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Quantum Firmware: Engineering error-resistance at the physical level for robust quantum computation

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Châu thank you it's understand and accept the likely uniform up to date is usually high pace after much all talk today about a series of projects that involve experiment and theory of the experiment was mostly done while I was Apple NIST in the storage group and I'm presently setting up a new experimental group that the University of Sydney is part of the Centre printed systems all acknowledge bright funding sources we have but all give generally a talk that follows this outlined by a very very brief bit of motivation I think this this group doesn't mean very much and then talk about this concept of One firmware prayer suppression at the physical level the the and gives away the shell but all speak a little bit more about exactly what I'm thinking and then move on to a few different more technical topics 1st the idea
of noise filtering which I described as an experimental friendly the analytical approach moving on to some demonstrations of 1 from were in the lab dynamical our suppression and then add noise filtering in non-trivial gates which is a new extension of beyond some of the work that existed previously so I mean this is familiar to everybody the idea that we're concerned primarily about the effects of environmental noise unwanted degrees of freedom that a couple to our system these are effectively in terms of the Hamiltonian that we can't write down or that we don't know and from experimentalist perspective region we talk about some coherence times but from the perspective of polymeric correction which is maybe more interesting to this
audience we can think about how these times in a very rough way give rise to some lower bounds on the kind of error rates key error probabilities that we can achieve and we see that the generally bounded from below by some op operation time relative to the coherence time this is a very rough approximation will see that it doesn't hold up under most circumstances but it is kind of a motivation for suppressing the effects of decoherence our system and we deal with these errors no there some fun things fine but how we deal with there's comes from a couple of different techniques that we for quite a lot about in the introductory talks yesterday and today but of course there's the closed-loop version of a common error-correction were we involve measurement and feedback but all be interested in and speaking about open the Control dynamical suppression strategies and open means we don't use measurement and feedback in the great canonical example of a canonical example to my mind is a sprinkler system it comes on every dataset time it doesn't measure with the grass is where it doesn't matter whether it's rained it just comes out it actually works pretty well most ones survive with this kind of system and the aim of the work all talk about today is to incorporate these open the control protocols into a more general setting where we ultimately wish to improve the performance of quantum error correction at by driving down physical areas that's mainly so all run through this in 10 seconds or less so we know that this is all based on the spin-echo where we talk about easing originally in the context of magnetization vectors in 1950 show this nuclear magnetic resonance but then dynamical suppression dynamical the coupling for the protection of quantum memory has emerged by taking the spin echoes and chaining them together into sequences in order to suppress errors at longer times and really the beauty in in this kind of application is that there's so much flexibility in how we do the quantum control what control we use how many pulses if we use pulses all pulsar timing the kinds of pulses as I said and all of the or maybe it's a black art even using the sequence and how we Cheney's Kwan control operations together to achieve some desired outcome and for the duration of this talk I'll be talking generally about post control but mainly because it's what's been studied primarily in the literature that for the last 10 years or so but said there obviously many other approaches you can take for instance continuous control that a Gaussian Christie's group has looked at quite a bit some that I wish to convey to you is
this notion of developing dynamical our suppression strategies as quantum firmware 5 minutes see but I think it does in fact capture there are some real concepts the 1st is the idea that this is a very efficient and simple approach to suppressing errors at the physical level so it's very easy in the scheme of things compared to many of the quantum error correction of a lot of and what not but implemented and from a system-level perspective we can very easily think about absorbing this into a city into a kind of machine language where it's extracted away in the program of the quantum computers or even your algorithm design has no idea that this is going on in the background but is also useful to know that this is a potentially important as Roman was speaking about earlier for kind of any quantum technology it doesn't have to be quantum computation that uses this we would I would generally argue that most things that we wish to exploit that Kwan coherence in some way it from this kind of protection against error and so this 1 from where it can be useful in a variety of settings the back to quantum computation by if you start worrying about well how difficult it is to do all these things in the background of a quantum computer it's useful to know that there is already a precedent for this and it exists in pretty much every laptop or sure every laptop in this room and that's the idea of deer D-RAM works that stores information by charging a capacitor each cell is 1 resister 1 capacitor and over time the charge on a capacitor leaks often physically migrates off the capacity trench into the substrate so roughly once every millisecond you perform what's called rascasse sequence are accessed row-column axis true you apply a voltage pulse open-loop control and you refresh all the spins albeit not spend all the charges in your system right this kind of firmware exists and the only impact it has is that the level pH level for programmers is that induces some latency right you have to wait until these refreshes adorned but otherwise you don't know about it I mean you don't worry about refreshes as you access memory and the concept that I'm wishing I'm trying to convey to you is similar here so my interests my group's interests are really in taking these high-level concepts and making them useful at the 1st is making these dynamical espressione strategies more accessible and for those of you with the you know pop I apologize this is cycle joke but he got a good response there and and it is in fact true but I really don't like when people talk about her theory to because I don't understand the idea then is using this accessibility in how we interpret these dynamical error suppression strategies and using them to calculate real error rates instead of assuming some key that's extract let's calculate what P is based on real environmental noise let's consider realistic constraints as Lorenzo was discussing yesterday imposed by hardware and let's take these constraints into consideration when we try and design Kwan control approaches to suppress errors so 1st I wanna speak about this tactical topic of noise so if you want understand how some environmental noises going impactor kibet you can start off this way will take some Hamiltonian that has an unperturbed splitting and then a classical random variable bit of were beta just captures the noise before the theorists in the audience counts on me and argue how this is in sufficiently general that is a true statement but it turns out from experimentalist perspective the simple Hamiltonian of just sigma the noise dephasing noise actually captures almost everything we care about their very few circumstances in which it doesn't and in fact even kind of the most quantum mechanically well this system most expected to be fully Kwan mechanical its interaction with the best that is the central spin problem is actually better models that by this kind Hamiltonian where you assume a fluctuating Overhauser field in single triplet qubits than by the detailed model of a spin interacting with the high seas so this is where we start and then you can say over time you end up with some accumulation of phase that's the error in your system in the rotating frame you apply some dynamical error suppression which involves a series of pulses as we heard about but you can calculate what the net areas at the end by taking this nasty convolution of this time fluctuating beta T and this control sequence and you can try and calculate that phi you can do it but it's certainly not intuitive as an approach to understand what kind of you get and it's it's pretty nasty mathematically what's really nice is that we can exploit the fact that convolution of the control in the time domain with the noise gives us a product in the Fourier domain and this was shown by many people Shor did this 60 years ago but during and she went he wrote a few papers a few years ago there were really lovely in in calling out these relationships aquatics and effectively taking any arbitrary sequence in writing down there in the Fourier domain what's called now the filter function this is a spectral function that defines the action of your controls so if we have some noise that's characterized in the lab statistically by a power spectrum the power spectra densities in arbitrates all the the way that this is what we have to worry about so we wanna suppress so if we make our sequence by modifying the locations of the pulses in our in our control such that it filters out the parts of the noise power spectrum that a large you suppress there's this is the simple way it works and you can write this down in terms of a coherence function W which is an exponential this kind of T where ki is this integral a product of S the noise and after which describes the action of your control sequence it's that straight forward the coherence is preserved so long as this filter function is small where the noise is large now you can take this filter functions and calculate them out using this analytic in analytical formula numerically for an arbitrary pulse sequence and then you can analyze the action of that filter function where you can analyze the filter function and interpret it so it's effect using graphs like this this is the filter function on a log-log plot is a function of frequency in some dimensionless units and there are a few characteristics that that reported to call out the 1st is around 0 frequency there is little for in the low frequency limit there's some slope to how this filter function increases and he can be shown rigorously that this slow entirely captures the order of our suppression that we talk about in perturbative expansion so the more steep this is the better the order there's pressure we can then talk about things from filter design theory in electrical engineering or in digital signal processing where we talk about the 3 the point of our filter where does it start to turn on what's the stop band what region-based as it prevention what region of frequency space this past all these things from a very simple mathematical formalism and it's important to note that these filter functions are always high-pass because if things fluctuate very rapidly compared to the interpulse time as we heard then the noise gets through unimpeded you don't do well with the sequences now this is nice to me because I can now understand the action of an arbitrary control sequences by examining this thing I can calculate in a way that's very similar to the way that I choose electronics when I go to many circuits I don't calculate overlap integrals I look at a filter response of a high-pass filter and I say well OK this has a 3 point roughly the frequency I care about sensor noise a 10-megahertz and it's sufficiently low this is 80 dB of suppression that this is the right fielder for me I can do the same thing now and 1 controls and what's really nice about this is in addition to simple analytical approach to compare sequences we can also get some information that doesn't come out quite so explicitly for instance the year dynamical the coupling sequences is really very interesting I'll talk about this more in in a few minutes but in addition to the price that then call that yesterday in terms of the number of qubits there are other prices for instance in order to make this sequence behave as expected because the pulse locations are rational you need infinite precision in order to do this sequencing and if you start impose things like clock periods that he can only define the
location of a pulse with a certain precision you see that the filter function which is very steep here meaning that noise in this rate regime is is suppressed very strongly starts to creep up and as the precision is reduced the effectiveness of this sequence gets squashed so this is revealed as by the numerics of the filter function and I can understand it just by looking at this much the same way I select filters and looks at so in order to deal with that there was a study that we started with the Lorenza and if Hazan topical just looking at sequences that we call digital modulation sequences whereby we no longer rely on these rational locations for pulses but instead by impose a constraint that all pulses occur with interpulse period some multiple of a minimum period a a clock period and what we called on to was this idea of the Walsh functions these are a family of square waves said that's where we're analog of the signs and cosigns in some respects and this this family of functions that were studied a lot in the 19 seventies for communications but turned out to be really interesting because each function which is a square wave and some form can be affiliated or associated directly with the control propagator for a dynamical the coupling sequence the transitions correspond to pulse locations in a kind of diagram that's familiar if you are in this body of literature but has idea benefits by its digitally compatible these sequences are extremely easy to generate each 1 of them even though they look funny I can be generated just by multiplying together periodic square waves which is great because it's compatible with very simple digital control electronics in Hardware you don't need a full microprocessor to do sequencing it's a very nice unified mathematical framework with all sorts of benefits for instance these red curve that I've called out here are concatenated dynamical the coupling there the CDD traces of different orders that popped out immediately from the Walsh the family of of of sequences and there many others that are of interest if you want a more about this you should see public justice talk on Thursday so I encourage you to come to that or ask questions at so what about doing this in the lab without really doing experiments so our experimental of platform is a crystal of trapped ions but each blue dot here is a single beryllium ion and they fluoresce about 313 animators which we can realize you some opposition laser systems when we later call them using a simple Doppler cooling they crystallize into these nice erase the crystal structure has been studied extensively in the nineties and early 2 thousands and anybody's interested in the system can asked more for the sake of time I won't go into it very much but these are in a Penning trap which is a slightly different kind of trap then you may be used to an ion traps it certainly different than what a buyer will talk you about tomorrow but the generalities are a similar we get some three-dimensional charged particle confinement by using electric in this case magnetic fields and then we use the level structure of the trapped ions as a means to realize on a mechanical manifold so this is the level structure brilliant born at Tesla which is used for trapping and I'll call your attention to a transition here it's a pure electron spin-flip transition at 124 gigahertz which is a nasty frequency but it's something we can control and the presence of a strong we're allowed cycling transition between the upper stable manifold and the double P 3 halves excited state and beryllium which is used not just forgot the cooling but also as a form of projective state-selective reader right the upstate is bright when you shine a laser on it in the downstate is not so we can measure or qubits and a projective way in this way so we do quite control experiments and I'll skip over a lot of the details of how we do that technically but we can for instance to Iran's experiments see that over some time of order MS at the time we were doing these experiments a we had some decaying fringe contrast for measuring the population of being in the upstairs downstairs and this of course is due to some random term in the Hamiltonian some noise magnetic field fluctuations so that cause a net decay of now here to was about to enact MS and it's pretty straightforward and not at all unexpected that by applying some chains of pulses these C. P. M. G. its multiple spin-echo we can take that the data are just compressed here the bottom scale is expanded we see that the coherence time can be improved about 10 times for 10 pulses so that's that's fine it's not very exciting but but What's more exciting is how well the filter function approach works so this is now error probability as a function of by the length of an experiment for different pulse numbers not 4 times by pulses it's 4 pi pulses that different dots at 2 different sequences UTD in in open markers and C. P. M. G. and in black markers so what you see of course is that as you increase the number of pulses the coherent stays good longer low error is due at the end more important were I should say more important and without the end what we can do is generate the soliton and in this case day after that give us a theoretical fit to our data that just using the measured noise power so this is what we actually measure by putting an antenna into our magnet and measuring the fluctuation and the analytically defined filter function for our sequence appropriate perceive and unity and we spit out these curves and you can see that with only a single free parameter which is just the strength of the noise is there's an inductance in this in this intended that we don't know what we get extremely good agreement between data and theory and in particular the presence of this funny spur 153 hertz which it turns out was due to a chiller 3 laps down the hall is entirely responsible for these funny bumps wiggles that you see at intermediate times all we've done is taken the overlap integral of the filter function and this measured noise and we get this kind of agreement which was very exciting for us this simple technique worked extremely well now we can do some other things as you may have seen we don't get very much of a difference between C. P. M. G. UTD at the time we were really interested in demonstrating for the 1st time that this UTD approach of modifying the filter function for a particular kind of noises we heard with high-frequency cut shop I can work and so they are my quit system replacing a stable oscillators with a frequency modulated oscillator we can generate noise in our system this is noise in the control with the power spectrum that mimics something of interest rate so this is 1 of a raft with as well it's 1 over omega with a sharp eye for to cut up and this is something that looks like omega only noise the upshot is we can model the dynamics of other quantum systems and probe in detail at the functionality of the Surete approach and so just very very quickly as the noise gets stronger so this is injected noise and omega saying relative to the background which is this dashed line that's the stuff I showed you a few minutes ago as the noise strength that's artificial goes up the relative performance of CPM GUT gets flipped so this was the 1st demonstration that this UTD approach when we have strong high-frequency noise will in fact give a benefit so this work it was really nice us but we can go much further than that we don't need to stick with things that are defined analytically and some arbitrary and idealized way we can actually do feedback of measurement feedback in autonomous the control in order to generate new sequences that are numerically optimized so what we did here's with what Mrs. P. gene unity and then we pick a particular value of of time this is the length of our experiment is somewhat and at that point we started a multidimensional America had no the need search algorithm that move the pulses around relative to 1 another to find the optimum air at that point and then we can trace out we find that we get even better yeah suppression by doing this numerical optimization what we're doing is tailoring the filter function of our sequence to the actual measured noise in our system here this is injected high-frequency noise so we can do better than you and in this case these values are kind of meaningless because we're injecting very strong noise to swap that but the upshot is we can do better by these numerical techniques now I want to
give an interlude because there's been a fair bit of discussion about this UTD sequence we heard about yesterday not familiar it's an optimized sequence that I guess very nice scaling an error in the order of the suppression with the number of pulses the Prize that was to obviously very interested in studying it but I've come to the conclusion over the past couple years that it's likely that to meet its end at some point soon I don't think it's going to prove to be very useful the fact that you require this infinite precision in order in in the pulse sequence in order to get the benefits of its incompatibility with it'll clocking at some other effects that a really suggest that it may not be the solution that best tailored to large-scale systems sure confined by some niche applications but I don't think it's the be all and all that some people had anticipated originally but that doesn't mean it's not useful but what's really important about the uric sequences that think about these problems
of gun control in a very different way your work gave us the filter function this filter design approach where the filter function an analytical method end he made us think about pulse
timing as a degree of freedom that hadn't really been considered in in quite as much detail as previously so it's had a huge amount of benefits but I personally I'm not convinced that it's going to have a very long features it may I may be wrong but we did a number of studies looking at different kinds of optimization published in a variety of outlets in a few years ago but there's a key point I want to get across which is why this work in our system it works because I conn control had a pretty good fidelity that there was this was set up on 1 of the slides earlier today they using this crystal and randomized benchmarking we got to a single qubit it fidelity of 99 comma decimal 9 2 per cent the real big change man original results was that we moved from laser mediated gates to migrate to the gates and in this system again 124 bigger it is a pretty nasty place to work this was pretty good for us that but it's this very high fidelity that gave us the ability to do these studies without what measuring quantitatively the effects of environmental noise without measuring just the effect that all so what I've told you about so far addresses this date set by only focusing on on 1 operation that is memory or the identity operator and what we're really interested in is expanding this general approach filter on firmware and 1 control
for error suppression toward other things that are of interest to anybody who's looking to apply universal gate said so I wanted to mention the briefly I think the decoupled and compute the strategy is incomplete in that ignores what happens during the operations during the compute part so I think we need both approaches we need to worry about the decoupling and then we need to make these things robust against errors as well so the key question is how we actually actually accurately calculate P. for a particular date in the presence of environmental noise that often time-dependent and how do we improve data and this is the subject of some work all talk to you about for the next few minutes it's work done by an extremely talented undergraduate student I typed green at City and I think it will relate to some of the work will hear about later today and maybe tomorrow as well so if you just think about performing some 1 operation that's nontrivial for instance of pirate two-pulse where we go from the north pole to the equatorial plane in this simple depiction if we have some nonzero detuning error this is written in the lab frame what you find in this is this is early quantum mechanics or or the 1st semester on mechanics is that the net effect of that operation you a rotation about a shifted tilted axis and that's incomplete right so you perform some operation that's not what you wanted you don't end up on the green dotted line you end up somewhere over here what's important to note there is that a pure dephasing environment this is just a sigma error during a control operation will give you this general depolarization where you end up off the equatorial plane as well as accumulating and what becomes really nasty is that if you think about this delta being a function of T it becomes difficult to treat this analytically and you're not 2 0 rotating about some fixed tilted axes it's now axis that moves in time and its again important to note that this is not so abstract as to be useless this captures a wide variety of environmental sources but also intrinsic sources that we have to start worrying about when we think about error rate the fault tolerance level the most important of those is instability in the master oscillator phase noise in a master oscillator is manifest as this kind of the noise delta T. right here the frequency of the oscillatory changing in time in in a in a statistical way so what we use in order to address this problem as effective Hamiltonian theory goes back to some work from runs many years ago where I we take this Hamiltonian I apologize again change notation out a T for the noise and we can write down an effective Hamiltonian and the control propagator more propagator that looks like the effect of a time-independent average Hamiltonian instead of nasty time-dependent Hamiltonian meters and technical details of how we do it such that if we wish to implement some gate some operation but you write down the total the propagator for it as time some error so this exponential captures the yeah if you have questions about this you can you can grab a afterward the question then is can we apply this to some non-trivial gate and calculate effects on the fidelity of nor in this case so yes we can use the trace fidelity we get something that looks like an exponential of these terms here which are the subscript l or the Cartesian coordinates so these are the parts of the of the terms that are proportional to pally operators X Y and Z such the average fidelity in the presence of this environmental noise is given by a form that looks very reminiscent to this calculation I did before where the coherences EU the minus piety implies some overlap between noise in a filter function well here is something that after 1st order Magnus expansion looks very much like a filter function where each 1 of these corresponds to x wires right so now for a nontrivial date not just the identity operator we can write down a filter function that captures the effect of the quantum control and the effect of the noise so for some classes of sequences that are of interest as this is but it will be you can apply this to arbitrary modulation but it's useful to think about sequences where we can apply some arbitrarily chosen rotation rate and some arbitrarily chosen rotation axis but we just applied the constraint that each segment of piecewise define control gives us a Bibles you apply apply pulse you apply Bibles about a different axis dynamical the coupling is chapter your you particles about X and then troop I pulses in a row about the identity operator so these piecewise defined control functions capture a broad class of things that are of interest what's nice is we can write down using this closed-form solutions of the filter function you can write down filter functions analytically for again any sequence but its new year if you make this requirement and they have some more terms so that I can again explained anybody who's interested but what's very important is that not only do we have a filter function for the effect
phasing we now have a filter function because the effects of polarization
damping the buildup of x and y and worldwide there's in our system when we're applying control in the presence of defacing noise and it's it's nice mathematically that if you look at the pre factors here they look at very reminiscent to what you expect from a master equation treatment of a driven harmonic oscillator in the presence of some damping and it's kind of as expected were doing a driven rotation in the presence of some dissipation of course these are important only in the statistical ensemble so what can we do with this well we can treat a couple different nontrivial gate constructions that are of interest of course there's the simple trivial gate there's a potholes and then there's that dynamically corrected gate this is what Lorenza told us about yesterday where you have a series of 5 pulses and then Popal's as they go in the other direction such as changing the face of the oscillator and at the end there's ups that just takes twice as long and as half as large in amplitude but it's all this but also so we can use this filter function approach that I told you about a moment ago and try and analyze the performance of these things because wall the general performance has been studied in a perturbative approximation of from our previous work by Lawrence and how they I swear to god that when I look at Telegraph my mind starts spinning and I think this filtering approach is is as a experimentalist a little more straightforward so here are the filter functions for this simple pie poles and the DCG gate black is the pipe pulse the primitive and red is the DCG so what you see the water of error suppression is improved in the filter because the slope of the filter near 0 frequency is enhanced in the DCG if you look at the high frequency regime there is an effective extended time this thing is 6 times longer than the simple gate operation that means that if you have lots of noise up here that's dimension the scale that you're going to get hurt it makes sense if you make mitigate longer anything that fluctuates on the time scale that extended is I'm not going to influence the primitive data strongly so that's captured here but then the effective dynamic protection comes in here where the order of the air suppression is enhanced using a simple dynamic and I won't talk about this but that talks about the different quadratures you can but now calculate the error as the probability error in total so what's the total probability you not where you expect it to be but also what the probability of ended up having EC services here and we can validate this using some brute-force numerics this is error probability as a function of time in some dimensionless units for a particular kind of noise environment and the solid and the dashed lines are calculations using this filter design approach where we write down the filter functions and just take the overlap integral with the noise and then the data points are the expect were outcomes of he's detailed simulations were you trace the block vector over the Bloch sphere and you average over many iterations and we get very good agreement with about 10 or 15 or 20 per cent and remember this is a logarithmic scale here so 20 per cent error is very small and frankly I don't care and I don't think anybody here cares if the error is too but 10 to minus 4 or 2 comma decimal 1 by 10 to the minus 4 they care about the 10 minus 4 so this filter design approach even though it's 1st order Magnus expansion that really captures a lot of what we care about from a practical perspective so what comes next well this was the microwave system that we used 24 gigahertz it's really nasty It's custom-made by all these oscillators are involved at all we can do with it is on off pulsing it's pretty restricted so we can replace that now by moving to a lower magnetic field a lower frequency with the box from agile and that it's expensive but it does for program around the vector IQ modulation so we can do amplitude phase frequency control and this gives us a new wide range of capabilities to perform dynamically corrected gates and new kinds of continuous control that we not previously studied and using these filters out approaches we think we can do optimizations well so here is the summary of my talk I hope I've convinced you of this the utility of this concept of quantum firmware and how we can develop new analytical approaches for noise filtering that capture the average effects very well that without doing detailed time-domain calculations we can treat things that vary in time using this average Hamiltonian theory that filtering during gate operations is now something we can do I think will hear about it 1 of the talks in a few minutes and we've done a variety of experimental demonstrations of a small scale which started to now consider what happens if we wanna move to something bigger what happens if we think about constraints as again Lorenza talked about yes that have not traditionally been of concern at the lab I can do my sequencing perfectly well using it in FPGA a programmable logic device and a PC but I wanna build something bigger I need to worry about a difference and again marketing is the only application so I wanted to acknowledge the collaborators of particular green in the 2nd half of the work I talked about today plug the Kwan from where collaboration which has been very fruitful for me and I've been very pleased to collaborate with learns and cover a mere and then do a little bit of smarmy advertising about what a nice place it is all had to live in Sydney and they fight to anybody who's interested come talk me so thanks for your attention if OK very nice questions so the group that has try to make the exercise and
so strong component of this filter function you point so it works very well for this limited class of models of the classical be facing noise if your noise is more general than that if you have spin-flip noise etc. then you know just have 1 filter function in principle you have a filter function for every element of the tiny trees or something like that I just 1 if you have any comments sincere going down this road kind harder and whether that's going to be fruitful when the noise is more general sure so that if there's 2 parts to that 1st I well there's 3 parts and we we showed 1st of all you can write down filter functions that capture the average effects of errors during I have a get there during control operations in the X and Y so the amplitude quadrature so this general approach can work for characterizing statistical errors that doing this more genera and error model that explicitly accounts for t 1 that's something talker but you have to keep in mind that most 1 processes are not reversible if it's spontaneous emission it doesn't matter right so you just have some error probability and this sets a different bound but if it's a coherent rotation error but something a little bit different and you can start to consider I think writing down filter functions for that but again just emphasize that this classical dephasing model captors almost everything we care about and if you have some other uncorrectable error coming from T 1 you can just add that on top here the questions I should adjust it back I kept the question that looks like you have a huge dynamical range because you'll procuress spinors milliseconds and you're working at 100 gigabits the well I understand it correctly so in principle it's under 24 gigahertz carrier in that particular experiment in the new ones it's it's 28 by what matters is how long it takes to do the control so it's the Robert time in those experiments it was it was tens of microseconds and we can get that down at 2 tens or hundreds of nanoseconds but here the range is more limited than 1st years virtually all this stuff which happens so that the edges of the Balsamo liver is associated with the past shaping it's not a concern for you right it has absolutely not an exact I think OK well when we have the next speaker is set up for the other questions the let's thing right again press 2 considerations
Bit
Nabel <Mathematik>
Stichprobenfehler
Gruppenkeim
Reihe
Firmware
Quellcode
Physikalisches System
Physikalische Theorie
Übergang
Geräusch
Theoretische Physik
Firmware
Mereologie
Uniforme Struktur
Projektive Ebene
Quantenfeldtheorie
Speicher <Informatik>
Offene Menge
Bit
Puls <Technik>
Quantenfeldtheorie
Gruppenkeim
Versionsverwaltung
Kartesische Koordinaten
Hamilton-Operator
Eins
Gebundener Zustand
Puls <Technik>
Typentheorie
Kontrollstruktur
Analytische Fortsetzung
Kontrolltheorie
Einflussgröße
Folge <Mathematik>
Nichtlinearer Operator
Sequenzdiagramm
Approximation
Kontrolltheorie
Stichprobenfehler
Firmware
Programmierumgebung
Kontextbezogenes System
Bitrate
Arithmetisches Mittel
Verknüpfungsglied
Menge
Festspeicher
Strategisches Spiel
Vier
Ordnung <Mathematik>
Programmierumgebung
Schlüsselverwaltung
Instantiierung
Rückkopplung
Subtraktion
Geräusch
Term
Stichprobenfehler
Freiheitsgrad
Quantenelektrodynamik
Geräusch
Perspektive
Quantenfeldtheorie
Soundverarbeitung
Fehlererkennungscode
Protokoll <Datenverarbeitungssystem>
Zwei
Gibbs-Verteilung
Vektorraum
Physikalisches System
Inverser Limes
Fundamentalsatz der Algebra
Rückkopplung
Flächeninhalt
Loop
Offene Menge
Quantenelektrodynamik
GRASS <Programm>
Offene Menge
Quantenfeldtheorie
Nebenbedingung
Formale Grammatik
Maschinensprache
Ungerichteter Graph
Abstraktionsebene
Hamilton-Operator
Raum-Zeit
Freeware
Puls <Technik>
Algorithmus
Vorzeichen <Mathematik>
Gruppe <Mathematik>
Gerade
Phasenumwandlung
Addition
Dicke
Befehl <Informatik>
Hardware
Kontrolltheorie
Elektronischer Programmführer
Stichprobenfehler
Güte der Anpassung
Digitalfilter
Dynamisches RAM
Biprodukt
Rechnen
Bitrate
Fourier-Entwicklung
Dichte <Physik>
Motion Capturing
Digitalsignal
Injektivität
Menge
Datenverarbeitungssystem
Rechter Winkel
Physikalische Theorie
Festspeicher
Heegaard-Zerlegung
Ablaufverfolgung
Ordnung <Mathematik>
Charakteristisches Polynom
Fitnessfunktion
Instantiierung
Subtraktion
Große Vereinheitlichung
Geräusch
Doppler-Effekt
Systemplattform
Stichprobenfehler
Leck
Bildschirmmaske
Domain-Name
Informationsmodellierung
Reelle Zahl
Perspektive
Globale Optimierung
Theoretische Physik
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Datenstruktur
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Propagator
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Eindringerkennung
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sinc-Funktion
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Suchverfahren
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Total <Mathematik>
Minimum
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Syntaxbaum
Schnitt <Graphentheorie>
Kontrolltheorie
Analogieschluss
Einflussgröße
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Quarkconfinement
Reihe
Quantencomputer
Globale Optimierung
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Datenfeld
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Programmiergerät
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Information
Pendelschwingung
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Zellularer Automat
Punktspektrum
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Physikalische Theorie
Ordnung <Mathematik>
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Subtraktion
Mathematische Logik
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Geräusch
Sigma-Algebra
Stichprobenfehler
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Bildschirmmaske
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Soundverarbeitung
Verschiebungsoperator
Transinformation
Konvexe Hülle
sinc-Funktion
Wärmeausdehnung
Hill-Differentialgleichung
Resultante
Punkt
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Minimierung
Adressraum
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Übergang
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Physikalische Theorie
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Quantenelektrodynamik
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Firmware
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Großkanonische Gesamtheit
Bit
Punkt
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Momentenproblem
Quantenfeldtheorie
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Kartesische Koordinaten
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Kardinalzahl
Einheit <Mathematik>
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Analytische Fortsetzung
Kontrolltheorie
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Lineares Funktional
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Kontrolltheorie
Stichprobenfehler
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Firmware
Digitalfilter
p-Block
Rechnen
Frequenz
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Nebenbedingung
Subtraktion
Quader
Wasserdampftafel
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Globale Optimierung
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sinc-Funktion
Klassische Physik
Spinor
Sequenzdiagramm
Dämpfung
Rechter Winkel
Mereologie

Metadaten

Formale Metadaten

Titel Quantum Firmware: Engineering error-resistance at the physical level for robust quantum computation
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Biercuk, Mike
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 10.5446/35323
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract Realizing functional, useful quantum computers requires that the research community address both fundamental and practical challenges pertaining to how hardware errors are suppressed to tolerable levels. In this talk I will focus on efforts towards the development of dynamical error suppression as "quantum firmware:" protocols that are designed to suppress hardware errors at the physical level. We introduce an efficient, experiment-friendly filter-design framework for understanding the performance of various pulse sequences, making connections with familiar concepts from electrical engineering and digital signal processing. This perspective allows a concise formulation of known sequence characteristics, but also reveals previously unappreciated practical impacts of system-level constraints. In addition to studying dynamical decoupling, we extend this approach to nontrivial logic gates, providing a simple new technique to calculate and suppress hardware gate error rates. We validate the filter-design approach through experiments using trapped atomic ions as a model quantum system. Our results reveal the performance benefits of optimized dynamical decoupling sequences and demonstrate a technique for sequence optimization through multidimensional search and autonomous feedback.

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