Superposition in Quantum Computers - Computerphile

we talked about uh the links between physics and computing in different contexts like things like reversible computing a little bit the ultimate limits of computing did a little bit of neuromorphic computing and things like that what we haven't touched on which would seem to be the obvious one for physicists is quantum computing the thing that is always described as sort of the most mystical element of quantum mechanics and it it irritates computer scientists and it irritates physicists there's a guy called scott aaronson from a computer science perspective he really demolishes this myth well the way quantum computing works is you basically set up your system and the the the quantum bit can be in any possible state in all these different parallel universes and basically because you're trying all the answers in parallel that means you can pull out the right answer that's rubbish rubbish there's an awful lot of hype about quantum computing that doesn't mean that the science and the mathematics and the physics isn't valid it very much is obviously i'm not going to be able to explain the entirety of quantum computing in 10 minutes you're not going to get this is exactly how it works in any 10-minute video but what i really do want to get to the the core of is something called superposition and that's this is the thing where almost everything starts to go wrong in terms of descriptions of what's going on with quantum computing in that okay we've got a classical bit that can be zero one then the argument is well with a quantum bit it can be some mixture zero one and therefore we can have any possible mixture and therefore because we can have any possible mixture suddenly your answer da da appears by magic and it really does seem to magic superposition um this idea of something being in two states at the same time always dressed up as this weird isn't it really isn't there are two approaches to broad approaches to quantum mechanics there's something called matrix mechanics which computer scientists love obviously because it's got matrices and vectors and it's easy to set up on a computer and it's easy to um to think about lists of numbers and how those interact and how you change those however equivalently and it is completely equivalently we have something called wave mechanics because ultimately quantum mechanics is all about the physics of waves and not just from a very abstract um perspective in that we can represent these quantities as waves here's a whole series of different images taken with something called a scanning tunneling microscope in this for example this is taken from work by ibm quite a number of years ago more than 20 years ago at this point they formed a ring of 48 iron atoms that's not the good bit the good bit is if you look inside this ring it's as if you dropped a stone in a pond time and time again we see these waves matter behaves like a wave when you get down to the atomic level which means that all of the the classical physics about waves and all the classical mathematics about waves we can pour it into quantum mechanics i'm not going to go through each and every one of these images but what you're seeing here each time is how electrons behave right down at the at the atomic level how does this relate to superposition well superposition is painted as this weird quantum effect but actually any time you pick up a musical instrument you pluck a string what you have is a superposition of waves on that string this string can be in a range of different types variety of different types of modes of oscillation waves of vibrating when you pluck that you're not just exciting one wave you're exciting a whole load of waves together what are those waves well monkey which is um making his debut i think on computer file so this is a large scale demonstration of a guitar string and there are special modes of vibration called standing waves or resonances or if we want to use the mathematical term and perhaps the term computer scientists are a little bit more familiar with and a more quantum-y term eigenstates special states of the string of the string that we can build up any particular pattern of waves on the string using just these particular states and these resonances here's the lowest energy one where we've got what's called an anti-node in the middle maximum vibration in the middle and nodes at the end of each string now i'm going to try and get the second one so i have to wiggle a little bit more quickly as does monkey there we go okay so that's our second mode that's our second special motive and get it right i'm blaming the monkey so second special mode or second resonance or second standing wave or second harmonic or second eigenstate all those oh that was close what have you done right he's got a malicious look and he's he has he definitely does i think that's the third mode right so i have to pump in quite a bit more energy for that one and i'd have to pump in more energy there's a whole series of these here's our um two points where it was fixed so i was one end monkey was the other end our first mode looked like that our second mode of vibration looked like that our third motor vibration looked like that and i ran out of steam at that point but there's a whole host of these all the way up um in terms of different resonances and the thing that connects all these they're the same type of function it's a sine function and in terms of the physics of the problem what when we write down the equation that describes this our solutions or signs and what are what are called our boundary conditions are that it just needs to go to zero here and here there's an infinite number of these solutions that work on the string i don't have infinite energy so i can't excite all of these but what we can have and this is key when it comes to superposition and quantum mechanics is we're not restricted to these of course a string doesn't just vibrate like this or this or this if i pick up the base and plug the string it'll turn around so this is the first mode plus the second mode plus the third mode plus the fourth etc etc if sean were to pick up his guitar and play a an e note on guitar um exactly the same e note so if we looked at it in musical notation it would sound different or better if sean were to play it on on piano it would be the same note exactly the same note in terms of a treble clef in terms of musical notation but it would sound different and the reason it sounds different is because we have a different superposition of those resonances if i play an e note on bass you play an enorm piano can you tell the difference well yeah you know you know that you can just hear the different instruments right yeah you can hear the different instruments it's the same note but you can hear the different instruments the reason you can hear the different instruments is a lot of although it's the same note therefore is the same frequency therefore repeats with the same period in time the pattern the overall pattern is different and the reason the overall pattern is different or the overall waveform is different is because you have a different mixture of these harmonics on the string so the each instrument has its own signature mixture of those particular states on the string eigenstates on the string and therefore you have a different superposition and in terms of quantum computing it's all about controlling how those different states on the string in this case interfere with each other and you let the system evolve so you pluck your string you wait for a certain amount of time for those waves to interfere with each other and then you make a measurement to pull out the the overall answer that is not at all the same as saying that what we do is we have an infinite number of answers and we pull out you know we just let it run and as if by magic we pull out an answer what we have to do is very very and when i say i i'm not involved in developing these algorithms so people who develop these algorithms have to think very carefully how do we engineer those waves how do we engineer those states to interfere with each other so at the end when we make a measurement out pops the result we want so superposition in that sense is just classical physics it's been physics that we've known about for two or three hundred years of course that's not all there is to quantum the issue of course is when we um make a measurement of our quantum system so for example imagine this is our measuring instrument and i plug that base string okay we're going to measure what the b string is doing and we hear it quantum mechanically that's not what happens quantum mechanically we plug this string or we set up this quantum state this um superposition state when we then make a measurement if we make it want to know the energy of of the string what happens is that it falls into one of these states with a certain probability why if you know that you get a nobel prize that's the confusion thing not superposition per se because superposition you know is is there in classical physics it's the question of just why when we make a measurement it's even called the measurement problem in physics so we can take our um guitar string and we can port it all the way down to the quantum level it's it's amazing this is a paper published by a stefan fralsch's group in berlin this is absolutely beautiful work they've taken indian atoms and they formed a line of indium atoms which acts as a string basically along which the electrons can can move and the red bits represent where there's a high probability of finding electrons and the darker bits as you can see represent where there's a low probability of finding electrons and it's exactly the same as we just was we saw on the guitar string low at the ends high in the middle then when i vibrated monkey a little bit faster we had um low peak then we had a minimum then a maximum then a minimum just as i've drawn on the on on the paper this is right at the quantum level so this is why physicists often get very frustrated when quantum mechanics is painted as this incredibly mystical um very weird wacky it is it has its elements but an awful lot of it is very very understandable using physics and maths that we've known for a very long time so where does this go in terms of quantum computing well what we could do is let's say we're going to use the first mode of our quantum string a zero and the second mode of our quantum string is one so what we can do is we can have a mixture a superposition of our zero and one states as a qubit as a quantum bit so it's not just zero or one it can be a mixture of zero and one so what we have is this and this and we have some mixture we have some superposition of just those two states right so we could have ten percent of this and ninety percent of this or fifty percent etcetera or forty seven percent one fifty three percent of the other what i've done here is set up a very simple simulation which basically simulates a quantum string in that we've got our zero and our one states in terms of the the lowest mode and the next high next lowest mode just so just as i demonstrated with the monkey the first one and the second one they can be our zero and one in terms of a quantum bit and we can have a mixture of those so that's what we have we have 50 mixture of each of those and here's how it evolves in time this is telling us how our probability the brighter it is the higher the probability of finding the particle there this is a quantum particle and this tells us about the probability so the wave is telling us about the probability of finding a particle you can see it's just basically an intensity map of this all of that is is pure classical physics here's where it gets strange if we now make a measurement and we try to well let's see let's make a measurement of the energy of this this string this this state if we do that that's what happens and it collapses into that state so it stops making the noise and it also starts making a noise because is that oscillating sean no that's what we call a stationary state and we've dropped the system into that state that's weird that's really weird moreover that's if we make a measurement of energy if we make a measurement safe position all hell breaks loose so let me slow this down as well so this will make more sense to you so we'll reset it we'll run it and now if i measure position and slow it all the way down so you can see how it evolves just what's happening right so that's it so now we've measured we found our particle is here but that's just a ton of waves if we now let the system of i've i've stopped it in time now i'm going to let it just move forward in time and all those waves are spreading out which is what would happen on a string as well the the waves you know if you pluck it here obviously the waves travel that way they travel that way and they hit the ends of the the string they hit the walls they bounce back and all those different modes are now interfering with each other we speed it up we get all those different modes all interacting with each other now we've got a superposition of very many states but now again if we decide we're going to measure the energy bang it collapses into one state with a certain probability and we know the maths in terms of how to work out what the probability of it going into that state or a different state is the difficulty is we don't know why it does that when we make a measurement of position what we do is we we find that what we're doing is saying that well because we've now made a measurement of the position we know that the particle is in a certain region of space but that is just another wave that's just like when you pluck a string imagine plucking a string localized little point so that means that is the sum of that plus that plus that plus that plus etc etc etc so what we now have is this plethora of different modes vibrating and that's when you get this mess and then you know this is why if you think of it in terms of waves quantum mechanics is i wouldn't say it's simple but it makes a hell of a lot more sense than you if you think of it like this because if you ask yourself i've got a particle in a box which is what we're representing with this and you ask what its trajectory is look at that if i were to say how is it moving it's very very difficult because you've got all these different waves interfering quantum mechanics is fundamentally about waves hence wave mechanics and this superposition idea although it's really complicated to understand in terms of objects like that which are classical objects we're interested in if we think of it in terms of waves it makes a hell of a lot more sense if we just scroll forward in time we can see that as things start to happen we get to this point where everything starts to reroute and rather than going directly to facebook you can start to see all this w this is some actual cipher text that we'll be breaking later does it honestly start with zoos as in conrad's use the reality of random

Channel: Computerphile

Views: 174,869

Keywords: computers, computerphile, computer, science, computer science, physics, quantum, University of Nottingham, Professor Phil Moriarty, Quantum Computing, SuperPosition, Super Position, What is Quantum Superposition?, 4k, UHD

Id: kv-YXKRUheQ

Length: 15min 58sec (958 seconds)

Published: Tue Oct 26 2021