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Experimental Quantum Error Correction

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they were in a start up this morning with the actually I should I should have found that what of where you are you are a keynote speaker tutorial speaker your keynote speaker is it we have a speaker and it's from like you see in Waterloo notice title is that it doesn't say here but it'll tell us and at that time thank you John for that wonderful introduction wonderful and stimulating and now that you're facing the you can look at what is the title of my talk and maybe I should start the same way as then L started the title of mice caught in a similar way The title of my talk is high the same 1 is the 1 I had 4 years ago not in the title but the and the things that happen in experimental quantum error-correction and this is where I'm going to talk about for the next hour and Thacker will not talk very much about what happens before 2007 and I'll try to gonna fill in the gaps of some of the interesting things will be a bias of view and it will be some many of the things will be related to the work we've done and Waterloo but I will add some pieces which I picked up from other people around the world and when I was preparing my talk and then though that some of those people would be here like Reiner or about you read so I will skip on them but I'll kind of make some comments about my views of some of the work some of the time both both because of the things that the work which left to be done so if they look at the interesting things that happen implement for me in column error-correction in the last to 4 years I'm thinking about British benchmarking in certifying gates for understanding and noise that we have on our quantum system trying to figure it out in experimental away make a relation with fault quantum computing is 1 of these work led of progress has been done and I think about half of the time of my talk to mentioned these results and after that I'll talk about some of the implementation of quantum error-correction in different ways and the places where I thought the result of the and I will conclude and I should say the conclusion will be in case you get distracted between here and the and the conclusion is that as there has been a lot of very neat results we are starting really with and to have small palm processes where the ideas of quantum error correction can really be implemented and we've seen this in not only 1 technology but many of them but I would say the the other side of the which can be seen as a plus or minus is there's a lot of we did go before we get really fault devices so that can bring some questions for that the addition of are we really going the right way or for the expanded list many many things to do and the day-to-day and I prepare s slide to talk about the accuracy traveled Iran which is really underlying this presentation polymeric action but do stock was so great that lighting and then escape it but in fact had that and I was going to skip it until Robert Res send-off made a comment yesterday that you can find them up there he says I Q situational their improve what is left and then he says this 2 things left what is the value of the Trishul in what is the operational cost of doing this and then just move on I am so maybe this is the 3rd call point of view I wouldn't that 1 more is that are we really going in the right path with all the surrogates that was The and John Presco stock yesterday goes of an interaction of you should think about topological systems can we do need a more robust or are the ways that we can fine to make you called quantum processes more robust in order to reach these thresholds that Robert are going to give to us in this short time and the 2nd question I would add also is that can we implement this experimentally all these all these at this protocols and ways of doing less and I'll come back to the to this in a few minutes with and comments that I've heard yesterday that kind of should be taken again with some where we see a gap between theory and experiment was formerly part of this is really to understand what can we really do fault around quantum computing and get work and we go with the device that we have today when Adi assumption between this there and of course at the end is at the end so it must be right but there's a bunch of assumption in their bodies assumption realistic or not and then I'll come back to Andrew Starck and he put some of these mean insight in different orders and these ingredient all folder and polymeric rection at parallel operation so indeed they are devices that were around today which do not that our operations ocean will be read will them out and my view it is yes if you really want to have a large from computer but you want to have a small processor where some you want to use it as a sensor maybe there are things that you can use a farmer action without having parallel operation and improves it is devices for large scale quantum computing you need that operation we also need uncontrolled then I will talk quite a lot about this how much control we have other we improved and and trying to see how much improvement was seen in the last 5 or 10 years on give some exam concrete example in about much improvement we've seen so mention this ability to extract can and should be as something that needs to be done David Corey mentioned about that this yesterday and it might talked for years ago I mention about how going to make cooling so decided that wasn't going to mention it again today but we'll see a of this related to the ion trap quantum error-correction place where they are able to extract the entropy make measurements and kind of go many rounds of error correction in the last part is the knowledge about the noise how do we know what is another word of ice so my friends that is comes in and they say we have an devising model there is independent from punitive give it would go and make this construction with this and is that we are not and this is that when as motivated me to you and fag doing that I was wondering here's a specific device can we don't go in and check some of these assumptions and I'll come back to this in the next hour and the underlying assumption that comes in also and lots of Jubarte him my friend the computer scientists as you don't have to worry about this because it's only a bilinear mount so so I do not worry about this so I go back and look at this graph
here which it has number of TV it number of qubit as a function of time adapted from Michael man and bird genocide somewhere where that it's rules data and in 1 of the pair talk about this and we shared that overhead something like 3 is better than 10 to the and I look at this and I said that was that had the time that slide in front of me I said I wish this would be the log of a number of qubits as a function of time and this is about 10 or 11 13 here and this is 3 here so if you do the logic that would be in good shape in practice were not so people have claimed to have many belated up to about a bit more than a dozen of common but if you look at the pieces in red on the ones where we have a the device as prepared specific states and the other colors are 1 where the claim is that the candy universal probably Asians so very few number of quantum bits so as soon as you think about more than 2 0 4 5 then very little control and find the action and when we have seen in the last couple years on polymeric error-correction is more down here so there's devices and trap it's become a king cubits was gonna be labeled man a few qubits with the ability of showing the 1st demonstration that we can't we have enough control to indicate that 1 day who might be able to do minor fraction I think this is humble enough as a step and it opens the way in the future to do much better the 2nd part I want to mention which is related to what that link here is increasing and out of control so I remember maybe 10 15 years ago having people telling me that it might be impossible to control quantum system with accuracy more than a few persons the world it was even some basher comments that it was impossible to control quantum systems so we know today that is not true we can control them as well as we can but we have ideas of how to make these this control and how to improve it and we are right to values of error pair gates which starts to be reasonable from than minus to the minus 3 minus 4 and even more recently some the comments of 10 minus 5 and I will come back in the US so I want to and mention out we benchmark gates and this is work which make Kmail as put forward and the basic idea is to bid for a certain gates and to have an idea of how much control we have and use this value of what is the control is quantum gates and try to related to values of actors threshold we usually think of we usually think of quantum computers as System which prepares certain states let's the state 0 measure answer basis and then make a set of in certain universal gates and engine usually in your 1st intron computing with thing about any generate to Cuban gate for a given given gate antigenic 1 1 chicken to the date it turns out that for folder in Sweden and we've heard this from Andrew and all yesterday then it's quite hard to do this it takes a lot of overhead so they had been ideas of using CIMPA sets of gate for example only that kefir gates they cite the what why would Asian and an X-radiation around of I would too in a box here measuring in the car combinational basis in preparing the state 0 and using these gates because they have nice falter and so implementations unfortunately this is not universal but it can become universal B 2 with 1 addition 1 extra states generally call and a magic state heated by over at 8 states cost by worried 0 plus signed by over 8 1 or what is called the magic states 8 which is on the rocks equi distance of the axis X Y or Z so the focus on benchmarking gates will be mostly on this and then I will come back at the end and talk about how the magic state in the Bartlett distillation if we have imperfecta marching magic said so the idea
of mad he was can we get 1 number of our good we are at doing 1 cheated gates and his idea was but if we can in some way kind the noise into some the pricing noise there would be 1 number that comes in the parameter the did parsing noise and if we do this by making a sequence of 1 or a certain set of gates and now the largest the gate and the a larger number then we can I do this final line in there which gives the despair and this would be independent of the error the errors in the measurement the errors of others in the state preparation but the idea was to use Clifford Gates and we know that if we use gates when we combine them wind up with a K for gates that's easy to invert so would which would end up at the end should be the state that we've prepared independent in some way of the state preparation and then we can go can measure some slopes of this and gives us an idea of how well do we do so the idea again as I mentioned is to prepare many instantiation of let's say adding 7 gates in there make minions sensation of them so you'll see these old does the same thing for another random number it's 13 and come after 37 seventies and increasing this number does this line and you can show that the mall of the the noise when you have these random gates that comes in and looks like a depolarizing model that makes sense as long as the noise is independent from gate to gate and the gate is that the noise is not time dependent so if you do this this find this number and here's a list of different prior qubit errors of the then publish from different groups and you can get the value of them which is between 10 minus 3 can minus 5 there from their progress if I go back for 5 years ago would get important it's a 10 years ago we get 10 minus 1 to 10 minus 2 so the progress of 1 to 2 orders of magnitude in there and you will see improvement in this as people can have tried to challenge the devices that the I have to get better better so error rates but the few comments in there I look at the single ion trap a result which was published very recently 10 minus 5 should this should be compared to a result that the ad to 4 years ago where and again about and the minus 3 and interested it for me and there was to see what they have done to make it 2 orders of magnitude in the space of 2 at the years and it is really care system of designs can careful pulse generation that they had so they have a series of places where they could make small increments here and there were so many kind of the error rate kind of can go down by by some original about the 3rd 1 thing I found interesting is that this experiments here was done on an ion trap wordy use within the group of wine and the use of my career radiation to make the 1 cubic gate and the build a small and then the next to the ion trap so that they can read what is the feel that comes out of there might wave and be sure that it is the end until at the act and this is something that we had done also in some some years ago and as we gates by a kind of pulsing with certain shapes to kind of mitigate the effects of some imaging the sum of fund the amplifiers are impor- effect that we don't make square shapes that want to do some make the simulation the varied a shape so that it does in the big that we want but when we send it to amplifier then there are distortions and he's distortion will lead to errors by with the soul and it has that we put in there we can be but if still looks like we can make it a feedback loop correct it and then we get the pulses that we want so this gives an idea of the the error rate for 1 qubit gates which are are going to words but people believed the Trishul would be a fool to have a scalable device for this is a great improvement show kind of really Yeah progress and the ways to scalable quantum computation but this should be careful when I mention this is not too far from the Trishul because these are a phony 1 qubit system and with people or have been doing and you can see this and I in the and dropped it was a trap for single ion and the had in their gates if they have a single ions in there they might be which are in use in the 2nd gates which were not taken directly in the we took 1 molecule which was the best molecule we could think of and then we can have optimize everything for that part to achieve it so if we try to think about this for larger systems then we have to start to think about who it's going up and the impact and the high up to here so late the idea of generalizing many ideas too many tube it's kind of hit some problems because we did know all this noise will come of go down to to for the prize
model and having a single parameters to crime characters noise and here's something that that we've taken that look at Waterloo on yes our so we've Belarus recently it's hard to be able to do some quantum computation and we implemented this benchmark to look at our group this that would be I was working together is an example of using the best to get that we have it's the nitrogen the act on an urgent and inside a inside the Covent 60-ball so this very well isolated from the rest we have a sample of those and then we can go in there you played a system going kept this benchmarking so you can see the number of gates we do out about 280 many sensation about 20 to 30 instantiation of each of these again draft this line and and what we get we can fit that this line get the permitted B which is related to the Europe have gates in the year periods in that case is about 10 to the minus 4 so show that we can have control there but if we go to to to bits and try to do the same things they would have a very different effect movies engage not only of how with that cube it is but how was the apparent is that we have around to control the cube it so part of both of them I should mention that the value of their per gate is not the value of what we would get if the air we come only from T 2 and this was the same as what we had in the inner mark so which tells us that there's something in the apparatus which control this cube bits that we don't fully understand or maybe the Hamiltonian that we have not exactly the right amount on it but putting this all together it tells you that we still have a reasonable amount of control in the system and that least bunch of it things that we have to be very careful at if the error rate starts to be begin my street the minus 4 then just the calibration of what we mean by a by which a gate starts to be very important so we have to have better and better idea about we calibrate the initial state or the gaze that we want to do so very yeah a bunch of things that we learn by doing that here is
a marking of gates and this is not done where this random randomization of the different gates except for an attendant in liquid state NMR but this is something of Look at the the literature where people have either implemented some algorithms or claim that the certain appeared date back to Cuba gift they had it's a debated 2009 2008 but it gives you an idea of where it is and how different it is from the 1 qubit gates of the error rate to begin gate is about 1 person for most of the device that we have compared to the 10 minus 3 the mice for that we have in the brisket my bet is that people can do a little bit better in this point 5 % but as soon as you arrive to to you gates again see things become harder system how quality to go from 1 to 2 is hard wanted tree and work is being done in Joseph Emerson that war was been working on make a benchmark for more than 2 cubits the so this has been an important common naming it the to generalize to the nineties procedure to you to go to teach you that so the next thing that I
want to do is how the we when we think about benchmarking to tube at all 1 2 or 3 GB dates or Clifford dates in general would get 1 number what is the pair gate maybe you should think about benchmarking or certain fight certain types of gates and which is the 1 that you are gonna use now upon completion and I would we do it's so suppose that we have a gate which correspond to serve a certain suffered the coating on the fiber codes other we know of good we are doing this or if we have attended told or a 20 bit other we are we sure that it is really doing what we expected to do so 1 way of doing this comes into a place the tool to some work of done with the Jožef Amerson some years ago and characterize noise and systems and will see how we can add this to certify certain that aid in Parker and the Clifford once in order to think about this I have to kind of go back and think about how do we characterize noise we know what to do this exactly which is by using tomography so we can evolve the head and the matrix and we can describe this solution to cross operators in the basic ideas of go and find these cross operators 1 way of doing this which is cited friend is using what is called the Ky matrix it makes sense and when we think about error-correction as we can become matrix essentially expansion of these days in terms of tensor product of bullet poly operators which I called pieces appear if we want to do their time matrix of exactly and find that we can do this by Cliffy he can we can we quickly realize that it is very hard to do it for more than a few qubits in fact for single cubits we need a dozen of Parramatta's for N cubits we need Fortinet to an end for the door and goes very fast especially when you're in the lab and here's an experiment the result all of there's something missing here so I had that as an example of the 3 qubit system where the process tomography had done exactly by David Corey around 2004 2005 so you had this matrix of a few thousand element in there it looks like a skyscraper of New York City of all these old block in there and it says you when you look at this you can see there's the theory looks pretty much like the experiment but it's very hard to make any quantified quiet quantitative comments on so how could we get something
quanta dibbers which would help us to characterize noise and and if you want to do error-correction when an interested to know about all the correlation between the noise but we interested in only a few parameters what kind of damages would we be interested in but I would be interested in knowing which student is good of as errors on it we win the debt interested to know exactly what is the details of the air so that would be able to give you what is the probability of 0 where what is the probability of 1 and 10 of which cube is independent of it is X Y or Z here what is the probability of 2 where's of course if we then the processor will review we can find that we just kind of course going all these numbers and then you can get this but the question is can we do this efficiently without having to go to a process tomography it is of the answer is yes and the basic idea is instead of coarse graining the data that you observe maybe you can cost window the the noise that you're doing so working on the noise many parade so that what comes out but pops out of the experiments it hard these numbers so if Europe for unique thing about cause winning is really to apply symmetry the question is where is this symmetry which corresponds to a bunch of Q. that's where you want to know these numbers so the first one it is just fermentation of your attributes so you just as you do your protocol define these numbers here that permit you qubits all the time so that doesn't depends on which key exactly the errors occurred the 2nd 1 to find and or it's public give that's a 0 where the idea is to average over the as you do group or each of the tube it so if you do this then you can find these numbers that comes 1 by 1 X and they're doing into gold in the lab but like she gets isn't that hard fortunately people realize that doing this and you all all over the city to point to the cube it is equivalent to a sum her had Atefeh group and discovered this thing for my friends a computer scientist circle to designs and this makes it more at amenable to apply it in the lab with the idea that playing a discrete set of gates that we can implement in our system in fact and part of the if you look at this and you think about it every group as being implemented by the simpler the group and the pollen group then the idea is just to apply these gates in these gates and make a sum over all of them if you look at this poly group and you make the sum here you're all the poly grew its impact will be to kill the off-diagonal terms of the sky matrix and if you implement the symplectic group the effect of that is that he will randomize the error X Y and Z so that you cannot distinguish between each of them so the number of X errors will be the same as wire because this group is gonna just kind of shipping with each other so by implementing their petition group into what happens is that this guy matrix become vinyl and is only and plus one had numbers that are left with this which correspond to the probability of where 1 yeah to where's 2 years so the particle
goes as follows start with a given state and then we'll call that 0 there was a little it's really good to start with this 1 because it's already symmetrized applying this symmetry group thank you don't really have to do this because it's always fun then applied at every groups and the the 1st ever groups then the noise commonly system applied the dagger of the from pure but then simmer tries and an observed in which you see him when you go to the details of the protocol as the poly matrix that will come in the X and the wise well flip some of these bits and then you'll get a sequence of zeros and ones can measure the numbers of 1 and by repeating at the experiment many times you can extract a probability of 0 errors when nothing happens here problem the of 1 errors when there is only 1 1 which happens here probably have to errors windows to thank is slightly different than what I'm just saying because if have errands here they don't observe it so then there's a the transition between the probability of the numbers of one's that comes here and the poverty of X Wiesel's EasyCASE that comes in but the upshot of all of this is that you can go and measure the probably of 0 1 to 2 years coming out and in a if you implement a full symmetrical and if group itself become mechanics financial but fortunately again my friend the computer scientist say you don't need to do all of them he just can't sampled so make samples the carefree groups implement these and then you can go ahead and many of these problems can you can do this number of gates which doesn't go up exponentially and then you can estimate these values of errors readily efficient so this is a work what was done roughly at the time of the last you see conference and what I want to mention right now is to out and add this to so certified tougher gates so instead of would were certifying is 1 part clever gate is the unit operation can we do this what other gates and the answer is yes we can do this so this is the prodigal lot just mentioned to you spend that hard to realize that if you want to certify then you can add new a new dagger and here's if you is that if a date we know that I we can implemented efficiently in a quantum computer and we also know that the impact of this clever gate under the Keffer Gate Altona 3rd Jaffa gate they were measuring and then the computational basis and we know from the nail I got us meant there is that it evolving with tougher gate is just a change of basis which really gonna change the zeros and ones that other there will be related and it is packed classically efficient too compute the relationship between well with measured before and the impact of 1 single in here so if we can of I realize that this is only the measurement in a slightly different compilation basis that can be to efficiently and we can think about measuring in that way and what is left is the game that we implement physically the noise that comes in and then the 2 that we started with and with this we can certify gates intended efficient wait and see I would we at doing this so here's an example of this for small quantum processor it's solid state system with 3 quantum bits that 3 carbons which are in the middle here and and wanted to certify a good we are at doing 1 and in fact tricky to be gates and here lift to attribute this to treat you begin to have done then nothing operation and then the implementation of the con- America decoding at operation that we 1st did the benchmarking for the 1 midgate and values which are of the order of 10 to the minus 3 and then we have to do this is that it when we do nothing we get about 98 per cent so that parted to forget of doing nothing but turned out to be hard and them are doing nothing because the Hamilton is always there we get there is about 2 per cent errors about 2 per cent of what we do this we also then something related to what we call pulse fixing I mentioned to you that we send all and then was down the this down the bore of the magnet in gonna be sure also that we do is exactly what or very similar to what we had thought here is an example of a balls and you see small this in the green is the ideal the red is what's come out of a the amplifier and can see small difference in there and that small difference was enough to change the person by 10 per cent so in there we were able to kind of gage division process and see how good we are at Keating this systems so and that gives you ideas
of we characterize noise for both 1 qubit and gates what I want to do for the next scan of about half an hour is to go to some of the error correcting part procedures that they've been implemented and see how are we in that direction so we have an idea about to correct raise noise where the idea of good we are doing this now let's try to implement the did is explicitly their correction so many of you might have seen this this is not the new result is something that we've done when I was was many years ago with David Corey Mikhail and others and was in with 1 molecule Tricolori Thailand where we implemented the error correction procedure so we encode we prepare appear state we encode we need some noise the noises of 2 types either we implement noise by hand and do bit sign flips or we leave the national noise getting into systems which will lead to T 2 and then we do the error correction we do the decoding and error-correction if we just do the decoding we get a soap which was like this we do the error-correction we get something which is slightly better and the demonstration that we had enough control for the process of our correction comes in looking at the scares and then we can see it starts at time equals 0 we don't get field there 1 because implementing these gates don't come for free are errors and perfection that comes in so 20 per cent of the felt they just by implementing the encoding decoding error correction and then but the demonstration on a claim that we had of their error correction demonstration here was in the 1st follow the 1 there was decreased by a factor of about 10 having sort them out of control again that perfected as our used pairs are not perfect so here
is the same thing that was done a year ago the same molecule and pretty much the same couplings and the ones and the twos and say different spectrometer so I can go back to the sum of doing this and we did this with the 700 spectrometry instead of 500 Marlow and put all this together we can see that the field is much higher in there so there was result the new 1 for that of scatter cell but if you turn this into equations would you can see the
1998 result is there and then the 2011 result is here so you you see that and then had 0 time the encoding decoding error-correction procedure was much more precise so 20 per cent higher filled the west you get the error rate 1 minus the felt they about 1 per cent instead of about 20 per cent so about an order-of-magnitude increase in that set of gates the 2nd thing is the 1st turned here it is about 10 times smaller than a war 5 small it would be at the previous years so Here's an example of control that we have in our system now this this mean that we are doing full quantum error-correction yet we just it just means we have the control of doing it in we have to prepare this through pure state the take signal way and this is 1 thing that we have to get over with the food but really wanted this must-read full quantum error-correction I'd ask what is the difference of control what is the difference scheme that we have but we use with is called these grape also instead of doing very sharp kind of 90 degree balls we say here's the unit their transformation that we want to the desired that we want and we go and calculate 1 by by modulating the frequency field so that we get as near as possible of this 1 also only we can have continous false instead of these blocks that we had before and when I mentioned before being using the feedback will inside the the spectrometer division of the pulsar we do are really the 1 that was his art so demonstration of progress in there
and here's another demonstration of polymeric action a superconducting qubits in that you read is here and I think that give a talk straight up me so and I mentioned very much in there so again demonstration here of error correction that this curve is flatter than what we have to when you don't correct for errors you can compare different fell they hope is a plus minus and missing there so the filled the and 0 time is about what in was 10 years ago that 2 was surprising much harder in superconducting qubits but if you look at the slope of the progress they might well take over other technologies in that too long especially in the number of quantum bits to be manipulated if you mapped here for some reason I don't fully understand the the mad this with a first-order terms so if the do they have 0 comma decimal 0 3 which is the left over 1 qubit errors which would be had that compared to this if you don't do error-correction and then again an improvement effect about 20 solar demonstration that read they are getting to control drawback of this experiment that benefit different from they are not able to be said that you can do many rounds of error-correction yet so what he did is implemented the gate and then we after 1 round if they want to do it again the news you need to more cubits prepared and is there a state and going into its so that they want to do many rather erection the measurement needs to be improved here's another experiment begin with demonic acid here is doing to rounds of error-correction so we do 1 on america action within around and look at what is the result as I mentioned we cannot be said the bits here so the way that we did this is doing very similar to what the optics people do so post selection of the results for selected in 1 the state of the qubits part of the insula are over there but all of this together which is what we get no error correction of the curve in blue the Quran red is if you do 1 shot her attraction and if we do 2 shots America we have a fixed amount of time and then we try to factor 2 shots of error correction or 1 child and and if we do 1 to their higher filtered to start with but solely to to to bit errors are starting to catch up and then solid father they go down if we do to show their affection and probably the initial problems is lower we can of the faster and c longer with a decent probably so again this is another demonstration of to run ever attraction a full to round ever correction because we have that we said a Q That's that is the mensuration where the control of being able to do this and I've sides related to and right you Blatt's experiment on trap is going to talk about it at the end of the week so I'm going to be very very fast on their that is to do many rounds of error correction and the and the varied devices where somebody can be said the students and they decayed it's kind of come back to the old and then some process again you look at the probability of getting
back to the right state and they're kind of going down and 90 per cent 80 per cent 70 per cent so it tells you told of doing this error correction but that also if you don't do their direction then you would have errors which would be your along to each other and choose a curve the the errors are correlated the bigger the green curve uncorrelated there's is in the red and so again be the demonstration that's only we can do error correction and then we can do in some devices repeat Hairer Kochan many times and I read this paper it was not clear to me if the noise in here was the natural noise in the trap or into if it was errors which were use in there so we can see that quite often in some the maturation of error-correction people do this for noise that the engineers is a good demonstration of control but is not exactly where we want to go on the final set so it is a step toward a correction and writer can correct me either now or in the so in that on Thursday when he gives a stock at exactly this a
few more experiments with topics this time of area codes here there erasure code which correct for 1 lost of 1 to get somewhere and demonstration by the group of fine china and show that they can implement these particles from this quite interesting that by using only some pieces about down conversion and are able to reach the skilled and be able to do error-correction self as you know which which photons very hard to do to attribute code it too could be their gates but they are able to find some ways in the will to to do this the go with these initial state and show that they are able to kind of get back with decent so the about 75 per cent I get back to the initial state drawback of this is that when the AirAsia comes in is an erasure by hand so they say OK we're going that going but the from of 1 of these detectors you put your hand and you go and look at the is also a demonstration again that yeah the control but is is not 1 that you could use that you can say you can go further it's a on the optic fiber to going to reach a longer distance at least not yet we don't have the possibility of doing this similar experiments done chin
Denmark grow faster now that using the full had the the standard of freedom or the proposition of the photons but is variable and in the same thing here they do this and they kind of put a the block 1 of the beam there initially can recovered information there gage of how good it is is they do this if no entanglement in their initial state and get a red bar and in the blue bars when they haven't Tangermann 50 per cent of the attending claim that this is sufficient and and slowly getting to the end of my presentation and want to show 1 more example of and neutron of error correction in this case will be of the the quantity subspace where it does make a difference and where doing error-correction here is very you you useful so in that case it's not the full quantum computer is just a small device neutron inter from matter and where so many by thing about it from the Kuala formation point of view you gain by doing a certain process the the basic idea is you can use neutrons to an from image certain device you don't comes in here and then you can think about it until the direction from here the new drawing instead into kid this displayed here which looks like an at the center makes the being here and then depending on the length of the path here than the neutrons that there in the top on the bottom line is in there we can use this to interfere in to imagine certain objects in a biological system fuel cells or devices where we put 1 of the that on 1 part of being and then you can kind of use this as a typical interferometry the problem with the you interferometry and if you look at these devices is a few centimeters long so about the size of the length of this laser pointer of that wider it's made of what 1 block of silicones which has been patched and the reason which has been hatchery precisely is the wavelength of these neutrons is about 1 Angstrom so the great thing about this is that you can image things on the size of actual neutrons can go to matter and kind of way of aspect it can learn about the magnetic properties or a kind of Hadamard properties of stems you could look at cracks on the size of an ancient but you know that if you're innocent back strong and 11 from which is a size of this very tiny small vibration identical pretty persistent so if this center from Inter by more than 1 angstrom then in the Inter ference pattern here was going be distorted so the way that people do this at NIST there and to and from really that they take this small devices and they put it on an optical bench and then the optical bench is supported with the usual kind of isolation which is now on a block to about 40 tons of concrete which is also supported with a kind of different pension to reduce of I gracious possible the room is isolated with 1st it I cost insulation and thermal insulation with this if you look at the small devices which is about that big it's in the room which is probably it 1 6 of the room in here and then nothing can move in there nothing can enter and then you can go in image your in your device that you want to go and look at so what does this have to be with the occurrence for subsidies if you think of this as an intro from you can thing about the state going through there as spoke position of 0 nothing come in here and 1 and then as soon as you go to the 1st beam splitter you get this progression of 0 1 1 0 and then you go through this it interfere and energy in a visible position of offers open the 1 which comes out of there and if you look at the dominant who noise it turns out that the dominant noise in his rotation of the devices that way which corresponds and this encoded cubit as easy to that he does so if I write the broad project in the Indian the problem in that way how you would go into could make the
system more robust so you just below the chords free subspace which would be its pollution of many of the states so if you look at the 1st mean I mentioned with this with 1 0 0 1 and 1 0 1 in 1 0 and then you go there was sort 1 1 of the state 0 in state 1 if you go in and more if you good had more blade and you can the thing about this is then going in there make in supervision is the year when 1 of the encoded 1 here when you get the 2nd laid then you have 2 possible that you go to the go to the top or the bottom here going to talk on the bottom of the state of the top can be thought as the state 1 1 the state is the state 0 1 the state 1 0 in the state of the bottom Z was 0 you look at this rotation is elastic the state 1 1 Bostick 1 0 0 but this year 1 and 1 0 ll get compensated the same way get come and see in the same way because this 1 goes down as 1 goes up which was different than the past in there so if you're a rotation of the c-axis in there then some lady piece to a distance gets common city which each other when it relates and you can go to another blade make and fair and going to so you can go and do this it had the same using the center for a record with more raids which most of the new to a natural matter would think if you add more raids things will be more fragile but if you restrict assumes this stick that pack then you can becomes more robust and this is really kind of the path that you can see here if you think the pattern in red instead of the 1 which the brewer there then you become makes the whole interferometry more robust you take this central from measure that we've made 1 and you look at what is the Impact when there's no know Barbara the assessment and then the you can add the vibration and thereby making this table shake in this direction and then you get something where you lose most of the contrasts you did the same thing with the 5 beta from matter and then you can look at what happens when you do not have rotation and when you habitations and you can see that you can recover was the contrast in both places so here's an example of error correction or Dfs where solid makes a big difference how did differences is that
these can certainly take the interferometry that you put in that table and you can put it outside the speaking so so maybe we can make this happen because the signal-to-noise ratio and
here is increased by about 600 person so created improvement in the place where you can really make a difference with
quantum error correction and they're running out of time and the last thing on the dimension magic say distillation so we've heard yesterday that if we have a Clifford gives we can go into to conquer mutation in falter and wave using transposal gate but in order of becoming universal we need to add magic state problem with magic state is what happens if they are not perfect but you make them better so that was the work of the Kenneth and Brad the that some years ago showing that if you don't start with a perfect magic state 1 with people to 1 in here how can you find a way to distill them and it turns out we can distill them through the 5 the decoding of the 5 Cuba their curtain so the basic idea is 5 copies of imperfect magic states making in making them go through the decoding of the 5 decode go and measure the state and 0 for the last 4 events and then you'll get role and prime at the end and when they showed is that if the prime is greater than 0 point 6 6 5 heart's leave a greater than this and you get the P prime prime when the n which is greater than this so by doing this relation you go up here on the line and then we can start again sorry again you do this then you go make yourself I'm up that way for the 1st time I read that this is how Gore the mice at all this is very need for this is the line which is between the center of the box here to the point which is equidistant of X Y Z on the blocks here so if you're for far and near enough the magic state then you can make many copies of the static state and make make it converged to automatic states is this robust with is if you're that outside this line so you're not exactly I from that line with you able to convert to that place and it turned out that the answer is yes as can view near enough this part so even if you're not exact on that line all but on the side you can see that it is converging to this point so once you have this you
can say OK you can go into some experiments and here's a result of this experiment this is not in the solid state that have mentioned the past or the US arts and back and the solids in the liquid state the place where we have more than 3 or 4 qubits we needed 5 ha here so the colony acid that reviews fast and then you can see the input state that we started with the output state that we got and you can see some desolation here go to 96 and 95 94 so the 88 and so you can see the points here the red line corresponds to the assimilation of of the distillation process when we would to to and the the blue line is with keys to start just to give us an idea of what is the effect on the course ring drink the process so here's a link if not that line here we have successfully distill when were at the low then we make the state's worse than what we started with so we were able to show and demonstrates know that this magic state distillation here conducted OK have run out of time so in conclusion so I hope I've convinced you that there's been progress of on experimental quantum error-correction the last few years in part to having a better knowledge of the noise methods of finding out what is the noise in our quantum systems have my friends that there is who says if you get the church old then you're home free but what is this value of their brigade what how the way get this number once in the lab and a bunch of gates which are impor- affects how the way reach this number in the set at them both understanding how to get there and it has been part of my comments today I I would definitely improve the amount of control in many devices super conic its prime Trapper yes in the last 5 years pub in order of magnitude more control than what we had before is still some room to go so for some a single qubit gates I believe when this and pretty much how to do this and for many stupid gates then we need to employ again but it's the fact for compelling action and build the jet extract pro and should be in the experiments of writing about different at a way of doing this and that mention about calling something that I mentioned 4 years ago it's a place where and maybe superconducting qubits to go into and and lead to do this so we definitely have at some progress but it's only the beginning of Experimental Quantum Error Correction and its falter and implementation thank you the the Hi thanks Ramon for this beautiful talked exciting to see all the progress that's been made in the last 4 years we have time for some questions so you mentioned that there their open gate is higher than can be explained only by defacing by 61 processes the coherence that means that you perform in the control passes the try how to prevent and so my question is people that discussed the environmental the noise of the of their environment without control use for example correlation time to see what is the for statistical description of the noise can you do did you do this you know analysis to the noise in the control for example if I give 2 passes close to each other they're probably correlated elastin if the time is out it's Uncle if they can come out from your analysis yet so when you 1st look at the the doing these curves to find what is their per gate to get to the depolarizing model we have to assume that the errors in it than as independent from gate to gate and time-independent if you add time-dependence you'll see that it will not be a straight exponential curve but you'll see it kind of going away a little bit from this and we've seen this since some example in would gradient effects of gradients or we can also see it when we make more and more gates the amplifiers heat up and then some they can of it so that kind of out of whack and so he can see these things so you can make it in the air the time dependence is small he can do perturbation theory and look at what is the effect of this is going to look at exactly what you're thinking there's a very nice paper by Joseph Emerson have a model you know kind of this and all the jails how to make this happen questions yeah I have a question about the plea for all groups anybody cannot how efficiently these 2 samples over that you mentioned that but in passing I understand that for a single pubicly forward and then use the channel bound its own OK I thought maybe b seeing if you have many fewer bits in principle asked estimating efficient so in that case only know how to do it efficiently so it's really a computer scientists comment and rigidly would be the best person to answer this and in the protocols that we have here we just have to be doing the 1 qubit gates when we get this that's yes and it has brought about that so can if if you want to sample the 2 and 3 I don't know what is the answer that but I know who has the answer for that and then Richard as the person anyone else I have a question had you remind ever personally bent world and so I the I expected a festering that so we that by golly a maybe that by about your suggestion I would say that the massive and very disoriented OK what may be the next speaker should for the again thank you
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Metadaten

Formale Metadaten

Titel Experimental Quantum Error Correction
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Laflamme, Raymond
Lizenz CC-Namensnennung - keine kommerzielle Nutzung - keine Bearbeitung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nicht-kommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/35303
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract The Achilles' heel of quantum information processors is the fragility of quantum states and processes. Without a method to control imperfection and imprecision of quantum devices, the probability that a quantum computation succeed will decrease exponentially in the number of gates it requires. In the last fifteen years, building on the discovery of quantum error correction, accuracy threshold theorems were proved showing that error can be controlled using a reasonable amount of resources as long as the error rate is smaller than a certain threshold. We thus have a scalable theory describing how to control quantum systems. The next step is to turn this theory into practice. I will give an overview of some of the progress towards the implmentation of quantum error correction around the world with a focus on results since the last Quantum Error Correction conference at USC. I will compare the various achievements and point towards what still need to be done to get robust quantum information processors.

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