John Preskill “Quantum Computing and the Entanglement Frontier”

welcome everyone it's my pleasure to welcome you to what by my count is the 39th Lee page lecture series these lectures started 49 years ago to honor the memory of Professor Lee page who was a professor in this department the physics department from 1916 until his death in 1952 today it's my great pleasure to be introducing to you John press kil who's the Richard Fineman professor of theoretical physics at Cal Tech John got his PhD at Harvard under Steven Weinberg and his career is noted for an amazing breadth of activity and that started even back then when he was working on both Technicolor alternatives to what we would call now the standard model of particle physics and also a a cosmological production of monopoles a problem that was eventually solved by inflation his work in particle physics cosmology and gravitation led him in the early 90s to be working on quantum black holes and interesting problems associated with quantum information in that system and that that theme of quantum information has been as marked as work since that time in 2000 John became the founding the fun of the fount he founded the the Caltech Institute for quantum information that's now an NSF frontier center and it's now referred to as the Institute for quantum information and matter and he's the director of that Institute if you've looked at the titles of his three talks you'll know that he has a wide breadth of expertise and and will be able to enjoy that through these three talks it'll also be our pleasure to enjoy his clear lecturing that's been rewarded twice by the Associated Students of Caltech Teaching Award so please help me welcome John Prescott well thank you very much Paul and excited to be here at Yale one of the world's great centers for quantum computing research and quite honored and humbled to be the lead agent is expressive information technologies today but we also know that those technologies are going to be surpassed in the future by new technologies that we can't really expect to imagine today it's interesting just the same to speculate about future technologies I'm not the ideal person to do that I'm not an engineer I'm a theoretical physicist and not really all that knowledgeable about how today's computers really work but as a physicist I know that the crowning intellectual achievement of the 20th century was the development of quantum theory and it's natural to wonder how the development of quantum theory in the twentieth century is going to impact 21st century technology quantum theory by now is rather all the subject but some of the ways in which quantum systems differ from classical systems we've come to appreciate only relatively recently a lot of those differences have to do with the properties of information encoded in physical systems to a fittest this information is something that we can encode and store in some physical system like the pages of a book but fundamentally all physical systems really are quantum systems governed by quantum mechanics so information is something that we encode and store in a quantum state and physicists have recognized for a long time that information carried by quantum systems has counterintuitive properties that's why we like to speak about the weirdness of quantum theory and we cherish and take pride in that weirdness but we can also ask whether it's possible to put the weirdness to work to exploit unusual properties of quantum information to perform tasks that wouldn't be possible if this were a less weird classical world and that desire to put weirdness to work is driving the emergence of a field that we call quantum information science which gets a lot of its intellectual vitality from three main ideas quantum entanglement quantum computing and quantum error correction and in this talk I'll try to explain these ideas I'd like to start at the beginning you know that any amount of classical information can be expressed in terms of indivisible units of information bits and we can think of a bit as an object like a ball which could be either one of two colors and I can take a bit and I can store it inside a box and then later on when I open the box the color ball that I put in comes out again so I can recover the bit and read it in quantum information information carried by quantum systems two can be expressed in terms of indivisible units what we call qubits or quantum bits and for many purposes it's useful to envision a qubit as an object stored inside a box but where now we can open the box through either one of two complementary doors those doors corresponding to the different ways in which we could prepare or observe the state of the qubit and I can put information into a qubit through door number one or door number two and later on when I open the same door the color that I put in comes out again I can read the bit just as though it were classical but on the other hand if you put information into a qubit through door number one and then open door number two then even though we know exactly how the qubit was prepared we can't predict what we'll find we'll see either a red or a green ball each with probability one hand so that means that in order to read the quantum information you have to do it the right way or you'll damage the information and you can appreciate one consequence that if you think about copying quantum information suppose I had a quantum copy machine what would that mean it would mean that if I had put information into a qubit through door number one then I could make a copy of the qubit and open door number one on the original and the copy and the color that I put in would come out of both doors on the other hand if I had put information into door number two and made a copy then I could open door number two of the original and the duplicate and the color I put in would come out of both boxes but in fact there's no such physically possible machine we can't copy an unknown qubit and the reason is that the copier has to probe inside the box to make the copy and if it guesses correctly the door that I use then it would be able to copy the ball just as though it were classical what if it guesses wrong and opens the wrong door then it will damage the information and there won't be any way to build a high fidelity copy so we might be able to clone a sheep but we can't clone a qubit now as you've seen I like to think about qubits in kind of an abstract way that's often useful but qubits can have many possible physical realizations and I'll mention a few others later but if you'd like something to come concrete to think about you could imagine a single photon a particle of light which has a polarization it's electric field say can be oriented either horizontally or vertically corresponding to the two states that we can see when we open door number one on the box on the other hand we can consider polarizations along the 45 degree rotated axis corresponding to door number 2 so I could make for example a horizontally polarized photon and then measure the polarization along the Tilted axes and I wouldn't be able to predict what I'd find it would be one polarization or the other each with probability 1/2 now the really interesting differences between classical and quantum information can be appreciated only I want to consider systems with more than one Cuba so let's suppose we had two qubits they could be far apart from one another one at Caltech in Pasadena the other and the custody of my friend and the Andromeda galaxy and some time ago these two qubits were both on earth and they interacted establishing a correlation between the qubits with some interesting properties namely for this particular state of the two qubits I can open my box through door number one or door number two and either way I just find a random value with probability one half of being red or being green and the same thing is true from my friend in Andromeda he can open door number one or door number two and either way just finds a random bit so neither one of us by opening the box acquires information about the state of the box and that's kind of peculiar because with two qubits we should be able to store two bits of information where is that information hiding in this case well the answer is that all the information is actually encoded in the correlations between what happens when you open a box and pasadenian and a box in Andromeda because it turns out for this particular state of the two qubits I can open door number one or door number two and I see a random bit but if my friend opens the same door on his box he'll see the same thing that I saw so if we both open door number one won't be fine could be red or could be green but it's guaranteed to be the same for both of us and the same thing if we both open door number two and we know this is true because we've tried the experiment a million times with identically prepared pairs of qubits and it always works this way now there are four distinguishable ways in which a qubit in Pasadena could be correlated with the qubit in Andromeda we could see the same color or different colors when we both open door number one or when we both open door number two and by choosing one of those four ways we've encoded two bits of information in the two boxes but what's unusual is that that information is inaccessible locally it's stored entirely in the correlations and I can't acquire it and pass it or my friend and Andromeda and that property of quantum information that it can be shared by two distantly separated parts of a systems what we call quantum entanglement and it's the really important way in which quantum information is different than classical information correlations themselves are not unusual we encounter them all the time and daily life my socks are typically in the same color so when you look at my right foot and observe the color you know what color sock to expect when you look at my left foot and you might think it's pretty much the same thing with the boxes if I want to know what my friend will see when he opens door number one and Andromeda I can open door number one in Pasadena to find out I want to know what he'll see when he opens door number two I can open door number two in Pasadena to find out so aren't the boxes just like the socks is know they're really fundamentally different and the essence of the difference is they're just one way to look at a sock but we have these two complimentary ways of viewing a qubit and that makes the correlations among qubits much richer and more interesting than correlations among this this phenomenon of quantum entanglement strange correlations between parts of a quantum system was first explicitly discussed in a paper by Einstein and collaborators over 80 years ago and Einstein quantum entanglement seemed unsettling to indicate that something's missing from our current understanding of the quantum description of nature and that paper elicited some thoughtful responses including an especially interesting one from Schrodinger and Schrodinger put it this way he said the best possible knowledge of a hole does not necessarily include the best possible knowledge of its parts so what Schrodinger meant was that even if we know as much as can possibly be known about the state of our pair of qubits one in Pasadena and one in Andromeda as much as the laws of physics will allow us to know I'm still helpless to predict what I'll see when I open the box in Pasadena or open it in Andromeda and it was Schrodinger who suggested that we used the word entanglement to describe this unusual quantum correlation and he added it is rather discomforting that the theory should allow a system to be steered or piloted into one of the other type of state at the experimenters mercy in spite of his having no access to it well shirting are meant by that is it seems strange that it's up to me to decide by either opening door number one or door number two in Pasadena whether I'll know what my friend will find when he opens either door number one or door number two and Andromeda but Schrodinger understood well that these correlations don't allow us to instantaneously send a message from Pasadena to Andromeda when my friend in Andromeda opens his box through door number one or door number two he just observes a random bit irrespective of what I did to my box in Pasadena so there's no communication of information from one box to the other nevertheless there are unusual correlations between the two qubits now this idea of quantum entanglement didn't advance very much for the next thirty years until the work of John Bell in the 1960s and with Bell we started to think about entanglement in a somewhat different way not just as something strange about quantum theory but as a resource which we can use to perform useful tasks they'll describe games that two players can play the two players Alice and Bob are cooperating they're both trying to help each other win the game and these games have the following structure Alice and Bob each receive inputs and they are to produce outputs that are correlated in some way that depends on the inputs that they received and they're allowed to use correlated bits that might have been distributed to them before the game began but under the rules of the game they're not allowed to communicate between when they receive their inputs and when they produce their outputs and for this particular version of the game if Alice and Bob play the best possible strategy then averaged uniformly over the inputs that they receive they can win with the probability of at best seventy-five percent but there's also a quantum version of the game where the rules are the same except that now Alice and Bob are allowed to use entangled pairs of qubits that were distributed before the game began and using those qubits they can play a better quantum strategy and win the game with a higher probability of success about 85% instead of 75% so they've used the entanglement as a resource to do something to win the game with a higher success probability an experimental physicists have been playing the game for decades now and winning with the higher probability of success which Belle pointed out quantum mechanics allows so these super-strong correlations which are different from the correlations and classical systems quantum entanglement really do seem to be part of nature's design Einstein derided quantum entanglement he called it spooky action at a distance which sounds especially derisive when you say it in German but nature is the way she is as experiments reveal her to be and we have to learn to love her as she is so boxes are not like Sox's quantum correlations are different than classical correlations quantum entanglement is something new you can win a game with a probability of success 85% instead of 75% is that really a big deal yeah yeah it's really a big deal and you're gonna begin to appreciate why it's a big deal if you think about systems with more parts I mentioned a book it's a hundred pages long if this were a classical book written in bins then every time you read another page you'd learn another one percent of the content of the book and after you've read all 100 pages you'd know everything that in the book but now suppose it's a quantum book written in qubits instead of ordinary bits and the pages are highly entangled with one another that means when you look at the pages one at a time you see only random gibberish you get almost no information that distinguishes one highly entangled book from another and that's because the information isn't written on the individual pages the information in the book is encoded almost entirely in how the pages are correlated with one another that's quantum entanglement and what's interesting is that these correlations are extremely complex so that if I wanted to give you a complete description of all the correlations among a few hundred qubits if I wanted to write down that in classical bits then I would have to write down more bits than the number of atoms in the visible universe so it's never going to be possible even in principle to write that description down and that feature was very intriguing to the physicist Richard Feynman it led him to make this suggestion in the 1980s that if we could operate a computer which processes qubits instead of bits then we ought to be able to perform tasks that wouldn't be possible with ordinary digital computers what finally had in mind is that if we can't even write down using bids the state of a quantum computer with a few hundred qubits then by processing the qubits we ought to be able to do things that an ordinary digital computer would never be able to emulate and when finally was making that suggestion in the early 1980s there was an undergraduate student at Caltech studying mathematics named Peter shor and like all Caltech undergraduates at that time he was required to study quantum physics as part of our core curriculum and like many of our undergraduates he retained what he learned and some years later put it to good use in making a remarkable discovery an example of a problem which we believe is hard for ordinary digital computers is factoring finding prime actors of a large composite integer and what you're discovered is that with a quantum computer factoring isn't a hard problem it's not much harder than multiplying two numbers together to find their product and when I first heard about this in 1994 I was really awestruck because I realized what this means is that the difference between hard and easy problems between problems that we'll be able to solve with advanced technologies and problems that will remain intractable even when we have very advanced technologies that boundary between hard and easy is different in our world because it's a quantum world then it would be if this were a classical world and that was one of the most interesting ideas I'd ever heard in my life now to give you an idea of what it means an example of a factoring problem that we can solve with existing technology is factoring 193 digits that was done some years ago now using a network of workstations that collaborated over the internet and it took a few months and from what we know about how the difficulty of the problem scales with the number of bits we can estimate how long it would take that same hardware to factor a 500 digit number and it would take longer than the age of the universe so the difficulty of the problem scales very unfavorably as we increase the number of digits but suppose we had a quantum computer and imagine that it has the same clock speed as that classical system it can perform the same number of elementary operations on pairs of qubits per second as this classical system can perform elementary operations on bits so you have to imagine that because we don't have that now but if we did factoring 193 digits could be done in much less than a second in factoring 500 digits in just a couple of seconds so the difficulty scales in a much different way as we increase the number of digits if we have a quantum computer running Shor's algorithm now does anybody care whether factoring is hard problem or not yeah quite a few people care about that because the security of widely used quantum Tsarina quantum widely used public key cryptosystems the security of those systems is based on the presumed difficulty of factoring and other related number theoretic tasks when quantum computers are widely available as they might be in a few decades then those protocols will become vulnerable and will have to protect our privacy in other ways there are alternatives to using the current public key systems but it's still not clear what will be the best way to protect our privacy in the coming post quantum world well the broader lesson that we learn from share is an algorithm and other related algorithms is there's this interesting classification of problems there exists a family of problems which are classically hard but quantumly easy that quantum computers can solve an ordinary digital computers can't solve with reasonable resources and it's important to understand better what are the problems in that intermediate class that are quantumly easy and classically hard we've made some progress on that in recent years but I think from a physicists perspective what's most important about quantum computing is that we believe that we don't really know this for sure that a quantum computer would be able to efficiently simulate any process that occurs in nature that's not true for ordinary digital computers which cannot simulate very highly entangled quantum systems with a quantum computer then we'd be able to probe the properties of complex molecules and exotic materials and also study fundamental physics in new ways for example by simulating high-energy particle collisions or the quantum physics of a black hole now there's a lot of theoretical work being done on quantum algorithms that could run on the quantum computer but we don't have the quantum computers yet so it's a little bit frustrating sometimes my friend Eddie far he wrote a Braille paper not long ago about a new application for quantum computers which inspired me to send him this poem which reads in part we're very sorry at FRP your algorithms quantum can't run it on those mean machines until we've actually got and the poem goes on but you get the idea we have lots of ideas about what to do with the quantum computer but we don't have one yet so why is that well it's really really really hard part of what makes it hard is that we have to overcome a formidable difficulty what we call decoherence physicists like to envision a cat which is both alive and dead at the same time we're funny that way but we never in our everyday lives see cats that are both alive and dead at the same time they're always completely alive or completely dead and we understand why that's true it's because a real cat will interact with its environments and those interactions with the outside world in effect measured the cat and projected onto a state which is either completely dead or completely alive that's decoherence and that phenomenon of decoherence is very important in helping us to understand why even though quantum physics holds sway in the microscopic realm classical physics gives us a very adequate description of most macroscopic phenomena well a quantum computer - though we may try hard to prevent it from happening will interact with its environment and those interactions will in effect measure the quantum computer and spoil the coherence of the information it's processing which will cause the quantum computer to fail so if we expect to operate large-scale quantum computers successfully we have to find a way of fighting off the effects of decoherence and other possible sources of error errors are a problem even in the classical world we all have bits that we cherish everywhere it seems our drag lurking who delight and tampering with those bids changing the color of our balls as it were but in the classical world we have learned how to fight off those dragons if I have a classical bit that I want to protect then I can store some backup copies of the bit and the dragon may come along and change the color or one of the balls flip one of the bits but I can employ a busy beaver who frequently checks to see if the three colors match and when they do not the beaver repaints the mismatched color so that all three match again so the dragon hasn't had a chance to damage two out of the three bits then the information can be recovered successfully because it's been redundant li encoded and we would like to use that same principle that redundant encoding protects against there but use it for quantum systems well it's not immediately obvious how to make that work as I've already emphasized we can't copy unknown quantum states so we can for example make a backup copy of the quantum information in a quantum computer in case the original gets damaged and in the quantum world we have to worry about more kinds of errors than in the classical world it could be that the dragon opens door number one of the qubit and changes the color of the ball and then reclose us the box that would be like a bit flip error that could occur to a classical bit but what he might do instead is open door number two of the box and change the color of the ball and reclose the box that's what we call a phase error which has no classical analog and we have to be able to protect both types of errors protect against both types of errors without knowing which kind might have occurred there's another way of thinking about the phase error which is we can imagine that the dragon opens door number one of the box and instead of flipping the color of the ball just observes the color and remembers it and that will have the effect of changing the color of the ball we look through door number two and in many physical settings it's easier to remember the value of a bit than to flip the bit and that makes the phase errors particularly pervasive in many different physical systems so really the key thing is that if we want to operate a quantum computer if we want to protect quantum information we have to prevent any information that's being processed from leaking to the outside world we have two perfectly seal off the information being processed from the environment or else the quantum computer will fail and that sounds impossible because our Hardware it's never going to be perfect well we've learned in principle how to do it by using quantum entanglement so if I have one qubit that I would like to protect I can encode that one qubit of quantum information in a highly entangled state of five cubits and then the dragon might come along and damage in some undetermined way one of the five cubits but because the state is highly entangled the information that's encoded in that block of five qubits is not accessible when you look at the qubits one at a time just like we couldn't read that hundred-page quantum book by looking at the pages one at a time so the interaction of the dragon with the qubit doesn't necessarily have to damage the encoded information and in fact we can ask the beaver to come along and make some carefully constructed collective measurement on that block of five qubits which will allow the beaver to diagnose the damage that was done by the dragon and reverse that damage and the beaver too doesn't find out anything about what the encoded state is which would cause the encoded information to class only learns about the errors and can correct them what makes it work is that the encoding is in a highly entangled State so this idea of quantum error correction is that if I want to protect quantum information from the environment I encoded in a highly entangled state in a system with many parts and then the environment will typically interact with those parts one at a time and therefore not acquire any of the information that's encoded and therefore it not damage it and we've also learned how to coherently process information that's encoded in this highly entangled form so we can imagine preparing an encoded state of a CAD which is alive and dead for at the same time and maintaining that state for a very long time and furthermore we know how to coherently process the state of a large quantum system suitably encoded so the theorists are very excited about this idea of quantum error correction it's kind of a theory stream so we wrote poems about it including my former student Daniel goddess Minh he wrote a sonnet of which I'll just quote one part we cannot clone for force instead we split coherence to protect it from that wrong that would destroy our values quantum bit and make our computation take too long so it was just a theorists dream twenty years ago but what's exciting is that today quantum error correction is starting to become serious laboratory science and it's now being carried out at places like Yale now in a small scale but with great future potential now one of the heroes of this subject with quantum error correction is my Caltech colleague Alexey kitaev the day we met in 1997 was one of the most exciting days of my scientific life when I heard his seminar and made these notes I felt I was hearing from Kataya ideas about quantum error correction that are potentially transformative the main thing I learned was the connection between quantum error correction and topology mathematicians use the word topology to mean the properties of an object that from variant if we smoothly deform the object without ripping or tearing it and likewise we would like the way a quantum computer acts on its protected quantum information to remain invariant as we deform the computation by introducing some noise so we'd like to use physical interactions with a topological character to do the processing and we know of such topological interactions and physics like the aharonov-bohm effect in which the quantum state of an electron is affected by transporting the electron around tube of magnetic flux even though the electron never directly visits the region where the magnetic field is nonzero and that change that a Cochran apone phase that the electron acquires remains the same if we deform the trajectory of the electron all that matters is the winding number of the electron around the flux tube and these types of topological interactions are much richer in two dimensional systems I can consider two dimensional media that support an exotic type of particle and we call an any on what happened here this doesn't want to advance okay and these particles have the following property if I have a two-dimensional medium that supports many anions there are many distinguishable quantum states of that system of many anions corresponding to different ways of fusing together the individual particles but all of those states look identical when we examine them locally I can't tell the difference between one state and another and when I visit the ions one at a time so that's just the type of encoding of quantum information we want to hide the information from the noise in the environment and furthermore we can process that information just by exchanging the anions and so we can imagine operating a topological quantum computer which we could initialize by creating pairs of any ions then process information by performing a sequence of exchanges on the anions so that their worldlines and 2 plus 1 dimensional space-time trace out a braid in space-time and then I could read out the information by bringing the onions together pairwise to observe whether they annihilate or not and disappear so the beauty of this idea is that the computation has an intrinsic resistance to decoherence if I keep the temperature low so there's no thermally excited and ions diffusing around and I keep the particles far apart from one another except at the very beginning in the very end then as long as we execute the right braids we're guaranteed to get the right answer in the quantum computation so again that's the theorists dream I was excited about this idea so I wrote a poem about it which reads in part alexei exhibits a knack for persuading that some day will crunch quantum data by braiding with quantum states hidden where no one can see protected from damage through topology any on any on where do you roam braid for a while before you go home and there's more to the poem but you get the idea we think it's an exciting dream but is it just a dream well here too technology is starting to catch up with the theorists dream and one way of realizing this idea uses another trick that Kataya taught us that it's possible to cut an electron into pieces that sounds ridiculous an electron is an indivisible elementary particle isn't it but in a highly entangled world amazing things can happen so an example of where an electron can divide into pieces is in one dimensional system a wire a quantum wire a quantum wire can be superconducting that means it can conduct electricity without resistance but there are two kinds of superconducting wire and the ordinary kind and the topological kind and at the boundary between the two there sits an object we call a my around a Fermi on and so if I introduce an extra electron into that segment of topological superconductor and that electron can in effect dissolve and disappear and in the process the pair of my Arana fermions at the two ends of the segment get excited but that excitation can't be observed locally when I look at the my Arana fermions one at a time it's really a collective property of the two Meyer on a fermions so that's an encoding of information whether the electron was added or not which is highly non-local and therefore can be hidden from the environment now there is highly suggestive experimental evidence that this type of topological encoding of information is possible in quantum wires though more definitive experiments still need to be done to make this fully convincing but it's very encouraging now I would like to be able to process this type of topologically encoded information by exchanging particles when I'm limited to a one dimensional wire the way I could do that is by having T junctions in the wires so that by controlling the boundary between topological and ordinary superconductors say with some voltage gates I could park one of the my Arana fermions around the corner move the one on the right over to the left and move the other one over to the right in effect achieving an exchange of the two particles that would be one step in a protected topological quantum computation that type of topological processing of my honor fermions hasn't yet been done experimentally but I'm hopeful that it can be in the next couple of years and that will be not just a step towards a promising new technology but also a milestone in basic physics I don't want to give the impression that this topological method for encoding quantum information is the only way to build quantum hardware there are many ways that are being pursued in different physical settings we can imagine a qubit carried by a single atom which could be either in its ground state or some long-lived excited state or we could have information encoded in a single electron which has a spin or magnetic moment which can be oriented either up or down corresponding to this two states of the qubit that's a remarkable encoding because it's just one electron carrying the information and yet we've learned how to control that electron spin accurately and protected from decoherence for reasonably long times or we could encode the information as is done here in yale in a ordinary superconducting circuit one way to do that that's easy to visualize is that we could have the persistent current and a loop of superconducting wire be either clockwise or counterclockwise in practice that's not really the right way to do it there are more clever ways that work better but it's a highly successful technology for realizing qubits and it's really a remarkable encoding because in this case the qubit is encoded in the collective motion of billions of electrons and yet it behaves like a single qubit of information like an atom or an electron spin so I have an emphasis in emphasizing three issues about quantum computers which I've been thinking about for a while one is why would we build one what can we do with the quantum computer and I think the best answer we have is that with the quantum computer we'd be able to simulate efficiently any process that occurs in the quantum system can we build one well now that we understand the principles of quantum error correction we're not aware of any obstacles which has a matter of principle will prevent us from realizing large-scale quantum computers and how will we build one what kind of quantum hardware is the right kind to use well as I've emphasized there are many different approaches to building quantum a hardware that are being pursued and it's important that these be pursued in parallel each one might find its own technological niche or even a hybrid technology that makes use of several different types of hardware could turn out to be important I felt for quite a while that although this is already a compelling research agenda that as our ideas about quantum information processing advanced we should expect those ideas to connect to other problems in physics and we're starting to see that happen in recent years and a lot of those connections have to do with what we call the monogamy of entanglement classical correlations are polyamorous that means they can be shared in many different ways so for example Adam and Betty can both read the same newspaper and that means they have the same information and they become correlated with one another but nothing prevents Charlie from reading that newspaper - and then he's just as strongly correlated with Betty and with that and Betty are with one another quantum correlations are different they're harder to share so that if any an atom are very strongly entangled with one another then Betty is used up all our ability to entangle with Adam and Betty and Adam can't be correlated with Charlie at all and if on the other hand Betty and Charlie are fully entangled with one another then they can't be correlated with Adam at all that's the monogamy of entanglement and the monogamy can be frustrating Betty might want to attain goal with both Adam and shortly but if she wants to get more entangled with Charlie she can do so only by sacrificing some of our entanglement with Adam and then monogamy has many different ramifications it's important in cryptography because Adam and Betty could try to use their entangled state to generate a secret key that can be used to encrypt and decrypt a private message that they exchanged and if they have a way of verifying that their highly entangled with one another then they can be assured that Charlie won't be correlated with that key he won't know their secret key so their privacy will be protected monogamy is important in the study of quantum matter because if I have a system of many particles many electrons say each pair of electrons may want to become entangled with one another but each time an electron becomes more entangled with one of its neighbors it will have to be less entangled with other neighbors so the electrons are frustrated and they have to find some optimal way of sharing their entanglement which makes them as happy as possible and that gives rise to different phases of quantum matter in which the entanglement is shared in different ways and we're trying to understand and classify those quantum phases the monogamy is also important in gravitational physics in particular in the study of black holes in the next few minutes I'd like to explain that classically a black hole is something from which nothing can escape if astronaut is foolish enough as to enter a black hole to cross its event horizon she will never be able to return to the outside or send a message to the outside but quantumly is we've known for 40 years black holes can radiate they emit Hawking radiation and eventually a black hole will radiate away all of its mass and disappear and that raises the question of what happens to the information that fell into the black hole and was lost behind the horizon if black holes are like other objects which emit thermal radiation then we would expect that information to be still present to survive but to be very highly scrambled to be encoded in a way that's so scrambled that it would be very hard to read and practice but in principle the information still exists but black holes are different from other objects and the important respect that a black hole has an event horizon and what that means I've tried to depict in this picture a space-time diagram with time going up for it the geometry of a black hole is so deform then it's possible to draw a slice which I've shown here in green which is really a space like slice it's a slice of a single time and yet it crosses both the collapsing body from which the black hole form and nearly all of the Hawking radiation that was emitted while the black hole was evaporating so if quantum information is encoded in that collapsing body and it is revealed in some form in the Hawking radiation that means the same quantum information is really in two places at the same time in other words the information has been copied but that's cloning of quantum information which I argued earlier is impossible so now we're really stuck because we either have to believe that information is destroyed and give up on a central tenant of quantum theory that evolution is microscopically reversible or accept the cloning occur either way the foundations of quantum theory would need revision well thinking about this back in the 1990's and came up with the idea called black hole complementarity and the idea is that we shouldn't think of the inside and the outside of a black hole has two separate subsystems of a single system instead for reasons that aren't obvious in which a theory of quantum gravity would have to explain the correct view is that we should think of the inside and the outside as complementary ways of looking at one and the same system one point of view is appropriate for the observer who stays outside the black hole the other point of view is appropriate for the observer who falls through the horizon and enters the black hole interior but because these are just two views of the same quantum system there's no cloning necessary for the information to be in both the collapsing body and the outgoing radiation and evidence accumulated over some years thereafter that this idea of black hole complementarity is on the right track but then I ran into trouble a few years ago through the work of the group known as ants black hole complementarity seeks to reconcile three ideas each of which on its own seems quite reasonable on the one hand a black hole doesn't destroy information but merely scrambles it up puts it in a form which is difficult to read on the other hand an observer who fought whoops an observer who falls through the horizon of a black hole doesn't notice anything unusual at the moment of horizon crossing at the moment of entering the black hole don't later on that observer will be crushed at the singularity inside and third that an observer who stays outside the black hole doesn't see any unexpected violations the usual rules of local quantum physics an amps argued that these three ideas can't all be compatible that we have to give up at least one of them and they advocated that the conservative resolution of the conflict is to give up on to that instead of an observer being able to pass through a black hole horizon unscathed that observer would be immediately destroyed right at the moment of horizon crossing in a sealing firewall that's a crazy claim because it's not at all what we find when we solve the gravitational field equations to learn about the black hole geometry so why would these smart people make this crazy claim it's because of the monogamy of entanglement because am sorry you then if it's true that an observer who falls through the black hole arrives and doesn't notice anything unusual at the moment of horizon crossing and that means the black hole radiation that's being emitted right now has to be highly entangled with degrees of freedom that are inside the black hole on the other hand if information really does get revealed as a black hole evaporates and that means when the black hole has been evaporated for a very long time the Hawking radiation that's coming out today should be highly entangled with radiation that was emitted earlier and if the rules of local quantum physics are the usual ones outside the horizon if it's going to be entangled with SystemC after it's pulled away from the black hole it has to already be entangled with system seen when it's very close to the horizon and now we have a problem because system B just outside the black hole wants to be highly entangled both with the inside and with the earlier radiation and it can't have it both ways because of the monogamy of entanglement and ants proposed to relieve the tension by breaking the entanglement between a and B but that would mean that the black hole horizon would be a highly energetic place the firewall and we're still really puzzled about this it exposed that we don't understand very well what the interior of a black hole is because of subtle quantum effects and the main reason I'm telling you about this is that this observation might have been made decades ago but it occurred relatively recently because only in the last few years have we grown accustomed to thinking about other problems in physics including gravitational physics from the point of view of entanglement dynamics and the properties of quantum information so how are we going to make progress on a problem like this one how could how are we going to understand what's inside a black hole well our best hope is to pursue the best idea we have about quantum gravity which is the holographic principle now this principle asserts that contrary to naive expectations all the information in a room like this auditorium encoded in their brains and our smartphones and so on can actually be read on the boundary of the room the floor and the walls and the ceiling but it's encoded on the boundary in some very very highly entangled form that's extremely difficult to read in fact we can think of the geometry of the room who in the auditorium is sitting close to other people as being encoded in the quantum entanglement on the boundary so it seems that it's really the entanglement which determines how space is held together which points are close to other points a geometry according to the holographic principle or so it now seems is an emergent property of a very highly entangled system and lives on the boundary we had a talk at Cal Tech last year by Robert dygraf the director of the Institute for Advanced Study and he was reviewing theoretical physics and he showed this slide which indicates how the different ideas of theoretical physics fit together and I thought it was striking that he put quantum information right in the center of things he wouldn't have done that five years earlier because it's only relatively recently that the idea that quantum information really is at the core of the deepest questions and physics has started to gain traction but I would like to go further than diagraph I would erase the theoretical from the diagram because quantum information really is an experimental science as practiced it places like Yale and if it's really true that we can think of quantum geometry as an emergent feature of very highly entangled systems and that means that we ought to be able to perform experiments on highly entangled systems to gain insights into the quantum properties of geometry so I expect that in the coming decades at a university like Yale on a tabletop in the laboratory we'll be able to do experiments with highly entangled systems which will give us insights into quantum gravity that would be very hard to acquire without experimental guidance so the way I like to think about quantum information science is that we are at the early stages of the exploration of a new frontier of physics we might call it the complexity frontier or entanglement frontier this is different from the short distance frontier we explore in particle physics or the long distance frontier of cosmology but like those it's very fundamental and exciting we are just now acquiring and perfecting the tools to build and control very precisely highly complex quantum systems with many particles systems that are highly entangled systems that are so complex that we can't simulate them with our digital computers or very well predict how they behave with our existing theoretical tools and that's opening great opportunities for new discoveries and Yael is one of the institutions leading advances at the entanglement frontier so I'm especially glad to be here this week at Cal Tech also we have an institute or quantum information and matter dedicated to exploring the entanglement frontier an account tech we have a slogan a tagline nature is subtle this is meant to do homage to Einstein's famous pronouncement subtle is the Lord but malicious he is not but the fact is despite all his genius Einstein was under estimating the subtlety of nature when he dismissed quantum entanglement as spooky action at a distance and our aim in quantum information science now is to explore and joy exploit the subtlety of the quantum world in all its many facets and ramifications so thanks for listening to me today and then tomorrow's lecture I hope I'll see many of you well I'll discuss in greater depth the connections between quantum information and gravitation Thanks so we have time for a few questions yes I mean there are none quantum things like photographic storage of information based on waves and interference in the heavens any of the same properties or these error correction it's a really entanglement because even with those holographic classical and coatings of information if you look at a small part of a hologram it certainly doesn't allow you to reconstruct the whole picture but it does give you some significant information about the image that's holographically store these entangling coatings aren't like that you can look at a big hunk of the quantum memory and still know almost nothing about the encoded state the question is how do you measure the entanglement and the answer is it's not an easy thing to measure and if I have many identically prepared copies of the system then I can make measurements make different measurements on different copies and thereby reconstruct enough about the quantum state to determine the entanglement but in general it's not a very easy thing to measure there are actually some some neat ideas about how you can measure quantities related to entanglement that tell you about the global properties of quantum correlations but they won't really give you exactly the well I didn't even say how to quantify entanglement I'll talk about that a little bit more there is a way to do it you can quantify entanglement essentially by asking how much information is missing if you look at Part A of the system and that means you're learning about what an observer who's confined to Part A can find out and that observer is going to be missing some of the information in Part A because it's correlated with Part B and so one way to do it is that many copies make different measurements in Part A and Part B but in the single copy case it's hard any large system in nature using a quantum computer better than we can do with a classical one so is the value-add entirely from the faculty to do more computations at a time and it's much faster or are there any types of computations so that the question is where does the advantage of the quantum computer really come from and the question was framed as is it coming from the fact that you can do many computation simultaneously this is actually a pretty subtle question so I was so little that was a bit cagey in not putting it exactly the way you did although you'll often hear people describe the advantage of a quantum computer that way it is true that if we consider a superposition of many classical states we can run the computation once and only once and to simulate with a classical computer what that computation does it seems like we would have to run the classical computation many times but the reason I don't like putting it quite that way is it's a little bit misleading because in the end you're going to have to read something out to get the result of the computation and you're quite limited in the information you can extract in that final measurement so the power really comes from designing your quantum algorithm in a sufficiently clever way that those different parts of the computation interfere with one another constructively on the right answer and that's why it's really an art to designing quantum algorithms that have advantages over classical algorithms and why in many cases we don't think profound quantum speedups of the computational problem are possible they didn't say this but for the hardest types of problems that classical computers can solve or we can check the answer efficiently the problems you know we call np-complete quantum computers can speed those up a little bit but not nearly as profoundly as they speed up problems like factoring so the problem has to be pretty well matched to these special capabilities of a quantum computer for a very big speed-up to be possible I couldn't hear you and starts when you observe those superimposed two-qubit you collapse it into one of two states always it's always one or two and that's no it could be one of many couldn't imagine using boolean logic when you're in people are talking about the sorts of things like you youyou said that the things are constantly easy surround the things that are classically easy but I've always kind of thought it was being really separate domains of computation so the question is why did I draw that diagram classically easy with quantum wheezy of being a larger containing set aren't they really completely separate things well what I meant by that is that in principle if you had a very well controlled quantum computer you could use it to do a classical computation it's pretty easy in principle to get a quantum computer to simulate a classical computer and therefore solve any problem the classical computer can solve it's hard to do it the other way to get a classical computer to simulate a quantum computer of course it would be kind of a stupid thing nowadays to give you the your classical problem to a quantum computer maybe someday quantum computers will be so advanced that it won't be so foolish but that was all I meant that a quantum computer at least conceptually can easily simulate a classical one np-complete we believe is outside quorum easy but there are also problems that are in quantum easy which are not an NP at all in other words it's not necessarily the case that a problem that can be solved quickly by a quantum computer can we can easily verify the answer with the classical computer and many of the quantum simulation problems have that feature

Channel: YaleUniversity

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Keywords: Yale, physics, quantum information, quantum gravity, quantum entanglement, seminar, John Preskill

Id: bPNlWTPLeqo

Length: 65min 24sec (3924 seconds)

Published: Tue May 17 2016