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Dynamical decoupling of encoded information
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but is it is good very OK and so on so I Gamonal paideia so we're ossify look at our next speaker is Hoare the puzzle that we talking about DDE and quantum error correction science so I tis with revenues in order on the issue of combining but were correction and the dynamic of coupling that would be some work we have been from work now with Daniel and here you see so let me give you some motivation 1st of all since it is acting for image and if you if you like the the and this what we call a 60 where access them for whatever you want but anyway so the meson information here you
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have your quantum appear which is true was Hamiltonian which that will age of as were I guess the form teacher went on in the
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descriptor that good so we have our our computer
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through will assemble day and then of course we have the
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vast and the about is really going to go with this furnace just trying to hear your your computer and the price of course that there this system of coupling which is trying to essentially cuticle condition fortunately we have seen that you can actually isolated computer using quantum corrections that makes sense for tolerance and that there is of course very good but the problem is that if you're that he'd amount of heat that is coming in on the size of usages too large then suddenly faulttolerance is not too effective in that it fails or you can you can also think about is that maybe you are given the correction default tolerance still works but then you you require a lot of resources to do so the court that about I because and other things well they actually had another filter to the city you could turn on the lower level of protection in this case in the form of dynamical adopting a back reduce the effective heat that the quantum errorcorrection sees in such a way that you can ask to either achieve the photons that you could not be caught or actually reduce the number of the amount of resources you actually need so let us start like
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what the point which 1 is nice we're thinking of we have opened computer balloting encoded in some KD called where n is the number of your physical give it some of them reflected cubic meter experiment Kay says december of political committees and these subsidies and from the capacity of common year of what is written on your it's you can recover from so initially hardware to conceal a case we have a Hamiltonian Ouch has a pop art is like you but in reality you can actually relax a bit is something that is not only about quality thus have to act vintage a system of linear with some this operator but for now let's consider this a entity and they have a system of Hamiltonian which can have terms that only in the system or also in the system and about but the point is that they are harmful terms that you really don't like right so in reality so this goes through some unitary over some call it up to and it will make sense of the words where these but this this is just of collisional it very evolution you'd actually quantify 98 and some effective iterates of is studies pressure which is just the norm of your system of Hamiltonian find that the time that it takes to execute it so I want to do way you win do dynamic of the coupling is set to the world I want to take a unified to Dagomba onto I knew unitary which in which is has 2 distinct terms the first one is the state's not our age and if you want what's going on we ask but anyway so this data and this it idea is that these guys harmless to use system so if you think about it in terms of a correction it could be that the stage not include statistical LaserPrinter they fit to stabilize the greater repertory would like because of your information is all of these not harm at such operators and you can actually not measure about effective array thinking in this scenario of some when you have achieved some that is America the coupling of order n and then this of course is just the norm of this and other term that you you have so the hope of course is that at some point you can show that the actual I effective rate we use only the open despite the gate accord operation taken longer than essentially smaller than that bear error rates so this is the wood and this is what you want to know who would like to show so that in some work done in this the user action and this was what meant was that a modest warning so in this paper up let's call it a and B that performed visiting they shouldn't go actually show them the enhanced political gates and the main prison that the media is that well you can think of applying simultaneously dynamically governing gates on each of the key words of the computer and while this is of course everywhere there that should of course for this to work well in some visible you cannot be in the scenario and regardless of how local using simulators B to be you can achieve arbitrary or the coupling and the marriage and is that if you look at the mine's expansion that you'll see that eventually you due which will give you will give rise to terms which actually commute before your operators and then you're kind of thing about about so to work on this problem and a part of the but to overcome the problem they introduced with it's called a local about assumptions and essentially these guarantees that higherorder and never gave rise to turn to actually have a strong and effective and that in terms that you can do with with higher levels of DG Competition so it actually part well that would be in the days use therefore for the stock of something is not maybe as generally most from ProHance supporter and so you can think of they where you can actually don't think well as is there any other solution to this problem can we actually Gowad no local assumption that our public assumptions you can probably count for the there is actually a solution secular stricter resolution can take you can take in in the language of dynamic of the company you can take that and she reads this is and or either degenerate of the full group if you're doing Didius prefer and the idea of course we will because you can achieve arbitrary however there may be in a couple of carrots that maybe there eventually maybe I put the vote that is well they they'd growth are useful initially as as a function of 2 and which words and you will recall and is a number of physical care and the really that the poles look the forces themselves although at the end you can you might say well because I'm doing the whole group at the end there flying effectively nor operation and the other day give it the report itself this may look as an era to the calls so you made limit in principle that some integration with other quantum approach based on approaches so what we actually want
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is will say we want to choose the right group right you have to choose the correct chemical and the write them a the bit sequences such a way that we need no extra locality assumptions that the pulses rely on lie in the code that that do not like errors and that had the idea you would like to add some shorter sequences so therefore you did nothing approach of course all these always only makes sense if we can achieve compactly show that our it's is better right so that's that's 2 blind and well them
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into a vision of course is that that the magic of everything is just a couple of right so if you leave your you look at the problem you say well if my group is too small then maybe that I can achieve arbitrarily coupling as was the case in B or it may not actually be able to because of science which though and if you do the group was too large then as happened the this is then maybe it's an hour kill you can give more terms that the 1 you need and more important well the shorter sequences that better discover a duration so the main tool that we haven't use here is this tool that was introduced in Reference where previous throttling in that was introducing their missed that read time ago the couplings item and that he is that you have done which will orthogonal said in this case all of those other condition that is the generators said it is that this is a bunch of operators on a guy that this great identity and that the commute or commute on to commit to each other so despite the middle and that this is important because you can formulate both and D in both of these terms you got to see that you conformidade a concatenated dynamical the governing using as the base group the group generated likely by these that is generated by these most and you'd like to the user who just plain nested and the same have the same so to what is that we are thinking of before we learn in reading the literature people have thought about using that a yes is study lattice of your group of your code as as I felt as though the coupling group and the result is a good idea but again using that you even think about it when use your mind suspension terms would make give you color and this little error commutes with your start so there isn't good because eventually even if you try to go into and that we the coupling to an audit of the coupling that with TB there so that is kind of a problem however if you actually add that to the smallest set of poly racist elements I think this is like a subscript superscript fidelity version of the user is then encoded in exon encoded scene and then you can actually show that these mosses breed is pretty useful there that is superimposed and that he has the following that you can still get this you if you right you dynamically w issues it well this not what is the word I'm would actually care about this what is my age not after the end of my them for the company which you can see that now the dynamic of the company which and thus proportional to the story like of my group and so this applies of course that seems biased might might write the code is chosen such at the start of stuff lasted then this is exactly harmless to the to the to my information when properly I think is that and if you recall that we were doing the sizes we assume nothing on so in principle it should be itself could contain analytic sort of political a retired hamiltonian and the 2nd ages be term will with should be pushed to the use of to that observed a couple part of your arm of revolution right so this is a highly beneficial actually and so will have a game with all these well in principle we have well what we have and that of course is there is no need for an extra credit assumption because essentially Europe for them or based on the coupling loop itself is powerful enough that you can always couple at every level of concatenation like all the other terms that we wanted a couple so there's no gender is both unthinkable and harmful by the next level of conditions so we can assume you can keep going I mean to higher the coupling as much as you want and well for that in the case that the the 2nd this proved your real were working out with 1 then right and then you can show that this the same decomposition induced by that this was a structure actually worry helpful in you can show that if you have the strawberry can and go into that job a carrier that cotton with these with these others can so now you see that the pulses we have chosen the UN our out beyond actually to the to the group right and you can actually also use them to be twice so that in principle known experimentally friendly but the transverse the code so for instance if you to think about assess cold then your X logical operator the legal operator is now be twice and phosphorous line principle respects your model so on the fact that of course the Michael system look there was prone principle allows for other protections interaction with other protections so what have we gained well let's stick out that's the together at the cost of in terms of free time evolution or if you want an end abusive particpants in fact that you can you can check out the if that's the length of the size supremos is not you can rewrite the Union should be the number of a the elastic plus 2 times the number of political operators but because of a star lies the properties you can you can actually re write in this way the case where there's no subsist energies equal to 0 and then you see there is is more advantage here that you have in mind is key but this is immediate and blast however that may be the model and of course this is here in this here I am showing that the cost of 4 with the coupling and give its so you see that there is actually a gain and that the more interesting case is perhaps we have system code and we have a subsisting code and you can do Frances this is just the the the sample of the makers sure called agency that actually the size of your of the fully the coupling moves the century of course to n squared because you have and and that's analyze but if you do that as they get to the version because you essentially care about the number of history lessons which is given expression and the water number of political directors because you only have 1 little Q within that 2 so then you actually being an order my will a power here in this you know the size of the
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moons and these of course perhaps more relevant and you think that is actually the exponent of some quantity regardless of what the hy ordered even use so I guess is what is better than the so so we're still missing to show out
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if we acted in something so we have to the it so that that's maybe there a traditional 1 to make is that at this point we are at work we have compared the distances in terms of the distance if you think about it is just that innocent between a and Qb states if you prefer however in reality were not truly interested in the distance between the encoder physical estates Stankiewicz eagerly state by the distance between the logical information to store the so in principle in operation so this is just not that they should not become fine but of course we're trying to work in just introducing the the compass idea the couplers alright the other approaches to mentally actually get the correct science but so this sort of a work in progress at the moment but nevertheless this so the promise of further thinking of these limitation of percolation thinking that I would say that their operations like the other approach the distance between the the information will be smaller than the 1 I'm going to show here but but this is too good a proof of principle aggression so the way of doing this is well we go to that appear results which was which which I think actually it's the this so we use a good lunch and the the the the the can compute the norm of the system of the system of that vector just about any of effective I'm not Hamiltonian at every level of any of the the concatenation so you can deduce rank and then use it you can get an a norm of this of this this is the 2nd system but at any level of concatenation and of course multiply this and the corresponding at time of total amplitude and at the same level of attention and the longest assured is of course that this is just a power of features betas and Bauer actually should be 2 plus on the the sort of thing but this and that is of course that we want to compare the product of these 2 quantities which is actually this 1 with this so we have to go ahead and do it just for some particular coding we chose them because culture code for because we already know that has a good scaling and easily gets so
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these upload here of data on the log of the ratio we were shown considering for and here I have corrected went through that recursive relations chips that in the in the then be there for this like the 1st of the nation's 2nd order to the nation and therefore other is that there's actually a nontrivial interplay bending of in between the degrees of the different degrees of the concatenation for different for the vendor said about his four J 0 0 and and G. J. this me where of course because the just the physical which has been and this year is the norm of the physical load up on the the so here in these gray areas you can see here is with were essentially where and there is no advantage of using the and you're actually hurt yourself so in this sort of make sense that all as serious studded led user probably deeper in the century relate to the fact that it is used to large well you system is willing to foster users loses its surprise properties so many of of something I should say is that what respect is that we the measuring that actually says measure including the errorcorrection their corrections or that actually science fiction delicate information this graph options improved right but this is of course the question that the car assembly sector progression so what is model with extra for us the problem of most of these that the fact that this limited by actually would actually mutations of the the the norm of its here is actually a point for that for the system but on and of course we want to but of course I should just show that memory sequence and this of course very means not there is a lot of attention but at the end we want to do so in in the in the grafted showed before is actually an implemented exactly calculations based on these on them and protective gates that Daniel talked about before were essentially do your friend you in so make investigate you dynamically cooking differences and that's and then you gotta do the same right and however also was unity which is a tree at the top performing which is which useful and India is that you can actually repeat the same you can't import the same sequences to our as it's the thing that's essentially what you're saying is that what you have to bring your favorite D. the sequence with metal doing gates 1 it's of using both of the beyond the quality the correctly well naturally of unit within a cold structure is just your and gold and they have some very good properties but when their experimentally friendlier to the to the guess that's so in conclusion well we have shown that the 2nd no need for extra credit conditions the pulses are in the code the sugar sequences that you have served as a quiz is the fully coupled approach so this is the this last point is actually what I was mentioned before that we assess note of demanding and it went into speak so you think for instance computer has are as a system but found on the tongue in that looks like a logical operator they see that regardless of a powerful loving if you have QC from the this logical operator can be dealt with because that's the minister last just jump on however if you try to use this eagerly copying of the 6 started as sky in the back to push this contribution to higher orders in time in such a way that juicy can take over from where it you know it's right and about this since it is the revision and 4 and their what we are trying to do now is actually doing this equation I was talking about them of including that have defected are actually doubt that power induced by the code that discover was progress and the idea you would like to do it to to see what is that the the the the rate we have to produce a quantum correction of gates for a minute I want and try to like our full Hamiltonian is but what that is but it's the kind of long the simple and what injurymarred will be up to buttons and questions I have a quick question 1 of the nice things about a quarter of the protein coat is that if you have spotted your locality in your model which will be reflected in your code that is you couldn't be nice and smaller everything will be better though with the most that you have the years scaling with the size of the number with the number of qubit systems exponential right in this yeah this strategy and look at the 1st order on the copying you can exploit the locality of the year among yes but if you want to to arbitrary or the the think you can you don't you can now because well so the world will only doing this in the other thing you see that even if the the have a 1 0 0 color or what the so regardless of the Erie in his locality there will be a minister at some point there would be at least your call by produce the distance of the code so that you can do with your tradable caffeinated more times in the because whatever if you yes sterilizer excessive called Azure operator we always jump forward so that's around keep that on the the teacher that the proper so there's like inherit standards but in addition you would have and is used by the default started time for 1 more question he established rather again if thank you that the
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Differentialgleichung mit nacheilendem Argument
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Titel  Dynamical decoupling of encoded information 
Serientitel  Second International Conference on Quantum Error Correction (QEC11) 
Autor 
Paz, Gerardo

Lizenz 
CCNamensnennung  keine kommerzielle Nutzung  keine Bearbeitung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nichtkommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/35302 
Herausgeber  University of Southern California (USC) 
Erscheinungsjahr  2011 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Informatik, Mathematik, Physik 
Abstract  It is widely accepted that a quantum computer will need some form of protection against decoherence, and to date the only tool capable of providing faulttolerance is quantum error correction (QEC). Here we study the interplay of Dynamical decoupling (DD), an openloop nonfaulttolerant capable decoherence suppression method, and Quantum error correction codes. Several schemes exist where DD is used to improve gate fidelities, such as Dynamically Protected Gates or (Concatenated) Dynamically Corrected Gates. Several authors have combined DD and QEC with different degrees of success, showing improved gate fidelity but at the cost of, in cases strong, extra locality constraints on the error model or a sequence size which is exponential in the number of physical qubits (n). In this work we introduce a dynamical sequences that use as pulses elements of the stabilizer and the normalizer of the QEC code (SXDD sequences). We show how this idea can be adapted to the leading DD schemes: Concatenated DD and Nested Uhrig DD. With this we avoid the need for further locality constraints and obtain shorter sequences while still obtaining fidelity improvements. Moreover, the fact that the SXDD pulses can be chosen to be bitwise allows a natural integration with faulttolerant methods and the direct porting of several DD schemes for fidelityenhanced gates into the SXDD scenario. 