cc  >> Cathy Vrentas: Hi, everyone,  welcome to Wednesday Nite  at the Lab here at  the UW Madison  Biotechnology Center.  Today's speaker is Susan  Coppersmith.  She's a professor in the  Department of Physics here at UW  Madison.  Specifically, her area is  theoretical condensed matter  physics, and her research looks  at a variety of complex systems.  So you'll be learning about that  today.  She did a variety of roles  including chair of her  department, as well as chair  roles with the Division of the  Condensed Matter Physics of the  American Physical Society and  with the board of trustees of  the Gordon Conferences.  And she's also a fellow of the  American Physical Society and  AAAS, as well as a member of the  National Academy of Sciences.  So please join me in welcoming  her to Wednesday Night at the  Lab today.  (applause)  >> Susan Coppersmith: Well,  I know I have a pocket.  Thank you, very much,  for coming. 

 And I really am excited to have  this opportunity to talk with  you because I talk a lot to  other physicists, some of them  are theorists and  experimentalists, but I also  sometimes talk to people on  planes or I meet people when I  take my daughter around to her  gymnastics or classes, and they  say what do you do?  And I say I'm a physicist, and I  have to say the answer is always  "Oh, I really hated that in  school."  And I say, actually I went  around for a while telling  people I was an interior  decorator even though I have no  artistic ability whatsoever.  And they sort of knew I wasn't  really an interior decorator,  but I realized that I really  want to have the opportunity to  explain to people what's  interesting about it and why  it's cool.  As opposed to just hard.  And so that's the goal of the  talk.  Is to just give you a some sense  of why it's a really neat thing  to try to do.  And second of all, if I do make  it seem too hard you can stop me  and the point of this is to try  to really communicate a little  bit about why it's interesting  and not just to make it sound  hard.  Okay.  So I want to say that up front.  So feel free to interrupt.  Okay, so the goal of physics,  and theoretical physics is part  of physics, is to try and take  what's so complicated about the  world around us and figure out  the parts of it that are simple. 

 There are laws underlying  apparent complexity that we can  aspire to figure out.  And the success of physics up to  now is evidence that this is  true and has had a lot of impact  in our daily lives.  And you don't even really think  about the impact physics has had  but the internal combustion  engine was developed by  physicists.  The science of thermal dynamics  needed to be developed before  people could understand how to  make engines.  Lighting, electricity,  computers, essentially all of  technology was originally  developed by physicists.  So the point is that if you  understand these regularities  and rules about what's governing  the world around us, you can  then actually do things that  have huge technological impact.  So the idea is that you're  really trying to figure out what  is at heart simple things, but  it's often very complicated to  figure out the simple things and  that's why physics seems hard.  And so at this point a very  important part of being a  physicist is understanding what  people already know and what the  limitations are to what people  already know, and then after you  understand that you can try to  figure out what people are  missing and to try to add it  that store of knowledge.  So the main thing is to try and  find concepts, and so I'm going  to give you a little example  about why that's so important.  That basically when you look at  things in the right way, things  look very complicated and  confusing can become very  simple. 

 So this is an example where you  look at those letters and you  say, well, what does that mean?  And then you could sort of think  about it for a while.  But when you first look at you  say, gee, that looks really  pretty confusing.  But it turns out there's a very  simple trick to it.  And if you take every letter and  replace it by every B goes to A,  C goes to B, N goes to M, B goes  to A.  O goes to N etc.,  then it just has this little  sentence right.  And you say this is so simple  once you see the trick.  And that's what the goal of  physics is.  Is to make everything simple  once you see the trick.  All right, so the thing that is  sort of the conundrum of  physics, and in some sense why  it seems so difficult, is it's a  moving target.  So there are the things that we  already understand. 

 So if I were to go and give this  talk again and make up a  different thing instead of  people in Wisconsin like cheese,  I don't know, let's go out for  dinner tonight.  But you would see it, you would  know the trick and you would  say, gee, this is really not  very interesting.  And that's the problem with a  lot that we know.  We think somehow that people are  doing things that are all really  boring because we know so much  about it already.  But then there are the things  that we just have no idea how we  would ever understand them.  So there's the boring and then  there's the intractable and the  goal of the whole thing is to  figure out what is tractable but  not boring, and that's this  little line here which is the  moving target of where you're  hoping to find current research.  But the point is we don't  actually know that what in there  is actually tractable or not  boring and that's why we don't  know how it's going to turn out.  But what it means is that, sorry  I'll finish this.  But what that means is that lots  of times when people are working  on stuff the great discoveries  come from things that actually  look quite dull.  And I'll give you an example of  a great discovery that was based  on work that really I don't  think would ever get funded in  today's funding climate because  it really does sound very  boring. 

 But then it turned out it was  the first point of some really  great stuff.  So the idea is that what we have  now is we have a bunch of stuff  that we know how to do.  Physicists know how to do a lot.  Your car works and that's  because we understand a lot  about thermodynamics.  And your computer works and  that's because we understand a  lot about the physics of solids.  And so we think of all these  things that work and we have the  concepts that we've developed  that enable us to develop these  things.  But there are all sorts of  unsolved problems that we have  no idea how to approach.  And basically the idea is to try  to develop new tools that will  increase the realm of what we're  able to do.  And so basically what happens is  there's a set of ways of  thinking about things and that's  the idea, that's what the wrench  is supposed it be.  And there's a set of problems  you know how to solve now. 

 And if you have, if you have the  right problem then we know  exactly what to do.  But then you may have a thing  where the wrench is no good and  then you actually have to figure  out how to make a screwdriver in  order to solve the problem of  putting the screw in.  So this leads to, excuse me,  this leads to a recurring theme  throughout physics.  And I actually at some point did  a study of this.  Where at every point in time  since the development of modern  science, it has been felt that  everything interesting has been  done.  And actually this is one of the,  sort of the modern science with  the physical laws and stuff was  sort of the first modern  physicist is considered to be  Newton and was around 1800 and  by 1871 people figured it was  over, right?  And so Maxwell, who is a very  famous physicist, was already  fighting against this and saying  there's a popular opinion that  in a few years all of the great  physical constants will have  been approximately estimated and  the only occupation will be left  to men of science will be to  carry on these measurements to  another place of decimals.  And now in modern times we would  be more politically correct and  we would say men and women of  science, but the sentiment is  actually quite modern and there  are several books recently  written about how everything in  physics has been done and  everything is boring and there's  nothing great left to discover.  Yes?  >> Did he say that before or  after he discovered...  (inaudible)  >> Susan Copperfield: That,  it was just after.  And he was saying, but it's  okay, there's still a few things  left to do. 

 And also Maxwell did a lot of  great things in thermodynamics  after this date.  And he was against it.  Now I have to say that I did do  the study and it's sort of an  interesting history that some of  the people who have been claimed  to have made this statement were  actually sort of aligned and  they didn't really say it but  that's a whole other story.  But there are quite a few people  who constantly say this.  So there's stuff from around  1900 it was popular to say this.  But then quantum mechanics  happened and you didn't hear  anything for a little while.  But then in the '60s it was  again popular and it's sort of a  popular thing now.  And again I think that this is  because of this thing that when  you look at things a certain way  the idea that there's actually a  different way that's profitable  is like really hard to imagine.  So that's sort of interesting.  So it's a really hard problem  because it's sort of hard to  sort of think in new ways that  are actually scientifically  valid and useful. 

 And you say, well, where do you  get the concepts?  And if this was easy, then I  guess maybe it would have all  been done.  But it's actually quite a  difficult problem.  And there's sort of two main  approaches.  And the first one is to actually  look at what we think we know  now and look for problems with  it.  And this involves a lot of  detailed and boring, sometimes  boring-looking detailed  comparison between theory and  experiment.  And the historical example I'm  going to give you was in this  case, and then occasionally  there was just the bolt of the  blue great organizing concept.  And however typically I would  say what happens is someone does  one of these great bolts out of  the blue, they tend to be sort  of nothing to do with anything,  and so in the end it all has to  get tied into verifiable, by  experiment phenomena.  And so typically, and this is  what makes science so dull to so  many people, is there is a lot  of stuff which is really looking  at the details to figure out  what exactly are the limits to  our knowledge.  So I'm going to give my example  to be quantum mechanics.  And I just give you a little bit  of the history of that. 

 And so the question is how did  it get started?  And it grew out of studying  light.  Now in the 1800s, Maxwell was  associated with this, it became  clear that light is a form of  electricity.  It's what's called  electromagnetic radiation.  And light is a wave of  electricity and magnetism.  And the wave nature of light was  actually quite controversial  because Newton did not believe  in it.  And even in those days there was  a thing of somebody very famous,  strongly held an opinion, often  that would sometimes overweigh  facts.  And so it was only later when  they were really very clear  experiments that it became clear  that light is a wave.  So just to remind you of one of  the key things about waves is  that you're used to seeing water  waves.  You put a rock into a pond and  then you get a disturbance that  spreads, and if you do this  twice, oops sorry, I've been  told to point with the computer.  So what happens here is there  are two little paddles here, and  this guy is tossing in a rock  and here is tossing in a rock. 

 And then you get this  disturbance and what you're  seeing here is actually light  coming up from the bottom of the  tank and it gets, the light gets  bent because the water is  thicker and thinner.  And you've seen this in a  swimming pool all the time.  That's why you get the bright  and the darkness is because the  water is thicker and thinner.  And what happens is if you have  two of these waves, they  interfere.  So you can have situations where  they're sort of doubly bright or  actually they cancel each other  out.  And the fact that you get sort  of bright, dim, bright, dim is  called wave interference.  And this is the water wave and  you can see here it's quite  clear sort of up here that you  see it's dim here and bright  here and dim here and bright  here.  Okay?  So you've seen this, hopefully,  and maybe you've even noticed  it.  And in the 1800s people did  experiments where they would  take a light bulb and put it  through a little slit, and then  here they'd make two slits, and  then they would see the same  thing where they would see a  light pattern and a dark, light,  dark, light.  So that was really pretty  convincing evidence that light  also was a wave. 

 Which was, again, not obvious  until people did this  experiment.  And in the 1870s, I guess this  is the actually date, so they're  very contemporaneous, that  Maxwell completed his work where  you showed that light was a form  of electricity and there were  these waves of electromagnetic  radiation.  That was in the 1870s, and this  had tremendous implications for  making electric motors and for  radio and all of this was based  on Maxwell's work.  And sort of throughout the rest  of the 1800s everything was just  sort of going great guns and  there was just a lot of evidence  that light was these  electromagnetic waves.  And we thought we understood  them all.  But then around 1900 people were  studying the light coming out of  a light bulb and it didn't quite  agree with theory.  So this is reprinted.  This graph is actually reprinted  quite a lot.  It was from 1901.  And actually I did it where this  is the actual graph, but here I  marked it up so you can see  what's going on. 

 So here are the data points.  The data points are in the  little circles so you can see  them.  They're sort of hard to see  because everything's drawn by  hand.  They didn't have computers in  those days right.  And then this line here, this  dashed line, oh, sorry, it's  hard for me a little bit, this  one here.  This dashed line there is what  you would have expected based on  Maxwell's theory.  And there was some other  ingredients but all extremely  well-accepted.  And these guys did this  experiment and again what they  were looking at is you have the  temperature of the light bulb  and you're just measuring how  much light's coming out.  That's all that's going on.  And it didn't quite agree with  the theory. 

 And these guys were careful  enough that they said there's a  problem.  And it wasn't clear what the  problem was.  But what happened was there was  a physicist named Max Planck  said, well, you could make up a  formula that goes through the  data points, which theorists  like to do, and that one of  these lines is Planck's formula,  goes right through the data  points.  But he didn't really have a  reason.  He just noticed this formula  would go through these data.  But why that formula would be  the right formula, he didn't  know.  And it turned out that the key  idea was Einstein's idea, and  this is the work for which  Einstein won his Nobel Prize.  And people say he should have  one for relativity, but I think  this is just really a remarkable  idea.  So what Einstein said,  postulated, he had a new concept  that actually light is not like  a water wave exactly.  Because a water wave you can  have a big wave, you can have a  small wave, you can have  different wave lengths. 

 And he's saying, no, if you have  light of a certain color then  the energy is packaged up into  things that he called quanta.  And so every one of these quanta  are the same, they have the same  energy.  So if you have red light,  there's a certain energy of red  light.  If you have blue light, there's  a certain energy of blue light.  And if you have dim blue light  you have fewer quanta but you  never have the quanta, the blue  energy and the red quanta have a  different energy.  And this, no one had ever  thought about this before.  You had this picture, you just  had this wave, it was a  continuous thing.  But here the energy was  quantized.  So we're used to talking about  quantum jumps.  And what's happened it's been  sort of bastardized because when  we think of quantum jumps we  think of big jumps. 

 But actually the quanta are  really little.  You know what I mean?  And that's why no one ever  noticed them before because  they're essentially pretty  small.  But the idea is if you know the  color of the light, you know the  energy of each one of these  photons.  And it turns out that that  concept is enough that it  explained the data, but more  importantly it turned out to  explain lots of other things  too.  So it turned out that these  lights, the light comes in these  little quanta and these photons,  the quanta are the photons,  they're guided by a wave  equation so it looks like a  wave but actually everything is  quantized.  And that was his new concept.  And the amount of evidence, the  support for this concept is  overwhelming.  So much of what we see in our  daily life is based on the  concept of quanta.  And so just to give you one  example, but let me just do this  point here.  So the point was that the thing  that motivated all of this was  extremely boring in the sense  of, oh, we're going to see how  much light comes out of a light  bulb. 

 But it turned out that by  measuring that carefully, the  experiments demonstrated that  there was a new concept that  needed to be developed.  And that was what's really key  here.  And they gave, and it was sort  of a simple enough thing that  you knew there was a problem and  there was really something  fundamentally incomplete with  the current knowledge.  So then the next step of this is  to say that this concept of the  photon is extremely powerful and  relevant technologically, and  one example of something that  came directly out of this is the  laser.  And the laser is, you know, CD  player, DVD player, they're in  cash machines, they're in my  laser pointer, they're in the  hard drive, it's how you read,  your hard drive reads, they're  used for laser surgery, and all  of this actually Einstein wrote  a paper in 1917 that had all the  concepts needed for the laser,  but it turned out to actually  make one of these things it took  quite a while.  And so the point here is that  the new concept happened but the  actually technological  innovation that led to product  actual took quite a long time,  and it was because it wasn't  until really the '50s that  people sort of realized that a  laser could do really  interesting things and it took a  while to be able to build one  and since the 1960 when the  first laser was made, they've  been continually developed and  so the latest thing is you've  heard of Blu-ray and the point  about Blu-ray is it's a blue  laser.  And so I was telling you about  the quanta, the red light has  certain energy, the blue light  has another energy, well it's  also true of the wave lengths.  It turns out the wave length of  red quanta is longer than the  wave length for blue quanta.  So what happens if you make a  blue laser, you can get more  information into the drive just  because everything can be made  smaller.  So that's the advantage of  Blu-ray. 

 And the blue lasers were  developed pretty recently but by  now they are actually less than  $10 so this is just driving down  the cost of technology.  But the point is, I don't know  if this followed directly from  the photon but took quite a  while before it was turned into  a commercially useful product.  So that's sort of historically,  that's my goal, okay, is to do  something that revolutionizes  science and technology by having  a good idea.  So everyday I go in and say,  let's have a good idea today.  But it's not so easy.  I should say that most days I  don't have any, well, I have  small ideas but not really good  ideas.  But I can tell you what I'm  working on which is, I think, a  lot of fun.  And I'll try just to give you  some sense of what I do now and  the kinds of questions that  physicists are thinking about  now and again to try to convince  you that there's actually a  whole lot left of really  interesting things to discover.  So the thing, one of the things  I'm working on is what's called  quantum computation.  So the rest of the talk I'm  going to try to describe to you  what it is and why it's  interesting. 

 So you all are familiar with  classical computers.  So you know what a computer is.  Essentially, it's a machine and  it manipulates what are called  bits, and bits are things that  are either one or zero.  So in your hard drive, assuming  you a have a hard drive, in your  cell phone or in your memory,  what happens is that there is  something that can be in two  states.  So in the hard drive there are  these little basically magnets,  and the magnets can point either  this way or that way, and if  they point this way it's a one  and if they point this way it's  a zero.  And what happens is just by  doing things you say this one is  one and this one is one and then  there's circuitry to do  operations on the bits and  that's what underlies all of  micro-processors and chips and  whatnot.  And so that's what a classical  computer is.  What a quantum computer is, but  I should say one more thing is  that the computer is  manipulating classical objects.  It's like a bunch of, it's a  little piece of magnet with a  lot of spins in it.  But we know now that if you look  at the atomic level, you don't  have spins that are sort of  classical objects that point  either this way or that way but  spins are also quantum. 

 Everything is quantum and when  it's small enough you really  notice that it's quantum.  So what happens is we're trying  to take advantage of what's  different about the quantum  nature of matter at the atomic  scale to actually do different  operations that could be more  powerful than what you could do  on a classical computer.  And this isn't to say that  classical computers aren't  enormously powerful and useful,  but it's to say that if we  actually took advantage of  quantum mechanics in the  computational scheme, we could  do even more.  And so that's the idea behind  it.  So the computer manipulates what  are called qubits which are  quantum bits instead of  classical bits.  Classical bits you know, they  are just things that are either  one or zero.  And so the questions that we're  asking are, first of all, what  can a quantum computer do that a  classical computer cannot do?  And that's one direction of  approach.  But then the other one is can  you actually build one of these  things?  And it turns out that building  them is not so easy, and I'll  hopefully tell you a little bit  about why it's challenging.  I think the progress that people  are making to be able to build  them is quite striking and I'm  optimistic but it's a huge task.  So the last thing, so this is  sort of the main, the last of  the things I want you to take  home. 

 It's just sort of what is a  quantum computer and why might  it be something that you'd want  to build.  So I already said a lot of this  in words without the little  slide.  Typically in a computer you have  a thing that each bit is either  one or zero.  But what happens quantum  mechanically is that you can  have a quantum system which is  in what's called a superposition  of ones and zeros.  So I have to tell you what that  is.  So what happens is you can have  a thing that's not exactly one  and it's not exactly zero but  it's not just that you don't  know but it's sort of a definite  quantum state but with  properties that sometimes it's  one, it seems like sometimes  it's one, sometimes it's zero.  So I have to explain to you the  weirdness of quantum mechanics.  And this is just a little bit of  the weirdness of quantum  mechanics because quantum  mechanics is quite weird.  So let me start with just  talking about a spin.  It turns out for quantum  computers spin is sort of useful  to do. 

 And again you should just think  of them has being arrows.  And you can think of it as being  magnetization, as what's in your  hard drive.  So if you have a spin, it's an  arrow, and I'm going to assume  the length of the arrow is --.  So really what you need to know  is the direction of the arrow.  And so what happens is you need,  there's sort of a standard  mathematical way of describing  that.  You say here is, we're going to  pick a direction we're going to  call it Z.  We'll let Z be up.  And if the spin is pointing  straight up, we're going to make  theta be zero.  And if the arrow is pointing  horizontal, then this angle  theta is 90-degrees.  But then if it's 90-degrees you  can go along in this direction  and then there's another angle  which is always called phi which  tells you which direction you're  pointing. 

 So you know where you are at  this direction, you know where  you are at that direction, that  tells you the direction of the  arrow.  So then you can say, all right,  how do I figure out what  direction my arrow is?  And you would say, okay, what we  could do is we could say what's  the, we can measure how much  spin is pointing this way and  how much spin is pointing this  way and how much spin is  pointing that way.  And if you do that you could say  along Z, first I get the full  length, then when it goes this  way I get not quite so much and  not quite so much, not quite so  much.  Then is reverses and you can get  any answer for the spin between  this and this, the component  along Z.  And this we know.  This seems so obvious that it  just wouldn't even occur to us  that anything else could happen.  But a quantum spin doesn't do  that.  So what happens with a quantum  spin, I'm going to tell you  about a particular case of the  quantum spin where the spin is  either up or down and it's  called --, and what happens  there if you measure the  component of the spin that's up  or down, you always get either  one number or minus that number.  And it turns out that number is  actually a certain value of the  magnetic moment and it's called  Planck's constant, the same  Planck.  And it's just defined to be that  number. 

 And as theorists we ignore these  numbers.  But you always get the same.  You either get plus that number  or minus this number.  You can't get any other answer.  So it's completely different  from a classical spin because in  a classical spin you can get any  number between this and this,  and quantum mechanically you can  only get this number or that  number.  And it doesn't matter what  component of the spin you  measure.  You could measure along Z this  happens, X, it doesn't matter.  You always get either what's  called -- or minus --.  Those are the only numbers you  can get.  Okay?  And so that's the qubit, you can  only get, we'll call this thing  one and this thing zero, you  only get one or zero, but it's a  quantum state and it has much  more information that you're not  measuring. 

 And so what happened was that  quantum mechanics was actually  developed in the late 1920s, and  everybody just, there's this  thing called the uncertainty  principle.  And the point was you don't  actually know the quantum state  because if you measure the spin  you get one of two answers, and  there's just much more  information, and so you're like,  well, the answer is uncertain.  But in the 1980s Feynman and  another person named David --  pointed out that well, we're  always thinking of quantum  mechanics as being stuff that we  thought we should be able to  know.  If we think classically, we  should be able to know the  direction a spin is in, and  quantum mechanically we measure  and we only get one of two  answers so it looks like we  don't know and so we're  uncertain.  But they said don't think about  what you don't know, think about  the information that you need to  figure out what you need to  know.  And Feynman was the first one to  point out that actually if you  look at the quantum state and  ignore the fact that you don't  know what it is, and you say how  much information do I need to  specify the state, you need much  more information to specify a  quantum state than a classical  state.  And this is sort of the key to  information processing using  quantum systems.  Is the fact that the quantum  state itself has lots more  information in it.  And this is supposed to show you  why that's true.  So the point is I was telling  you about classical spins, and  again you should feel good about  classical spins because they're  just arrows, and I can point and  I'm a classical spin. 

 It's just a vector.  But the point is you say now I  have a bunch of spins and the  key thing here is we're thinking  not just about one spin but  we're thinking about a lot of  spins.  And you say, how much  information do I need to specify  a state with a lot of spins in  it?  And basically, well, I need to  specify theta and phi for this  guy and I need theta and phi for  that guy and theta and phi for  that guy, and so for each spin I  need two numbers.  So that's how I said that if I  had a classical state I can  specify it with it with two  numbers.  Theta and phi for every guy.  But now with this quantum state  it's completely different.  So what happens is I say if I  measure the first spin I'm  either going to get one or zero.  If I measure the second spin,  I'm going to get one or zero.  But it turns out the  probabilities of getting one or  zero depend on everything.  So what happens is there's some  probability, or in the technical  language there's a wave function  and there's an amplitude, of  getting all zeros, which is  every spin is down. 

 Or I could have every spin but  the last spin be down and one be  up, and each one of these  things has a different amplitude  and it turns out there are  exponentially many of these  amplitudes because the first one  has two possibilities and the  second one has two possibilities  and there are exponentially many  possibilities in terms of the  number of particles.  So what happens is it means the  classical system has way less  information in it than the  quantum system because the  growth of the number of numbers  I need to specify is so fast for  the quantum system.  Now this doesn't show you that  you can compute anything with it  though.  Because, again, what I told you  before is when you measure you  just either get this or that.  So the question is can you do  something where you can actually  take advantage of the fact that  the quantum system has so much  information in it and actually  measure an answer.  And that was sort of not obvious  at all.  A great breakthrough was about  10 years ago a guy named Peter  Shor showed that there is a  problem where using a quantum  computer you can solve this  problem much faster than a  classical computer.  Now that has a particular  notion.  So it turns out the specific  problem is factoring.  And basically you know how to  factor small numbers, so you  know the factors of six are two  and three, and the factors are  15 are three and five. 

 But when you get to big numbers  factoring becomes more and more  difficult.  And it turns out the best known  classical logarithm for  factoring grows exponentially  with the number of digits in the  number.  And it turns out this has great  significance.  So not all of you, but many of  you in the audience probably  remember, first of all, before  cash machines.  You may remember that cash  machines were an innovation that  only came in the 1970s, I know  this is hard to believe, and  then there were another thing  that you may remember is that in  the old days when you charged  something on a credit card the  merchant would take your card  and they would actually call up  the credit card company, is this  ringing a bell?  They'd call up the credit card  company and they'd do your  number over the phone and it  wasn't automated.  Now you can swipe a card and  this is no longer necessary.  And in case you are wondering,  the reason why this is no longer  necessary is because of the  difficulty of factoring.  So here's basically the point.  So what happened was that the  credit card company wanted to be  able to approve this particular  charge but didn't want to give  the merchant enough information  to be able to crack their  computer system.  So the idea was that the  merchant wanted, you wanted the  merchant to be able encrypt the  information to send it but not  able to decrypt. 

 So that they couldn't get anyone  else's number or do any other  transaction.  So what happens is that the  merchant gets a product number.  And the product number is  sufficient for encryption to  send the information to the  credit card company.  But in order to be able to use  the card again they would need  to be able to factor this  number.  And it turns out that in many  cryptographic secrecy kinds of  applications this thing about  you're doing something where one  way of going forwards in the  calculation is easy and going  backwards is hard is sort of the  key to the encryption.  So when Peter Shor showed that  on a quantum computer, if you  could build one, you could  factor any large number in a  reasonable amount of time, the  National Security Agency got  really interested because this  would mean, and it turns out  that there are other  cryptographic schemes that are  sort of similar that quantum  computers can break.  So this is one of the reasons  why people all of the sudden got  very interested is because this  is, the one case which has been  proven where the quantum  computer, it isn't proven that  the quantum is more powerful but  it's proven that the quantum  computers can take a problem  that no one knows how to solve  classically and solve it means  that it has this potential  significance from a security  point of view.  And it also says we don't know  what else quantum computers can  do.  And so that's actually one  aspect of my research is to look  at other problems and say what  are the problems that quantum  computers can solve faster than  classical computers.  Where, again, whether it's an  encryption that you can do  quantum mechanically that can't  be broken classically or if it's  a thing if your adversary had  only a classical computer that  you would just be able to break  any code that they were able to  construct. 

 So that's one of the things  we're working on is to  understand the scope of the  problems.  Now it has been proven that  there are many problems that  quantum computers cannot solve  more quickly than classical  computers.  So at this point we just don't  know how powerful quantum  computers are.  It just happens this one example  was the key in terms of saying  there are interesting problems  that quantum computers are good  at solving.  And the other aspect which I'm  interested in is actually trying  to build a quantum computer.  Now here I just have to explain  to you why it's hard.  So I was telling you about the  quantum mechanics and one thing  that makes quantum mechanics so  interesting is that it's very  unintuitive.  Our intuition is classical.  We're used to thinking about  things that we know where they  are and how fast they're going  and we measure them and we get,  there's a dial and the dial can  take, has sort of a continuous  set of values.  And you say, why is it you don't  actually see quantum mechanics,  typically?  The answer is that what happens  is that the quantum state is a  thing that is very delicate and  so if you have a lot of  different quantum systems  interacting then sort of these  delicate things that are unique  to quantum mechanics sort of all  get washed out just by the fact  that there are so many atoms in  anything that you happen to be  able to see. 

 So it's the interaction of the  quantum system with the outside  world is the way we think about  it.  So if you have a completely  isolated system it's perfectly  quantum mechanical, but it's the  fact that it's not isolated but  it's connected to the world.  Now we do know how to isolate  systems so we can see quantum  mechanics all the time and it's  not like we don't believe it in  it because we can do  measurements and show that  things are behaving quantum  mechanically, but when you're  making a quantum computer, you  need to do more than that  because what you're doing is  you're not just taking a quantum  system and letting it do its  thing but you're actually  creating a quantum system that's  being a computer, and like a  computer you want to make it do  a certain set of operations.  Like you want to write the  program and make the computer do  what you want so you need to be  able to control the quantum  system without messing it up.  And that's the challenge and  that's what makes it very  difficult.  And as I said, there's been a  lot of progress in making  quantum computers, but the  challenge of making something  really large is what's called  quantum coherent and able to do  a large calculation, it's a big  challenge.  So right now I would say that  depending on the way people are  trying to make it, people can  get up to maybe sort of three or  four qubits, but to make  something that really has more  computational power than your  cell phone you would need about  100 qubits and no one has come  anywhere close to doing that.  This is mostly just to show you  graphs to show you a little bit  of the work done here.  So this is experimental work.  I do theory that tries to help  these experimentalists. 

 To give you some idea, it was  very much like this where  sometimes they just get data and  they just don't know why it  happened.  And so today actually I was  puzzling on some data which  absolutely, positively should  not have been, and maybe we're  seeing a new state of matter but  it turned out no it was some  problem.  But tracking down the problems  is also important when it comes  to figuring out what new  concepts need to be developed.  So I'll just show you a little  bit of data about what our group  is doing.  Our group is led by  Mark Erickson, he is the  experimentalist who knows how to  run all of the equipment.  Just to show you where we are  right now.  So this is actually only one  qubit.  This is silicon.  The computer is made out of  silicon and, in the end, so is  your computer and so is your  cell phone but it's in a  different regime.  And, again, the regime is that  your computer, it sort of works  with voltages and they're sort  of like a lot of and the voltage  you can think of they're a bunch  of electrical charges and you're  moving the charges around but  you're moving around groups of  charges. 

 Where here the idea is we're  actually looking at one electron  at a time and we're not actually  going to move the electron,  we're just going to take the  spin of the electron and then  we're going to be flipping  spins.  And the operations don't involve  moving any charge at all but  just changing the spins of the  neighboring electrons.  And then the electrons  themselves are placed by,  there's silicon below and these  are aluminum gates.  So we have voltages and  basically the idea here is that  the electron is sitting right  there.  And our quantum computer has one  bit right now.  That's all it has.  But this is, for us, a great  advance and the reason it's a  great advance is because we  actually have one electron in  it.  And that's actually what this  is.  So here this is a situation  where we're trying to get the  electrons out and again the  whole thing is to just have one  electron at a time because we're  trying to make it really quantum  right.  So here the electrons come out,  and every time an electron comes  out you get a line. 

 Here's a line, here's a line,  here's a line, here's a line,  here's a line.  And then there aren't anymore  lines and so then we say, ah-ha,  there's one electron right here.  So what we're doing in the lab  today, and it really is today,  we're trying to show that we can  manipulate that spin and flip it  from up to down.  And then basically then what we  want to do is to figure out can  we keep it quantum coherent.  Can we flip it, actually we want  to flip it, we flip it this way  and it will end up going back  and the question is how long  will it remain like this because  that's a measure of the quantum  coherence.  So that's the thing we're doing  today in the lab.  And so the point is all we need  to do is to make a hundred more  of these things and couple them  together and it should take no  time at all.  But what happens is in the  experiment when we see funny  things and again one of the  roles of theory is to figure out  what went wrong and why is it  not working and can we do  something to fix it, and I could  tell you about that at length  but I won't.  So I do want to do this one last  little picture of sort of what  the frustration of theory is.  And, basically, the goal is to  come up with different ways of  thinking about things that are  useful and interesting. 

 But the main thing is that most  everything is neither useful nor  interesting, and then there are  these little regions that here's  the useful region and here's the  interesting region and the  reason why we do it is because  there's this other little piece  right there which is both and  that's where we're aiming for.  And I hope to hit it.  Okay, thank you.  (applause)