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Bulk fault-tolerant quantum information processing with boundary addressability

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the well thanks very much by adjacent fondly and thanks very much the organizers for allowing me to tell you about some of this work and so I'll be talking about as a says their bulk fault-tolerant quantum information processing with boundary adjustability and it has quite a lot of relevance with the the last part as well so that's pretty handy so I'm from Macquarie University in Sydney and that where's that there we go
this so it's in the city of Sydney but we do have kangaroos on campus and that that beach is not actually on campus but it's actually on the play to island kangaroos on kangaroo island unfortunately not close to Sydney OK so what are we talking about the plan
is that do we have questioned that I've been asking myself the last few years is do we need completed but addressability so when we build upon devices and obviously wasn't on here the answer is no and but then the question is is how can we form a quantum error correction if we don't have complete addressability and in what more how can we do fault tolerant quantum error correction and and if we don't have addressability then we have to perhaps give up the idea of making addressable measurements and classical feedback and correction so we're talking a lot about coherence recovery and so and then we'll talk about error correction with coherent recovery that relates to the last and how to make that fault tolerant and then will try it and motivated OK it's a three-dimensional but we can also give you two-dimensional version of a semi global architecture that uses very little addressability at which is fault tolerant and can essentially do we act as a quantum fault-tolerant transport quantum wire or at full full blown contribution
so this is just a motivator you know as as as as we go to work very large devices do we actually need to control every single thing in in in the actual device and there's many different ways of of of was talked about on Monday different types of architecture for beginning at the main 1 I'll talk about his his the circuit based but to be quite interesting to see if the ideas represent here can be generalized to the other types of architectures and so do we need to have have control over each every single qubit and obviously now some would be and
why that is technologically very handy is that as you go to further complicated designs The control technology you need to do to actually address control each and every given here can will will get very complicated and consume a lot of real estate on the chip or whatever and so any type of idea to reduce the level of control would be good and what we're gonna do is we're gonna borrow a lot of ideas from cellular automata and then this is known now in the mature in terms of quality control as global control so this is topic of global
power plant control started long time ago actually as a satellite published 1993 an idea for a Universal part computer that was based on it spin chain isomer couple spin chain we only had 3 distinct species a B and C and there were coupled in in a 1 chain and it's alternating pattern and he showed how essentially could essentially put in a quantum algorithm and program that spin chain has to do whatever you liked then added later Simon Benjamin who's in the audience have a very nice scheme were again that you had an alternating spin chamber this time there's only 2 species A B A B A B and you fed in distinct types of patterns of Q. that's 1 type pattern and they moved to the right under certain sequence of pulses and these were global pulses on all of the the the B type spins at another pulses and other types of patents color control pattern which moved around and sort of independently of the the Green data bits and that it could affect gates at certain times under other types of pain so the basic rules are if you're not allowed to have the individual addressing or read out of individual cubits will you can have spatially structured arrays presidency here a B C a B and and but you can address and then read out the banks of identical cubits and a so it turns out there's essentially 2 types of schemes that we discovered so far 1 is this a scheme here for instance that has the data data patterns that move around and and control units the move around that essentially localize these global pulses produced local gates another 1 it are the ones that we discovered is 1 that Robert Rossendorf off and as well Joel FitzSimons myself found this games that used essentially filing finite the length of the chain to produce gates so
there's not many experiments have mostly the there and a mark on computing the here some results from an experiment on a Johnson Jones and Just Siemens and others the 3 cable experiment but there's plenty of ideas this is Corian and relive of make might might not might Moscow this is to amplify using class earlier automata the measurement result and here's the crystal of dipolar molecules that computers where perhaps although he doesn't look at this 1 could also do our global control here and here's a recent work by Thomas o clock with others on perhaps doing some quantum games life so OK so people have now built schemes which going back to these archaic gone back here the capable of doing full-blown universal propagating but how about error correction
and so we would like France and to have at least there's something friends like a perfect trapped 1 channel which is fault-tolerant all war or quality puting universe upon communing with fault-tolerant and can be done well and myself Joseph Simon's presented at the last conference several years go here a scheme which was a bit difficult and here we have a self-similar except the source fractal like structure of qubits and different species and the actual threshold was very small so it seems pretty hard but if it was possible if if if professionals were much higher will be much nicer so what I'm going to do is focus on this particular architecture this is this that scheme again where we have of the sequence of linear array of cubits and the couple stabilizing and 1 applies these were red and blue pulses these a homogeneous pulses of the C C phase the red or a sorry X well yeah that's right see phase gate and blue Allah have pulses on each individual key that so I could show and that if for instance you start with an X data on that's been it moves through xk here and use that gates and neighboring ones in this whole pattern this whole cubic pattern B localizes over the whole spin chain but if you repeat the poles as a number of times then this particular case here Rico here's on the spatial opposite side chain and indeed if you have a look at if you repeat this that this particular homogeneous pulse all have vitamin C phase gates endless 1 time for and is like number of qubits chain than whole spatial arrays of mirrors and this is independent of the initial state of of the chain so this is sometimes known as a mere operation and essentially if you have a clicker state on what Shane initially it would be perfectly transported to the other end of the chain in the spirit irrespective of of the state of all the other qubits in chain look pretty handy and they also works for seeing these
systems so here's the some work we did here the LDC phases now replaced by this type of unitary is just the position of the 2 harmonic oscillators coupled to each other and the they have either just have the rotation of harmonic oscillators score of rotation essentially we have a three-CD system and in some initial state after this after the spearing it's flipped so the idea we had that was to take care of this type scheme where you have been spends interchange and replace each spanned by a plane and so essentially this is a 3-D version of this this quantum wire and each plane will essentially undergo fault tolerant quantum error correction and these global poses our are now replaced by C phases which act down vertically here and and how the marks act on each claim individually so it's not completely global as as far as I've indicated here maybe on the next slide it's not completely legal and we're going to have addressability in this X Y directions of x y direction but everything is uniform in the z direction for later on we'll need to be able to address each alternate plain so we will have to keep this period addressability and a in the each plane essentially holes 1 encoded cubits corresponds to that Spain in the spin chain and the top and bottom and affable so this goes back to
did mention it but in this game I mention here how these all alternative alternative ahead of ardency phase pulses mere everything if you add to this particular scheme the ability to non Cziffra gates at the end of this chain the universe upon computing on this so the that that that corresponds to be able to do not
differ gates on the boundaries boundary the top
bottom the and the nice thing about this is that we have an air at an error in this global pulse then as essentially at each it essentially will be correlated errors in in a single plane different planes will have theirs so that are restriction now for the semi global paradigm is that we're not going to allow us ourselves to do India and measurement that war control inside the book interior planes of this device and we have to recover coherently from our errors using without mission essentially clear going recovery and we call that unitary corner so if I choose a colder quantum error-correction and and then we'll make sure cold and eventually will show you the area the thresholds that we found all here and so the the gate the gate of special but we found is is is about ten to minus 5 and the preparation so we do need to rest's reset the bits of of the 2 roots but the entry and preparation and then a measurement which we only have to do at certain times the is pretty high so the actual refresh fresh engines inside inside this device have can be pretty bad and this holographic control essentially all were doing most of the control essentially is on at the top and bottom lines so so essentially
talking about quantum error correction we we follow about this we need to be of pair states we need it in gates we need measure and what we're going to have to do with monica characterize the probability for 4 areas both in the preparation that is needed to build cold and so I have to take away the entity and the actual gates you gates we have to do and eventually the measurement and we have to make sure that there don't double line so
costs and this goes back to the previous talk essentially the the ideas were going to redundant redundant coding and we're going to concatenate and to try and make sure everything is transversal as much as much as possible and and I guess we know that if if we make everything fault-tolerant then eventually if we get a physical error below a certain the scale looks much like so the thresholds however it and the many things code design in their model many things but this management is a real
pain and I found this jigsaw pretty big jigsaw here so and essentially you can just figure out that is if you just have a moderately sized I guess well disposed at the moment is not a huge a hundred logical cubits 9 Cubitt make sure code then essentially you'll have about 10 to the 6 physical cubits and you'll be doing something like 10 to the 4 measurements at every error-correction step so where want to try and avoid that and the cost measurements even now OK that's measurements on traps but measurements perfect and so try to remove as much as possible the the the need to be measurement leave much technologically for much better OK so so something
isn't that were not going to see more not assume that all these error rates saying and we can assume that measurements take a long time and and unitary gates can be improved by the coupling as we've heard OK so this goes so now what we
want to do is to somehow to remove measurement from air error-correction syndrome so we saw we saw this it this type of circuit a few times in the in the last few days where it this is the 3 qubit bit flip circuit where you cold you have near decoding you you do the recovery and then you hopefully try to reset and repeat unfortunately here when when you do the recovery the decoded but of course we've heard now that 1 can measure the syndromes add a few more peanuts and essentially amateurs syndromes and do the recovery and this was nicely done in last or through a jump operators and however essentially unitary version of this would be this 3 toffee gates and that you would have to reset these 2 Lancelot's here so what we're going to do is
we're going to look at and make sure code and what's going to be very useful for us is something called a majority voting gate and that they're making sure code is and well here's a but essentially I'll show you this later on that in a minute but here's the 3 qubit code and this is what our baking majority voting get it will look like and I'll explain this in a few seconds but Assange collision recovery is pretty essential for most of the current experimental evidence and will hear about this later on this week traplines and circuit superconducting polymeric corrections all used to recover so well talk about a little bit is
this set majority voting gate which essentially repairs of single single qubit error in in this encoded in that state the Arnold step through this
bit by bit just show you how this works essentially if you imagine that was the 1st bit his flipped and we have to banks 3 and so so that
here here then the 1st gate 1st 2 gates
here this is just the simple acts and this is the Ctrl-X where the target is shifted to the right so that's that 1 then and you notice that it is here that this is for x that it's also shaped but that reflects that back to 0 and that when the psychic is shifted to the right so then you have to have this state and then finally we have this Ctrl-X but it's in the other direction and so essentially this is control off this middle the bank of 3 and essentially and you end up with this pattern and then find you do this bit wise topic to the top and if you notice now that that looked at flies top to topple correct that guide to 0 and correct that but 1 and now you but into a of state and and this is now being corrected and now you have to refresh these guys but the interesting thing here is that essentially OK on that OK so we'll use a big ensure code seen that many times user stabilizes is the logical operators and and we talked about this subsystem coders engaged freedom as well of the nice code as many the operators that we need to do the mirroring and the error correction our our our transversal really 1 that's not transversal was the same path which we won't actually need too much and only now and then at at the very end we'll have the measurements at the very highest concatenation of
so here is the actual error correction routine and through the fault tolerant error correction at the concatenation level so it very similar to what I had before and this is the 1 now adapted for the big chocolate and well there was all step to this that a bit by bit to show you how it works and essentially it works by using the Baker Shor code and extracting the syndromes again to the British Oracle but process the process the processing them in in the queue or petition color and correcting them back into to make sure via the column so essentially we need here is the actual data and we need some summer which I'll show you in a minute how we prepare and essentially this part of the the of the scheme corrects for X errors and this part of the scheme is the dual tracks for there's and the so OK so the 1st box the so I know
what I'll do is I'll just make a little power thing here is the data in the so is the K plus 1 concatenations 9 K and this is just the copy will last row show you what's happening these are all in the Big Shor encoding and this is in the queue encoding down here so this imagine that we start and isn't there it happens to be here like Serre in the 1st part of this block that we had in his Ms. majority voting type correction scheme 1st right is is to do this next copy and also rotated X copy down like it do this into the picture on select then what we do is we start we move on to the 1st part of this this is the and this just copies just Ctrl-X is everything into the last column which of just separated out here for clarity the 2nd part then converts it down into as a few art encoding so this now you have a very large due on coding and that is that you have type of code this last those the last part of that majority voting essentially those this Ctrl-X now again in the but are a toad rotating backwards so that becomes this just moves down like that and they'll find we do this but why is there a toughly with those who which can work this these are now classical at the farcical data centrally and we just go back and move up and down flip the columns and in the lecture hall and that produces an next for this particular set of syndrome and that's now to X there's just a gage 3 freedom so it's no longer it if we had started with 2 axes as an error that's just the gage theory of freedom you see what happens now when we copy this down using these these these two hour parts here the CX and rotate the axis you get this pattern appearing in in the insulin and then when you were Ctrl-X move that over all of them have already that those Council out to X the Catholic and essentially these the pros that you have in the if you are a syndromes and they do and the that's right because that's just a gage freedom anyway so that was there the fault-tolerant unitary aircrew recovery done and and concatenation level so how do we get fresh students because we need to withdraw and be all the time and so this is our our
picture of how the whole thing works we have to have with scattered within the each plane there are many many systems which can be reinitialized perhaps not very well that's refrigerator and then we'll have methods to purify them and then send these cold and still over to a computational engine and that can be different and could dates when of course can send them send things off here too to do magic say preparation and once we have cold magic states that we belong on her information cost now if I don't
want to do this then just this alone is this fault tolerant perfect transport Châu
so 1 way of preparing cold cubits is will have to have some physical systems that will be able to reinitialise so for instance if we have in these with an optically pumped then to initialize the initial state and might not be very very good initialization but as great if I mentioned yesterday you can use that a few rounds of algorithmic cooling to get extremely cold the initial states that we use this majority voting gate in a number of ways to prepare the and so here's a preparing logical and so therefore they make sure it just visible and telephony QR codes and
so that essentially does this fault-tolerant clone transport so to do the magic state we have to be non pivot operations on the boundary and essentially will do those at the highest level concatenation and we've heard this before to both Monday and Tuesday essentially what we have to do we we do distillation and we we make that many very initially bad states and we bootstrap of up to a not so good logical magic state and as so essentially this is what we do is we take the interstate we encoded into a larger version and once once if the states good enough then it's almost as if it's this has to be with a certain fidelity of of a magic statement and once we get there we can just use distillation what's gates are good enough get too much stake and when once we get to this magic fate for instance here this is teleportation that into the circuit together not to forget we only have to do this at the highest concatenation level and we do it on the boundary and this we do need measurement but it's at the highest concatenation so when we go through and
work out the the thresholds and so we're going work at thresholds for preparation that so initializing these entropy reducing sites and respect and measurement and also the dates we find we work through all the different types of modules and essentially this 1 has the highest error rate and we count the number of malignant pairs that's what was we did we find that for a for this type of life of threshold which is actually pretty commensurate with with the bell with measurement has and so a physical error rates for for dates and that has to be lower than the social now the measurements at the highest concatenation level so essentially can be very bad but essentially this depends on how good our preparation is and so if we have very good dates then argument that power in the cooling can work very well and very few rounds can produce very cold and select and so on are measurement and threshold can be very high and so there there's a bit of a degree of flexibility here so for instance if our physical and gate threshold of physical Gatorade much below this and then we can get our preparation error up to 1 per cent so that because and essentially a measurement error thinking to be very high so what we've shown now is
with but gotten in this type of 3-D architecture we have semi global poses a global global pulses and distraction but addressing in the x y direction and the planes need to be a be addressable and that's because instance when I do have a model a plane the bacon sure code it flipped the route corresponds to rotation when I'm degrees and also if I do this phase gate all at once there is a possibility having correlated errors across the plains so we do it in 2 parts now if it is possible through a bit of work to push this into a 2 D arrangement but have for that to be true we need have non nearest neighbor gates which might not be so easy in various so essentially that uses a fault-tolerant to move things around so the whole idea was to
see if we can reduce the number of controls that we needed to do various operations this on computer so we estimate now how many IoT dates and cubits we need to do as for Shor factorization with these numbers of edges of these number of that's and what we do is we compare that is the number of logical bits and this is the improvement this this particular architecture has up against an addressable circuit that uses unitary recovery and this is with an addressable circuit with traditional measurement recover and so there's some savings significant savings here so this is a times better 86 times rhetoric 2000 as the 4th of OK so this is my last slide
and my just so I've shown here is that global method where we have socially controls on the boundaries measurements on the boundaries and we call it Holographic and everything in the book is you is essentially happening essentially globally there is you covering and agree and entropy dumping happy all the time within the bulk of this this device that TD in 3-D designs and the thresholds that we've gotten seen on high with measurement based make sure so 1 thing is we could look at the future and always seems pretty of gold can we devise new designs which are more global and find that fairly read more decent thresholds for them so the design that joe 4 times and I found a few years ago had a very very bad threshold what maybe 1 could perhaps look at other types of cones planar colds topological codes and devised a new coherent recovery schemes for them and they might have much better rituals OK thanks for image and we thank you very much Jason address the aggression so there's that I'm trying to figure out where you where you would prefer to use these gadgets rather measurement because if you've got essentially two-dimensional addressability then you can do two-dimensional code supplied encodes topological cuts so it seems that what you're doing is replacing every measurement with a multi keep again and it seems that you can he therefore will require a system where the prior is on multi-key they get on very much less the mentioned terrorists under the theorist so I don't particularly very many experimental systems but that's seems to me counterintuitive keep up safe what which systems that's true on the planet that's not necessarily the case short and so the whole motivation behind this is as that there was mentioning I don't know I don't want to bring the measurement information backup the possible world and do a possible control back down to the Vice that requires an awful lot of technology if I have a large chip with many many cubits I have to then bring classical right at beside them I would have to have measurement devices buried everywhere and that all that signal would have come up to the possible commuter out of the juror out of the and the the cavity array and be processed and and a whole bunch of control technologies going back that every doing the recovery so that's what I'm trying to do away with all that layer of of technology matches comment on that too because especially for lines for other systems of of other related to that measurements are expensive they take a long time and they slow you down but orders of magnitude also the introduce errors that completely unwanted so I think this is the the right approach and I'm going to talk about that more than that more details I think that is very much depending on the implementation I just would but what is to to clarify something out when you do your algorithmic cooling in in the bog having truly is not everything in the book is unitary or not that's right rattled scattered throughout the bulk have to be these little coolers so this little nanodiamonds scattered throughout the boat which I can optically reset but we shown that they don't have to be vessel is there another version if those other case Mexican from a chosen and he comes to the
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Metadaten

Formale Metadaten

Titel Bulk fault-tolerant quantum information processing with boundary addressability
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Twamley, Jason
Paz Silva, Gerado
Brennen, Gavin
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 10.5446/35293
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract A globally controlled architecture for a quantum computer is highly appealing as one does not then require the technological capability of addressing each and every qubit within the device. Although several fully global controlled designs for a universal quantum computer have been proposed in the literature - and although it has been proven that a fully global fault tolerant (FT) quantum error correction scheme is possible in principle, no actual scheme for the latter has yet been advanced. In this work we go part way towards the latter and present a fault-tolerant semi-global control strategy for universal quantum computers. We show that an N-dimensional array of qubits where only (N − 1)-dimensional addressing resolution is available is compatible with FT universal quantum computation. What is more, we show that measurements and individual control of qubits are required only at the boundaries of the FT computer. Our model alleviates the heavy physical conditions on current qubit candidates imposed by addressability requirements and represents an option for improving their scalability.

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