sentence, very often these days,

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

00:56:06.160 and quantum technologies.

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,

00:56:13.960 these people are wrong.

00:56:15.000 I would say that a lot of the basic science questions

00:56:17.720 both on the hardware side,

00:56:19.560 but also on the conceptual side are still open.

00:56:22.400 And keeping these synergies in mind,

00:56:24.640 I think is something which is fundamental.

00:56:27.160 And then you hear discussions about the flagship,

00:56:29.520 you know, flagship for quantum technology

00:56:32.080 by personal wish would have been

00:56:33.840 that it was a flagship for quantum science

00:56:36.640 and quantum technologies.

00:56:38.160 And this is sort of the last remark

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

00:56:47.600 over has not come yet, okay?

00:56:50.360 So, cognitive relations, again,

00:56:51.960 to the Dirac medalist, prize winners this year

00:56:54.920 and I would like to conclude my talk.

00:56:57.680 Thank you very much, Peter, as a great presentation.

00:57:14.840 Any questions?

00:57:15.840 We have very short time, but any other question

00:57:18.040 will be welcome.

00:57:19.440 Yes, a question then.

00:57:24.240 Thank you very much, really, it's a perfect talk.

00:57:29.240 Just about the notion of entertainment.

00:57:46.240 Can we find another correlation type

00:57:48.160 than entertainment?

00:57:49.080 I was reading something about the Discord,

00:57:51.280 but I was reading the people's discussion about the Discord.

00:57:55.120 So, what can you say about this point?

00:57:57.920 Okay, so you would like to measure Discord originally.

00:58:00.400 Well, people have done these things

00:58:02.000 of measuring Discord, but I would say that, you know,

00:58:05.000 what we were interested in was the,

00:58:07.320 I would say, real thing of really this entanglement

00:58:10.680 and to-beast because this is the part

00:58:12.360 that's sort of interesting from the antibody point

00:58:15.160 of view if you are going as better person.

00:58:17.040 So, this goes in a different direction

00:58:20.360 and I think that we are sort of measuring

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.

00:58:28.680 Okay, yeah.

00:58:31.240 Thank you.

00:58:32.760 You can so, let's thank Peter again.

00:58:34.920 Thank you.

00:58:35.760 Thank you.

00:58:36.600 Thank you.

00:58:37.600 Thank you.

00:58:38.600 Thank you.

00:58:39.600 Thank you.

00:58:40.600 And I would like to call after I can.

00:58:43.240 Thank you.

00:58:44.400 Please join me to welcome our, after, and,

00:58:48.640 thank you for the pleasure.

00:58:50.640 APPLAUSE

00:58:54.640 CHEERING

00:58:58.640 CHEERING

00:59:02.640 CHEERING

00:59:05.640 CHEERING

00:59:08.640 CHEERING

00:59:12.640 CHEERING

00:59:15.640 Oh, does it work?

00:59:18.640 Does it work?

00:59:21.640 All right.

00:59:24.640 So, thank you very much for inviting me here

00:59:28.640 and I should say, it's all a gave me probably

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.

00:59:42.640 You only take them 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,

00:59:55.640 no, those are theories.

00:59:57.640 Well, working with experimentalism,

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.

1:00:06.640 So, I thought, you know,

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

1:00:15.640 who ventured into this field?

1:00:17.640 Anyway, but I should perhaps start by

1:00:23.640 congratulating the three people who got the direct prize,

1:00:32.640 Charlie and David and Peter.

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

1:00:44.640 about the work at the same time, you know,

1:00:47.640 that's such a vast area of papers that were produced

1:00:52.640 by them and that would, you know,

1:00:54.640 it was very difficult to find a theme that would somehow

1:00:58.640 incorporate everything that they did.

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,

1:01:25.640 and the colleagues created not only

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

1:01:37.640 a very peculiar atmosphere in this field.

1:01:40.640 So, everyone felt invited and was helped.

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,

1:02:23.640 you know, universe, everything.

1:02:25.640 In fact, you know, my first conversation with David

1:02:27.640 was nothing to do with quantum physics,

1:02:29.640 but it was all about Karl Popper.

1:02:31.640 And so, I just realized that I found a fellow

1:02:35.140 popularian in Oxford.

1:02:36.140 I thought, yes, I like this guy, you know,

1:02:38.140 I'm going to work with him.

1:02:40.640 But, you know, all my students, almost all my students ended up

1:02:43.640 working with David.

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

1:03:00.040 probabilities.

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

1:03:08.040 students in Oxford sooner or later.

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

1:03:19.040 exploded over the last few years.

1:03:22.040 And, you know, few, at the very beginning, it was pretty much

1:03:25.040 like a family business.

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,

1:03:32.040 in a small place, Broadway in England,

1:03:37.040 it was just, you know, pretty much everyone

1:03:39.040 who was working this field at the time.

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

1:03:52.040 in the quantum aspects of computation.

1:03:54.040 And then it exploded.

1:03:56.040 And many, many of those sort of meetings,

1:03:58.040 early meetings in quantum information science,

1:04:01.040 where David and Charlie and Peter attended,

1:04:05.040 was in a view like, well, you know,

1:04:07.040 why do you like, well, you know, Peter asked,

1:04:09.040 actually, there was a good reason.

1:04:11.040 So, what happened was that a person called

1:04:14.040 Giuseppe Castanioli, who was one of the directors

1:04:17.040 of the field site that is based in Torino,

1:04:20.040 had a friend who was Mario Razzetti,

1:04:22.040 who was responsible for Iranian Institute

1:04:25.040 and Giuseppe Castanioli,

1:04:28.040 who voted into business,

1:04:30.040 but he had some ideas about quantum computing.

1:04:33.040 He wanted to somehow, you know, sponsor something.

1:04:37.040 So, else, instead of giving money for you,

1:04:39.040 another art exhibition in general,

1:04:41.040 decided to sponsor a series of workshops

1:04:44.040 in quantum information science,

1:04:46.040 and Mario Razzetti somehow took care of it

1:04:48.040 from the logistic point of view.

1:04:50.040 So, I think, indirectly,

1:04:54.040 those people shaped this field.

1:04:56.040 And as you could see, those pictures,

1:04:58.040 were mostly, I think, taken by Charlie,

1:05:00.040 who at some point cleverly used,

1:05:04.040 I don't know what it was, photoshop,

1:05:06.040 or whatever you used, Charlie.

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.

1:05:15.040 So, every now and then, you can find them,

1:05:17.040 I got an artificial head popping up so that,

1:05:20.040 so that Charles, Charlie wanted really

1:05:24.040 to have everyone included in a true,

1:05:27.040 so all embracing spirit of the field.

1:05:30.040 So, which, by the way, I remember that, you know,

1:05:32.040 once I was invited to give a lecture

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

1:05:44.040 and I wanted to encourage him,

1:05:46.040 who wanted to join this field.

1:05:47.040 No matter what sort of directions you are coming from.

1:05:50.040 And, you know, I never used a word,

1:05:52.040 Catholic, in terms of word embracing,

1:05:54.040 but this sort of subconsciously,

1:05:56.040 I said, you know, come to this field.

1:05:58.040 This is a very Catholic field.

1:06:00.040 And, you know, imagine this.

1:06:06.040 This talk is still remembered in the Queen's University.

1:06:10.040 Anyway, so, when I thought,

1:06:16.040 well, should I really be talking about,

1:06:19.040 I started permuting my transparencies

1:06:21.040 and I think I sympathized my talk so much.

1:06:24.040 That this morning when I sent those slides

1:06:26.040 to the organizers of this meeting,

1:06:29.040 I actually, I don't know whether I'll have any real control

1:06:33.040 over this talk.

1:06:34.040 So, I'll just venture in the direction,

1:06:36.040 in one aspect of quantum computation

1:06:38.040 or quantum information processing,

1:06:40.040 it has to do with data security,

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.

1:06:58.040 You know, for one thing,

1:07:01.040 Peter's algorithm, as you know,

1:07:03.040 affects the security of public key crypto systems,

1:07:07.040 such as RSA, but not only, you know,

1:07:11.040 for example, if you look at the cryptocurrency,

1:07:14.040 say, Bitcoin, so the moment.

1:07:16.040 And the two important components,

1:07:19.040 for the whole thing to work, are digital signatures,

1:07:22.040 which are based on electric curves,

1:07:24.040 which can be broken with Peter's algorithm.

1:07:29.040 And there's also the mining process

1:07:32.040 that can be seriously affected if you can do quantum search,

1:07:36.040 for example.

1:07:38.040 So, quantum technology, those ideas,

1:07:42.040 sort of if they were, you know,

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,

1:08:07.040 and how most of the time they failed,

1:08:11.040 and go through the public key crypto systems

1:08:14.040 ending up with sort of a quantum crypto.

1:08:16.040 So, I'm not going to go into those details

1:08:19.040 because that's probably not important,

1:08:21.040 but maybe I'll just say a few words about

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,

1:08:34.040 and design a system,

1:08:36.040 which comes as close as one can possibly come

1:08:39.040 to perfectly secure communication.

1:08:42.040 And so, this, so the fact that on one hand,

1:08:47.040 when you have a quantum computer,

1:08:49.040 you destroy public key crypto systems

1:08:51.040 and it's a big thing now,

1:08:53.040 to design possibly new generation of public key cryptosystem

1:08:57.040 that will resist attacks from quantum computers

1:09:00.040 and people, as you probably know,

1:09:02.040 national security agency and some other people

1:09:05.040 are looking to replace none of RSA

1:09:08.040 going some directions possibly lattice-based cryptography,

1:09:12.040 but another candidate

1:09:14.040 for that is quantum cryptography, of course.

1:09:17.040 So, it's Gilebrasard put it,

1:09:19.040 you know, the quantum take of the way,

1:09:22.040 but also the quantum key to the bad thing

1:09:24.040 in the form of quantum crypto.

1:09:27.040 So, I'm going to talk about, you know,

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

1:09:37.040 then Charlie Bennett and Gilebrasard

1:09:40.040 turned it into quantum key distribution.

1:09:43.040 I had a slightly different approach

1:09:45.040 based on quantum entanglement,

1:09:47.040 which I will take, not because it is my approach,

1:09:50.040 but because it has it leads in some way

1:09:53.040 into something that I would consider maybe

1:09:58.040 an interesting part of cryptography today,

1:10:02.040 devising dependent cryptography,

1:10:04.040 and also it will take me to some speculations

1:10:08.040 about randomness and probability idea.

1:10:12.040 So, probably, most of you know that

1:10:17.040 any two individuals to communicate

1:10:21.040 in a secure way, it's probably not

1:10:23.040 if they share a private randomness.

1:10:25.040 So, if the two individuals,

1:10:27.040 we all just call them Alice and Bob,

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.

1:10:41.040 And usually, you know, in classical world,

1:10:44.040 so to speak, it's very easy to test

1:10:47.040 that something is random in the sense

1:10:49.040 that it's uniformly distributed,

1:10:51.040 but it's almost impossible to make sure

1:10:54.040 that those sequences are really unpredictable

1:10:57.040 so that they are not known to anyone,

1:10:59.040 but Alice and Bob.

1:11:01.040 So, this you can not really do,

1:11:03.040 in that non-quantum scenario.

1:11:08.040 The ones you have those random sequences

1:11:13.040 you can communicate, for example,

1:11:15.040 using a one-time path, which is one of the oldest

1:11:18.040 cryptosystems that was proposed.

1:11:21.040 And so, one way to make sure

1:11:26.040 that Alice and Bob ended up

1:11:29.040 with the strings of binary strings of zeros and ones

1:11:34.040 that are not known to anyone else

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.

1:11:49.040 So, it turns out that if you generate

1:11:53.040 a pair of entangled particles,

1:11:55.040 the stronger they are correlated with each other,

1:11:57.040 the less they are correlated with anything else.

1:12:00.040 And so, you can randomly test

1:12:02.040 and see that the two entities are really strongly correlated,

1:12:05.040 very, very 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

1:12:17.040 knows anything about it.

1:12:18.040 So, one way to do it is to run the bell test,

1:12:22.040 the test that was designed to test

1:12:25.040 for the local realism, but not necessarily going

1:12:30.040 in this direction.

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.

1:12:36.040 You measure a certain figure of merit,

1:12:38.040 call it the bell quantity,

1:12:40.040 and all these bases you can decide

1:12:45.040 how secure is the key that you generated,

1:12:49.040 how good it is for cryptographic purposes.

1:12:51.040 So, that's kind of an old story.

1:12:54.040 But then, at this point, you say far,

1:12:57.040 so you generated the key,

1:12:59.040 you can assess how good it is,

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?

1:13:20.040 Can you somehow counteract that on this?

1:13:23.040 So, oops.

1:13:29.040 So, this is actually not a sort of a

1:13:34.040 hypothetical question,

1:13:37.040 because there are experimental colleagues

1:13:40.040 who actually exploit the imperfections

1:13:44.040 in the implementations of quantum cryptography.

1:13:47.040 And that's a good work,

1:13:49.040 so they kind of quantum hackers.

1:13:51.040 And so, I just pick up this photograph

1:13:55.040 from Vadi Makarov,

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

1:14:07.040 all those things ideally.

1:14:09.040 And therefore, he is using his tool,

1:14:13.040 his famous suitcase that you can see here,

1:14:17.040 and to correct some supposedly secure

1:14:22.040 quantum key distribution methods.

1:14:25.040 But you know, in fact,

1:14:28.040 you can, you can deal with the situations

1:14:35.040 where you have imperfections.

1:14:37.040 As long as you can reach the level of implementation

1:14:40.040 of those built inequalities,

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,

1:14:50.040 with the directions

1:14:54.040 and with setting up this experiment in a certain way,

1:14:59.040 then what is interesting is

1:15:02.040 that the hardware doesn't matter anymore.

1:15:04.040 It just by correlation alone,

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.

1:15:15.040 So, in other words,

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,

1:15:28.040 there are a few assumptions.

1:15:30.040 So, one of them is that

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

1:15:40.040 random number generators.

1:15:43.040 So, just to be sure.

1:15:45.040 So, I'm talking about a scenario where Alice and Bob

1:15:48.040 can then purchase devices from,

1:15:53.040 you know, some kind of a dodgy dealer

1:15:57.040 who comes to them and say,

1:15:59.040 look, I'm selling you those at some discounted price.

1:16:03.040 Those are good quantum devices,

1:16:05.040 and you can distribute cryptographic key.

1:16:07.040 And you don't trust this person at all.

1:16:10.040 But nonetheless, if you take those devices,

1:16:13.040 you can, without knowing really what they are doing.

1:16:17.040 As long as they generate correlations

1:16:19.040 up to a certain degree,

1:16:21.040 you don't care what is inside.

1:16:23.040 You just simply say, okay, fine.

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.

1:16:31.040 So, in order to do this,

1:16:33.040 in order to run this test, of course,

1:16:35.040 you have to also rely that you have a source of

1:16:38.040 truly random numbers locally.

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

1:16:48.040 at the Alice and Bob have to dispose.

1:16:50.040 Otherwise, it would work very well.

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,

1:16:59.040 but so you purchase this device,

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.

1:17:12.040 So, somehow, you have to make sure

1:17:14.040 that your local randomness, your local random number generators

1:17:17.040 are either devices that you can trust,

1:17:21.040 or you can do something about it.

1:17:28.040 So, for example, you can just purchase a quantum random

1:17:32.040 number generator and plug in.

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

1:17:45.040 generators, you also would like to,

1:17:47.040 usually you don't produce them yourself.

1:17:49.040 You would just get them.

1:17:50.040 You also would like to self test,

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,

1:17:59.040 you know, that you can trust them.

1:18:00.040 So, the question is, can it be done?

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

1:18:12.040 is of this time.

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

1:18:22.040 and says, well, you know, go ahead

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

1:18:34.040 is doing what it's supposed to be doing?

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.

1:18:50.040 The frequency of 0's and 1 is the same.

1:18:53.040 The frequency of all pairs and subset of 0's and 1's is the same.

1:18:57.040 This you can test.

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

1:19:43.040 you are getting there.

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

1:20:03.040 and you don't understand the physics.

1:20:05.040 It's just most of electronics and gadgets there and you don't know

1:20:07.040 what's going on. So, how do you know?

1:20:09.040 You wouldn't know, basically.

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

1:20:28.040 analytical I.D. Quantique.

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

1:20:48.040 to the best of our knowledge, right?

1:20:51.040 The question I'm asking now is it, you know,

1:20:54.040 you may not trust those authorities

1:20:56.040 and if you sort of like a bit contrary in a

1:20:59.040 zone, you may not trust the governments,

1:21:01.040 you may not trust the authorities.

1:21:03.040 So, you would like to test yourself whether this device

1:21:06.040 does what it's supposed to be doing.

1:21:09.040 And so, the question is, can you do it?

1:21:15.040 One thing you may consider is, you know,

1:21:18.040 computer scientists have all kinds of ideas

1:21:20.040 how to amplify randomness, how to take something

1:21:23.040 that is, let's try that, for example,

1:21:26.040 and make it a bit more private.

1:21:28.040 So, you can use private simplification, for example.

1:21:31.040 But we know that, basically,

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.

1:21:48.040 For example, in computer science,

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

1:22:02.040 there's no classical randomness.

1:22:06.040 There's no classical processing of this randomness

1:22:09.040 that would allow you to expand it

1:22:11.040 or to make it more private.

1:22:13.040 So, it's a well established result.

1:22:15.040 However, you know, if you then construct

1:22:19.040 the random, you know, this can be bypassed

1:22:23.040 by using, again, monogrammes correlation.

1:22:25.040 So, if you design a quantum random numbers

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

1:22:36.040 between those two outputs.

1:22:38.040 And then, basically, pretty much by the same argument

1:22:41.040 about the monogrammes of entanglement

1:22:43.040 or monogrammes of certain correlations,

1:22:45.040 you can then sample from one of the outputs

1:22:49.040 and be actually quite confident that,

1:22:51.040 as long as there's a little bit of true randomness

1:22:55.040 in your input and you can amplify it

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.

1:23:08.040 So, basically, pretty much the case

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,

1:23:21.040 you know, using this in locally,

1:23:25.040 you can actually amplify this randomness

1:23:28.040 up to your satisfaction.

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,

1:23:54.040 if you take this path to secrecy

1:23:58.040 where you use quantum entanglement,

1:24:01.040 you can show not only that by testing

1:24:06.040 for correlations, for monogamous correlations,

1:24:09.040 you can get devices that you can test for security

1:24:18.040 of the data that you obtain.

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

1:24:32.040 very much to your own domain.

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,

1:24:53.040 which is actually quite remarkable.

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.

1:25:11.040 We can just about implement

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,

1:25:24.040 even though I like this narrative,

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,

1:25:39.040 and somehow we are cheating at some level.

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,

1:25:48.040 I don't think it is as simple as that.

1:25:51.040 There's lots of, you know, lots of interesting questions,

1:25:54.040 or fundamental questions that you can ask.

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,

1:26:05.040 and they're the real physical things,

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

1:26:16.040 in terms of, say, the average multiverse,

1:26:23.040 where if you assume, for example,

1:26:25.040 that everything is quantum,

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,

1:26:36.040 so that, you know, how the information,

1:26:41.040 in one particular part of the multiverse is restricted

1:26:46.040 by people sort of, but, you know,

1:26:50.040 the access, how the access is sort of restricted

1:26:53.040 in different parts of the multiverse.

1:26:55.040 So that's certainly one thing.

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,

1:27:10.040 well, is it really objective things?

1:27:13.040 Do we have truly random phenomena in nature?

1:27:17.040 And so that would be, you know,

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,

1:27:30.040 so there's no predetermined thing.

1:27:32.040 And, you know, that was sort of,

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,

1:27:39.040 it's most objective things,

1:27:40.040 atoms follow predetermined parts,

1:27:43.040 and it's just, what is random is due to the lack of your knowledge,

1:27:47.040 maybe, you know,

1:27:50.040 take this discussion where you want,

1:27:53.040 but the question is,

1:27:55.040 is this still relevant?

1:27:56.040 Because if it needed this,

1:27:58.040 the case that everything is quantum,

1:28:02.040 then, you know, what is really random

1:28:05.040 as in this sort of truly quantum universe,

1:28:08.040 and does it exist at all?

1:28:11.040 And it may be the case that it doesn't.

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,

1:28:21.040 you gave this interview,

1:28:22.040 and I think you really said this did you?

1:28:26.040 Right, so, you know,

1:28:28.040 it's just, you know, a valid question at this point

1:28:31.040 to go in that direction and think,

1:28:33.040 how the whole discussion,

1:28:35.040 the historical thing about randomism,

1:28:37.040 probabilities, is going to end up.

1:28:40.040 So, can we develop, for example,

1:28:43.040 physics where we don't use the notion of randomism

1:28:46.040 and probabilities as we do it today,

1:28:49.040 which is a very interesting question.

1:28:52.040 And I think I will probably stop at this point

1:28:57.040 because, as you can see,

1:28:59.040 it was sort of like a talk where I was trying probably

1:29:02.040 to take this notion of security

1:29:06.040 and the idea of pushing privacy to the limits

1:29:11.040 creates, generates lots of interesting questions

1:29:15.040 and fundamental questions,

1:29:17.040 and I think what is great about this field

1:29:19.040 is the fact that somehow more and more often

1:29:22.040 we can address those questions

1:29:25.040 in a rather technical and precise language.

1:29:29.040 So, again, I would like to congratulate

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.

1:29:46.040 Thank you very much.

1:29:47.040 APPLAUSE

1:29:55.040 Thank you very much.

1:29:57.040 I have to thank you for the very inspiring presentation.

1:30:01.040 Any questions?

1:30:03.040 Yes.

1:30:05.040 That's very exciting.

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

1:30:11.040 questions is that scientists in general

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,

1:30:19.040 and then you want to include them.

1:30:21.040 I don't know if you were that one,

1:30:23.040 we had a conference in Capri,

1:30:25.040 and there was a beautiful swimming pool,

1:30:28.040 and a lot of people failed to show up for the group picture,

1:30:31.040 which was around the swimming pool,

1:30:33.040 so I took them later on and then just cut their heads

1:30:35.040 and had them floating around in the water.

1:30:37.040 LAUGHTER

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.

1:30:57.040 Let's say, thank you again.

1:30:59.040 CHEERING

1:31:29.040 CHEERING

1:31:59.040 Thank you.

1:32:03.040 CHEERING

1:32:08.040 CHEERING

1:32:11.040 CHEERING

1:32:15.040 CHEERING

1:32:20.040 CHEERING

1:32:24.040 CHEERING

1:34:18.040 ..

1:34:23.040 ..

1:34:25.040 ..

1:46:10.540 Okay.

1:46:11.540 Okay.

1:46:20.540 Okay.

1:46:25.540 Yeah.

1:46:30.540 Okay, great.

1:46:33.540 And let's see.

1:46:36.540 I was here, hopefully.

1:46:46.540 Okay.

1:47:10.540 Okay.

1:47:34.540 Okay.

1:47:58.540 Okay.

1:48:22.540 Okay.

1:48:46.540 Okay.

1:49:10.540 Okay.

1:49:34.540 Okay.

1:49:58.540 Let's continue.

1:50:12.540 Okay.

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

1:50:21.540 matches of the three hour days.

1:50:31.540 So I will start with Peter Schor.

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

1:51:04.540 quantum schemes.

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

1:51:36.540 sensitivity of quantum states to noise.

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

1:51:51.540 open.

1:51:52.540 And Peter will give the presentation and the title will be, I will just read it, the discovery

1:52:00.540 of the factoring algorithm.

1:52:02.540 But before that, I will ask Peter to come here to, I can give you the rectangle and everybody

1:52:12.540 can give him a warm award.

1:52:30.540 Thank you.

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

1:53:32.540 around 20 years ago.

1:53:33.540 So, out line of my talk is first.

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.

1:53:57.540 So, first, the slide.

1:54:00.540 I opened my question.

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?

1:54:12.540 It's, you know, so obvious.

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

1:54:31.540 the factoring algorithm.

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.

1:54:42.540 Hope, and here is a physics experiment.

1:54:45.540 And I start working very much more.

1:54:52.540 And you can even see that the technicians were in the same uniform.

1:54:59.540 So, you are interested.

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.

1:55:08.540 So, here is a second answer.

1:55:10.540 A computer?

1:55:15.540 A computer answers mathematical questions.

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,

1:55:25.540 you probably don't want to use computers.

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,

1:56:07.540 show that 15 equals five times three.

1:56:11.540 It hasn't happened yet lately.

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

1:56:37.540 most hard to master physics experiments.

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

1:57:15.540 lightnessless.

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

1:58:03.540 natural class of computational functions.

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

1:58:31.540 it might as well be uncomfortable.

1:58:34.540 So computer scientists made this rather, well,

1:58:40.540 from some points of view, which probably

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

1:59:06.540 it as a practically computable function,

1:59:09.540 but it's also something that computer scientists could prove their own

1:59:12.540 sense about.

1:59:14.540 So once this wheel is wheelized,

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

1:59:33.540 by various computer scientists.

1:59:35.540 But I think column is actually the first, you know,

1:59:38.540 a Turing machine can perform efficiently,

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,

1:59:57.540 rather than about mathematics.

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,

2:00:06.540 as they had enjoyed.

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.

2:00:13.540 A number of years before he did.

2:00:16.540 So quantum computers can be built.

2:00:21.540 The really surprising thing is that this would imply

2:00:23.540 this folk thesis is not true.

2:00:26.540 And in fact, this folk thesis has,

2:00:30.540 because one of the questions I get asked,

2:00:40.540 about quantum computers,

2:00:43.540 as well, how much faster is a quantum computer than a classical computer?

2:00:47.540 And this isn't really very bad.

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

2:01:13.540 quantum period of churches thesis.

2:01:15.540 I think we have now gotten to the point

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.

2:01:34.540 So, part two, what led up to discovery.

2:01:38.540 So my first exposure to quantum computing was when I heard it talk

2:01:42.540 by Charlie Bennett.

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,

2:01:51.540 Charlie and Don Smolin built,

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

2:02:11.540 to take them seriously.

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.

2:02:34.540 So, we're looking at them.

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.

2:02:52.540 I was clearly wrong about that,

2:02:55.540 but had I also was not convinced at all that it was at all useful,

2:03:02.540 and I'm not going to say that.

2:03:05.540 I mean, I was wrong about that, too,

2:03:07.540 but that was, I don't think David's papers had any really useful algorithms in them.

2:03:17.540 So, for that, next thing that happened is,

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.

2:03:53.540 So, after I saw Ummish's talk,

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.

2:04:26.540 So, I saw it, I was very interested in it,

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.

2:05:19.540 So, what is Dan Simon's algorithm?

2:05:21.540 Well, it takes place on a hypercube.

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,

2:05:53.540 and let's try that with a different point.

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,

2:06:17.540 what color is this point?

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,

2:06:59.540 if this is D dimensional hypercube.

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

2:07:23.540 looks like, and what the distance is.

2:07:27.540 So that's an exponential speed.

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.

2:07:41.540 The discrete logs, as periodicity,

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.

2:08:01.540 The integers mod, I guess, some number.

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

2:08:16.540 how to do it.

2:08:18.540 But what happened after that?

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

2:08:34.540 lines on it.

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

2:09:06.540 out of the diffraction grading.

2:09:08.540 And the quantum Fourier transform really does the same thing

2:09:11.540 for a periodic function.

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

2:09:23.540 you can figure out the period.

2:09:25.540 And if you know some basic number three, which is well

2:09:30.540 known to quickly.

2:09:31.540 For panelists, you can turn factoring into a

2:09:35.540 problem of finding a period of a function.

2:09:40.540 Okay, so what happened after the discovery?

2:09:43.540 So the news of this spread amazingly fast.

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

2:10:07.540 me how it works.

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

2:10:15.540 factory algorithm yet.

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

2:10:38.540 managed to solve factoring as well.

2:10:42.540 So I could tell Uma Shvazirani.

2:10:45.540 And the news spread, we workably fast.

2:10:48.540 I kept getting, you know, email requests for the paper,

2:10:52.540 and I hadn't written it yet.

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

2:11:11.540 answer by sending them the latest draft.

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,

2:11:22.540 number 30 symposium in Cornell, and June,

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

2:11:44.540 a talk at Bila Guelino in Torino.

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.

2:11:58.540 Luckily.

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

2:12:15.540 Bernstein-Faserani paper talked about.

2:12:18.540 But after I discovered the result, I started talking with

2:12:21.540 physicists.

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

2:12:28.540 mathematics.

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

2:12:49.540 accepted model for quantum computation.

2:12:54.540 And let's see, I'm probably out of time, is that right?

2:12:58.540 Am I out of time?

2:13:00.540 Yes.

2:13:01.540 OK.

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

2:13:29.540 quantum computation does.

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,

2:13:58.540 you can't make another copy of it.

2:14:01.540 Can't measure to see if there's an error, because the

2:14:05.540 highs of the circuits are uncertain.

2:14:06.540 If it means that if you measure the quantum computation,

2:14:09.540 that would be disturbing.

2:14:11.540 And then, of course, if the computation is disturbed,

2:14:14.540 it won't give you the right answer.

2:14:16.540 So the resolution of this is,

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.

2:14:29.540 And how do they work?

2:14:30.540 Well, you'll arrange the codes so that likely errors are

2:14:33.540 orthogonal to the encoded state.

2:14:35.540 And what that means is you can measure the errors without

2:14:38.540 disturbing the encoded state.

2:14:40.540 And once you've measured the errors,

2:14:42.540 you can call back the errors.

2:14:44.540 So with this,

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

2:14:54.540 contender the fourth.

2:14:56.540 This number really depends on the exact quantum fault-powering

2:15:01.540 that makes you use.

2:15:03.540 And it's still unresolved as to what this number should be

2:15:10.540 a few.

2:15:12.540 But if you make a quantum computer,

2:15:14.540 there is fault-powered without using too much overhead.

2:15:19.540 So this is still very difficult experimentally,

2:15:23.540 but in the last few years,

2:15:25.540 various groups are coming really close to this number,

2:15:29.540 which is very encouraging.

2:15:35.540 And this is my last slide,

2:15:38.540 so thank you.

2:15:39.540 Thank you very much.

2:16:02.540 Thank you very much.

2:16:04.540 Very nice piece of history as a beautiful way to see how things

2:16:09.540 develop.

2:16:10.540 Any questions?

2:16:11.540 Any one comment or question?

2:16:15.540 Paulino?

2:16:16.540 Yes?

2:16:17.540 Yes.

2:16:21.540 OK.

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.

2:16:44.540 If you talk to Peter Sarna,

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

2:17:07.540 has discovered it yet.

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,

2:17:14.540 probably completely wrong.

2:17:18.540 Thank you very much.

2:17:20.540 Thank you so much.

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

2:17:51.540 born in 1943 in New York City.

2:17:54.540 He earned a BS in chemistry from Brandage University in 1964

2:17:59.540 and received his PhD from Harvard in 1970

2:18:02.540 for molecular dynamic studies, computer simulations of molecular motion.

2:18:06.540 At Harvard, he worked for James Watson,

2:18:09.540 one year as a teaching assistant about a genetic code

2:18:12.540 for the next two years.

2:18:17.540 He continued his research under Anisur Raman at Argonne Laboratory.

2:18:20.540 After joining IPM research in 1972,

2:18:24.540 he built on the work of IPM's Rob Landauer

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...

2:18:55.540 In 1982, he proposed a ring deputation

2:19:01.540 of Maxwell's demo attributing its inability

2:19:05.540 to break the second dot to the top.

2:19:08.540 So, to the top of the dynamic coast of this poison

2:19:11.540 rather than acquiring information.

2:19:16.540 And with James Brasser, sorry,

2:19:30.540 I think something's an interesting image.

2:19:35.540 I think...

2:19:38.540 I think...

2:19:39.540 Yes, with James Brasser from the University of Montreal,

2:19:41.540 I think I had to mention.

2:19:43.540 When it invented quantum cryptography,

2:19:46.540 where two distant parties share a secret,

2:19:49.540 a secret encryption key with security from Evers,

2:19:52.540 if strippers currently,

2:19:54.540 by the basic quantum limitations of measurements

2:19:56.540 of incompatible low-servables.

2:19:59.540 Menet and collaborative resource introduced quantum teleportation,

2:20:03.540 whereby entanglement and classical singers are used

2:20:06.540 to transfer quantum states.

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

2:20:14.540 of four pure systems,

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.

2:20:22.540 So, please join me to...

2:20:24.540 Join us for a challenge for this director.

2:20:49.540 Thank you very much.

2:21:25.540 Okay, and then Charles will give us a presentation building

2:21:28.540 a culture of quantum information.

2:21:37.540 Can we do the yellow?

2:22:02.540 Yes, so I'm very glad to be here.

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

2:22:11.540 for a long time.

2:22:13.540 I'm going to talk about the culture of really the culture

2:22:18.540 of information science,

2:22:20.540 because when you...

2:22:25.540 Well, I say other parts of mathematics,

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,

2:22:50.540 and by Shannon the...

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

2:23:07.540 by making these brutal abstractions,

2:23:09.540 but they were a little bit too brutal.

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.

2:23:21.540 And these were the reversibility,

2:23:26.540 questions of reversibility,

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.

2:23:41.540 These were both...

2:23:42.540 I mean, in all of the 20th century scientists,

2:23:45.540 they knew about quantum mechanics,

2:23:47.540 and they've been around for a while,

2:23:49.540 and they certainly knew about thermodynamics

2:23:51.540 have been around for over a century,

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.

2:24:03.540 Their states are reliably distinguishable,

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,

2:24:11.540 like what's in my left pocket,

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,

2:24:19.540 each one separately.

2:24:21.540 But of course, quantum systems don't behave that way.

2:24:25.540 But for most of the 20th century,

2:24:28.540 this was regarded as a kind of a nuisance,

2:24:31.540 because people focused on the uncertainty principle

2:24:33.540 causing quantum systems to behave less reliably

2:24:36.540 than larger systems.

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

2:24:48.540 for information processing.

2:24:50.540 Now, the first that I found out about it

2:24:52.540 is by my conversation with Stephen Wiesner,

2:24:55.540 who is my college classmate.

2:24:58.540 And he had some ideas that things you could do with information

2:25:03.540 that were not covered by Shannon's theory.

2:25:06.540 One of them was to combine two messages

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,

2:25:20.540 but not both.

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

2:25:27.540 and you decrypt it the other way.

2:25:29.540 So this, the idea that the uncompiability of quantum information

2:25:32.540 was something that could be useful.

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

2:26:05.540 about this in 1968, actually.

2:26:08.540 And I think he submitted it to IEEE

2:26:11.540 with then didn't follow up on it,

2:26:12.540 because he became interested in sort of political activism

2:26:15.540 and physics for another decade.

2:26:18.540 So, but I think this notes that I took on in 1970

2:26:24.540 with him maybe the first place

2:26:26.540 where the notion of quantum information theory

2:26:29.540 or the name even got mentioned.

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.

2:26:40.540 But of course, in the beginning days,

2:26:42.540 it's sort of obvious that these were ideas

2:26:46.540 that were so strange that most people,

2:26:49.540 even the people who were working on them,

2:26:51.540 didn't take them very seriously.

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

2:27:03.540 and quantum information?

2:27:04.540 People often ask me this.

2:27:06.540 And I sort of tried to say, well,

2:27:09.540 if you think of a space of four dimensions

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.

2:27:19.540 So I came up with this other metaphor.

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.

2:27:41.540 But unlike dreams, there's a well-known,

2:27:45.540 a well-understood theory of how the quantum information behaves.

2:27:49.540 And that's what the people in our field

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.

2:27:58.540 Oh, this is a very arrogant statement.

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.

2:28:11.540 We made an important improvement,

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

2:28:33.540 as part of their subject.

2:28:35.540 And when computer scientists and people

2:28:39.540 that I'm not sure exactly what you'd call them,

2:28:41.540 like David, began thinking about it,

2:28:44.540 they were realized it was very parallel

2:28:46.540 to the theory of classical computing.

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

2:28:57.540 in order to do any computation.

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

2:29:10.540 that Turing showed existed.

2:29:15.540 So here's an example of something

2:29:18.540 you can do with a quantum computer.

2:29:22.540 We can take a, there, oops.

2:29:25.540 I want the laser.

2:29:27.540 Yeah.

2:29:28.540 So let's take a vertical photon as a one

2:29:32.540 and horizontal photon as zero, and I have different colors

2:29:34.540 so that I can keep tracking them.

2:29:36.540 This is a conditional, not operation, or an exclusive bar.

2:29:44.540 So the first, the first qubit controls

2:29:47.540 whether the second one is left alone,

2:29:49.540 or whether it's flipped.

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

2:29:57.540 and horizontal and both being vertical.

2:29:59.540 And that's an entangled state that has no analog

2:30:02.540 and classical theory.

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

2:30:18.540 scientist of the 1980, very badly.

2:30:21.540 And they would say, you know, you,

2:30:23.540 this is a stone-even proof theorem, so how can I take what you're saying?

2:30:27.540 Seriously.

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

2:31:04.540 are with each other.

2:31:06.540 Of course the hippies weren't very good at monogamy either.

2:31:09.540 So here's how it works.

2:31:10.540 If we have two, two perfectly in,

2:31:14.540 well we get two separate systems.

2:31:16.540 We go through a very simple quantum operation

2:31:19.540 and we can get an entangled state.

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.

2:31:28.540 So he entangles himself with Judy.

2:31:31.540 Well the trouble with that is that that degrades his entangled with Alice

2:31:36.540 and his entangled with Judy.

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,

2:31:47.540 but this is not very interesting.

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

2:32:18.540 orthogonal values.

2:32:20.540 The classical wire is something that conducts classical information reliably,

2:32:25.540 but spoiled superpositions.

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?

2:32:54.540 So entanglement is ubiquitous.

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,

2:33:27.540 you find out what they had for breakfast,

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.

2:33:39.540 Well, how does entanglement hide itself?

2:33:42.540 This is sort of a quick version of decoherence theory in the version,

2:33:47.540 proposed by Voicic Zurich.

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

2:34:19.540 while obfuscating other 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

2:35:16.540 and good ideas sometimes slow it down.

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?

2:35:41.540 Well, now we know he was wrong,

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.

2:36:10.540 It's just not true.

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,

2:36:29.540 and I think in the early 80s,

2:36:32.540 Nick Herbert published a paper.

2:36:34.540 Well, actually he submitted it, and I forget if this was Ash or Paris

2:36:37.540 may have been the referee, and he said,

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,

2:37:13.540 sometimes retired scientific progress.

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.

2:37:49.540 Who here has heard of Maxwell's demon?

2:37:52.540 Well, this was an idea of the discovery,

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,

2:38:08.540 you could get all the hot ones on one side

2:38:10.540 and all the cold ones on the other side,

2:38:12.540 or you could collect them all on one side,

2:38:14.540 and you could violate the second law of thermodynamics.

2:38:17.540 And he sort of, as my science writer,

2:38:22.540 colleague, I wrote in Japan,

2:38:25.540 which Maxwell didn't solve the problem.

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

2:38:49.540 could push the door open.

2:38:51.540 But if they hit the door from the other side,

2:38:53.540 they couldn't go through.

2:38:54.540 And eventually, all the gas would collect on the right,

2:38:56.540 and you could run your pneumatic drill

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

2:39:08.540 and it was spring on, it was small 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.

2:39:21.540 But then quantum mechanics happened.

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.

2:39:40.540 And now, but by the mid-20th century,

2:39:43.540 after quantum mechanics had discovered,

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.

2:39:52.540 So Zillert's paper in 1929 was,

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

2:40:12.540 that computation could be irreversible

2:40:14.540 and it was the irreversible act of erasing information

2:40:17.540 that keeps the demon for working.

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

2:40:32.540 rather than breakthroughs.

2:40:34.540 It was a guy who came from other bar to buy BMs

2:40:37.540 and he wanted to work with our group

2:40:39.540 so he could break through discoveries.

2:40:43.540 And I was too kind to say,

2:40:46.540 but I said to my colleagues,

2:40:48.540 we didn't take him.

2:40:50.540 I said to John Smallen, I said,

2:40:52.540 that's like making a firm decision to be spontaneous.

2:40:57.540 So here we are in a situation where,

2:41:01.540 for years, people didn't take this subject seriously

2:41:05.540 and now maybe they're too optimistic

2:41:09.540 about what could be done right away.

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

2:41:24.540 in his life was on the variation project

2:41:27.540 and they had applied to make it go to all of outer planets.

2:41:32.540 But the word came back from Washington.

2:41:34.540 Because people don't know anything besides Jupiter and Saturn

2:41:37.540 just go to Jupiter and Saturn.

2:41:39.540 And they said, but the planets won't be lined up

2:41:41.540 in the right way for another 200 years

2:41:43.540 and the word came back from Washington.

2:41:45.540 Congress understands about two years,

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

2:41:58.540 as it was really needed to.

2:42:01.540 And each one said,

2:42:02.540 well, you wouldn't want the thing to fail just because this part

2:42:05.540 wasn't quite strong enough.

2:42:07.540 And he was working on the thermoelectric power supply for it.

2:42:13.540 So of course then once it was launched

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.

2:42:28.540 OK, this is my summary of the subject.

2:42:33.540 Thank you very much, Charles.

2:42:59.540 Way to behave with politicians or something.

2:43:03.540 So comments, questions?

2:43:10.540 Yes?

2:43:23.540 Yeah, so you spoke about entanglement.

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

2:43:38.540 rather than superposition?

2:43:41.540 Well, it's hard to separate the two because from the superposition

2:43:46.540 principle you get entanglement.

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,

2:44:03.540 involved entanglement?

2:44:04.540 And I think actually Peter would know the answer that better.

2:44:07.540 I think it does.

2:44:08.540 I think Grover's algorithm doesn't involve

2:44:10.540 but entangled states, right?

2:44:12.540 What?

2:44:13.540 It does.

2:44:14.540 Oh, it does.

2:44:15.540 Grover's algorithm involves entangled states, but it's not really,

2:44:20.540 it doesn't look like entanglement states.

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.

2:44:28.540 Yeah.

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.

2:44:38.540 So is there, yes?

2:44:41.540 You're very happy to be very right.

2:44:44.540 The only problem that I wanted, it's just a stupid remark

2:44:48.540 that since all of you have mentioned it,

2:44:51.540 they're not cloning theorems.

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

2:45:02.540 before.

2:45:03.540 You were two years before, Wooters and Zurich,

2:45:06.540 and takes it.

2:45:07.540 Oh, and there was also before that there was two years before.

2:45:11.540 Yeah.

2:45:12.540 It was even more than two years before.

2:45:14.540 I can send you to that.

2:45:16.540 Yes, no.

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,

2:45:28.540 but it was not noticed.

2:45:30.540 That has the proof in it, too.

2:45:35.540 That's the earlier one.

2:45:37.540 Yeah, so you got there almost at the right time

2:45:42.540 for it to be noticed.

2:45:44.540 Yeah, so this is almost most scientific discovery

2:45:47.540 is occurring this way.

2:45:48.540 They're discovered three or four times,

2:45:50.540 sometimes very well, and it's not the part of the discover

2:45:53.540 that it was not noticed.

2:45:54.540 It's just the time wasn't right.

2:46:00.540 Okay, so let's take a look.

2:46:02.540 Let's take a look again.

2:46:04.540 So now the last medalist is David Doge.

2:46:18.540 David was born in high-fying Israel in 1953.

2:46:22.540 The son of Oscar and Tigwadouge.

2:46:24.540 He attended William Ellis School,

2:46:26.540 and if I get North London, before reading National Sciences

2:46:30.540 at Clare College in Cambridge,

2:46:32.540 and taking part three of the mathematical drivers,

2:46:35.540 and he went to a world song college

2:46:38.540 for his doctorate in critical physics,

2:46:41.540 and I have to say that his supervisor was David Shama,

2:46:45.540 who was well-known figure here in Phieste,

2:46:48.540 and also the supervisor of big scientists,

2:46:51.540 including Stephen Hawking and Martin Reese.

2:46:55.540 And he wrote his thesis on quantitative theory in course,

2:46:59.540 in space times.

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

2:47:09.540 that is on qubits.

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

2:47:26.540 of three qubit logic gate.

2:47:30.540 They can ban it short and co-workers show

2:47:32.540 that sequences of one qubit case,

2:47:34.540 and one simple type of reverse world classical,

2:47:37.540 two-bit case of this.

2:47:39.540 Working alone, and with Richard Johnson

2:47:42.540 from the University of Cambridge,

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.

2:48:25.540 Thank you.

2:48:58.540 So David was given a presentation called

2:49:01.540 the Mathematicians Misconception.

2:49:03.540 Do you have slides?

2:49:04.540 No.

2:49:05.540 I was like so.

2:49:06.540 OK, David.

2:49:07.540 Sorry.

2:49:08.540 But you can choose this.

2:49:51.540 Hi.

2:49:52.540 Can everyone hear that?

2:49:54.540 Yeah.

2:49:56.540 OK, well, nice to be here.

2:50:02.540 A couple of years ago, the mathematician Hannah Fry

2:50:07.540 made a TV documentary about Ada Lovelace,

2:50:11.540 the 19th century computer theory pioneer.

2:50:15.540 It was about an episode in the history of ideas,

2:50:21.540 which would have been absolutely pivotal

2:50:24.540 if anybody had noticed it at the time,

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

2:50:41.540 of computation was actually Lovelace

2:50:45.540 and not her colleague, Charles Babidge,

2:50:49.540 the designer of the universal computer

2:50:53.540 that she was theorizing about the Babidge's analytical engine.

2:50:59.540 Never built.

2:51:00.540 But like many of these computers,

2:51:02.540 the significance was in the design and the theory

2:51:06.540 rather than actual building.

2:51:09.540 The thing is, the analytical engine

2:51:12.540 would have had two kinds of universality.

2:51:16.540 And Babidge was obsessed with one of them.

2:51:20.540 He had perhaps been the first human being

2:51:24.540 to understand what one could call arithmetic

2:51:28.540 or mathematical universality.

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,

2:51:48.540 conceptually very simple,

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.

2:52:08.540 So, this was arithmetic universality.

2:52:12.540 What Lovelace understood, I think,

2:52:15.540 was the significance of the analytical engine's ability

2:52:19.540 to compute not just any arithmetic,

2:52:23.540 but anything in the world, in the physical world.

2:52:28.540 She envisaged all sorts of applications,

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.

2:52:41.540 The abilities of the analytical engine

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.

2:52:53.540 Namely, while the analytical engine

2:52:57.540 could instantiate a tiny fraction of all,

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,

2:53:22.540 not just a tiny subset.

2:53:24.540 This physical universality is an intrinsic property

2:53:29.540 of the laws of physics.

2:53:36.540 It doesn't follow from mathematical universality.

2:53:42.540 It has nothing to do with the mathematics.

2:53:45.540 In fact, neither of the universality

2:53:47.540 is follows from the other.

2:53:50.540 Yet, it seemed that both of them were exhibited

2:53:55.540 by the same machine.

2:53:57.540 Why?

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

2:54:05.540 other than from the laws of physics.

2:54:09.540 This unity of the two universalities

2:54:13.540 was also conjectured later explicitly

2:54:16.540 by Alan Turing in the 20th century.

2:54:19.540 It's just Turing's conjecture.

2:54:21.540 Sometimes called the church Turing thesis.

2:54:24.540 It has various names.

2:54:26.540 But the usual way that this conjecture

2:54:29.540 is described is not that it's the unity

2:54:33.540 of those two universalities.

2:54:36.540 Why not?

2:54:39.540 Well, Turing's great paper presenting his conjecture

2:54:44.540 had an application, as he put it.

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.

2:55:11.540 In the 1930s, mathematicians converge

2:55:15.540 from several directions on the realization

2:55:18.540 that that is impossible.

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

2:55:29.540 propositions.

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

2:56:00.540 of the integers.

2:56:01.540 So nothing to do with computation.

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.

2:56:12.540 But there was no Goethe's conjecture.

2:56:16.540 Turing, who realized that that notion of what proving something

2:56:21.540 means isn't self-evident.

2:56:24.540 So he acknowledged it as a substantive conjecture,

2:56:27.540 the Turing 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.

2:56:41.540 Strips of paper divided into squares

2:56:44.540 with symbols in a finite set of discrete operations on them,

2:56:48.540 the universal Turing machine.

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

2:57:03.540 would naturally be regarded as computable.

2:57:07.540 Naturally.

2:57:09.540 At the time, the word computer meant a human being.

2:57:13.540 It wasn't one of these things.

2:57:15.540 A person whose job was to manipulate symbols

2:57:19.540 on sheets of paper.

2:57:22.540 And the manipulators obeying the rules.

2:57:25.540 Human beings are physical systems.

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,

2:57:49.540 might have been false.

2:57:51.540 But it turned out to be true in nature,

2:57:55.540 or rather very nearly true.

2:57:58.540 As Richard finally remarked,

2:58:00.540 they thought they understood paper.

2:58:03.540 But they didn't.

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,

2:58:20.540 nor Babidge's brass gear machine,

2:58:23.540 but the universal quantum computer.

2:58:26.540 But I soon found out that not everyone saw it that way.

2:58:32.540 I also had a referee problem.

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

2:58:47.540 naturalness, mathematical intuition,

2:58:51.540 not nature.

2:58:54.540 And so what I had proved wasn't Turing's conjecture.

2:58:58.540 It was about physics.

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.

2:59:23.540 But one thing they were all adamant about,

2:59:26.540 nevertheless, was that Turing's conjecture

2:59:29.540 about whether his mathematical model of proof

2:59:33.540 matched not the physical world,

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.

2:59:48.540 And computation is physical.

2:59:51.540 And hence, proof is physical.

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

3:00:03.540 I asked insisted on.

3:00:06.540 And most, not all, most non-mathematicians

3:00:11.540 who thought about computation didn't.

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

3:00:31.540 is physical and proof also.

3:00:33.540 Just to be clear, mathematical facts,

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

3:01:03.540 as that vague meta-mathematical idea.

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

3:01:15.540 from the conjecture.

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

3:01:29.540 the church Turing doic principle.

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

3:01:40.540 and arguably Ada Lovelace did.

3:01:45.540 A few years later, I gave a talk in Oxford

3:01:49.540 arguing that it makes no sense to regard

3:01:52.540 Turing's conjecture in any form

3:01:54.540 as something one might hope to prove one day

3:01:57.540 from logic like Fermat's last theorem,

3:02:00.540 but that it could be proved to be a property of quantum mechanics.

3:02:05.540 Sitting in the front row was Robin Gandhi

3:02:08.540 who had worked with Turing.

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.

3:02:33.540 He'd also given a talk at the same event

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

3:02:42.540 a grain of truth in there somewhere.

3:02:44.540 Let's talk about it later.

3:02:46.540 And we did discuss it later, but unfortunately,

3:02:49.540 we did not reach a resolution.

3:02:52.540 He was a mathematician.

3:02:54.540 He had the misconception.

3:02:58.540 Unfortunately, in the bigger picture,

3:03:01.540 the mathematician's misconception is done more

3:03:04.540 than just cause amusing anecdotes.

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.

3:03:27.540 Now, we know that Hilbert was wrong.

3:03:30.540 Ineffable definition of proof.

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.

3:03:48.540 There's the misconception.

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.

3:04:01.540 They differ only in speed.

3:04:04.540 So some people view this as vindicating

3:04:06.540 the mathematician's misconception.

3:04:08.540 But no.

3:04:09.540 First of all, we only know that they only differ in speed

3:04:13.540 from physics, from quantum theory.

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

3:04:53.540 that is provably impossible classically.

3:04:58.540 So the misconception makes people say,

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

3:05:48.540 or to supernormal aliens, snailions.

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,

3:06:25.540 you must start with laws of physics.

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

3:06:44.540 or logic or the supernatural.

3:06:48.540 Okay, that's it.

3:06:50.540 Thank you. Thank you.

3:07:06.540 Thank you.

3:07:08.540 Thank you.

3:07:09.540 Thank you.

3:07:11.540 Any questions from any mathematician?

3:07:14.540 I have a very simple question. What is physical?

3:07:26.540 Yes.

3:07:30.540 It's a bit like asking what is real.

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.

3:08:08.540 Laws of physics are things unlike that.

3:08:12.540 They are things that could be overturned at any moment.

3:08:15.540 We guess at them.

3:08:17.540 So I can't provide an answer better than that.

3:08:20.540 It's a deep question.

3:08:24.540 Yes.

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?

3:09:15.540 They're physics as at the top.

3:09:18.540 We conjecture laws of physics.

3:09:21.540 We test them from our physical intuition.

3:09:24.540 We then develop mathematical intuitions from there.

3:09:27.540 We learn about mathematics.

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.

3:09:46.540 It's true it's unnecessary.

3:09:48.540 Our knowledge is the other way around.

3:09:50.540 It comes via physics.

3:09:52.540 That clearly.

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.

3:10:12.540 Can you combine the two thoughts?

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.

3:10:33.540 That is not going to be proved false.

3:10:36.540 What is going to be proved false is what the multiverse consists of.

3:10:40.540 What the structure of it is.

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.

3:11:06.540 We know that is true.

3:11:09.540 But the details are going to change because quantum theory is in many ways totally unsatisfactory.

3:11:15.540 Look at quantum gravity, for example.

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.

3:12:28.540 We are just not in a good one.

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.

3:12:43.540 What is your reaction to that question?

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.

3:13:23.540 It is extrapolating.

3:13:25.540 And in order to reach that conclusion, you have got to extrapolate selectively.

3:13:30.540 That is one argument on the other side.

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.

3:14:24.540 Well, it is a very quick question.

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.

3:15:27.540 Very good.

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,

3:15:46.540 there is a special event.

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,

3:16:21.540 quantum technology flagship project.

3:16:24.540 So you all welcome to participate.

3:16:26.540 It's for general public.

3:16:28.540 And there is a boss that we hire that will take 50 people.

3:16:33.540 So all of the 50 of you who want to go.

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.

3:17:17.540 Thank you very much.

3:17:47.540 Thank you.

3:18:17.540 Thank you.

3:18:47.540 Thank you.