Yes.
STFC-RAL-CR03 R61: thanks very much for the invitation. And hopefully, let's say I'll give an idea of what the research I go into contribution for particle physics. So just before we start. You know.
STFC-RAL-CR03 R61: Ibm advertising, I guess. But this is a quantum feature. Let's see if I can work out Jesus.
STFC-RAL-CR03 R61: So I see the quantum future somewhere around here. And this is pretty pretty minimal and this is just all of its fridge. But I wanted to show this makes me look like I I'm not sure it's tonight. I'm other happy hands on experience. But
STFC-RAL-CR03 R61: so
STFC-RAL-CR03 R61: how we can use as a whole for general calculations. And then the whole and I'll give a couple of these spaces. So the showers, which is really why, I've been focused on in the past few years.
STFC-RAL-CR03 R61: And then a recent more experimental approach, which is a track finding, using this quantum template, matching approach and track finding.
STFC-RAL-CR03 R61: And so, to begin with, it's a bit of this, a new. So back in the eighties, Feynman said, nature is quantum. And so if you want to simulate it, you need a quantum computer in slightly more flowery language. But it's new power frames
STFC-RAL-CR03 R61: and since then quantum computers have really come on quite a lot. I'm back in 2022 they were in the breakthrough Friday that we developed back in the nineties and eighties and also the 2020 information really, Elaine aspects, and so on and and improving
STFC-RAL-CR03 R61: and so there since. The the, you know the sales of these devices back in the eighties there's been a huge effort into 3
STFC-RAL-CR03 R61: Most popular, in my opinion, are, are the superconducting bunch of computer which is based on on qubits definitely, in terms of analog using believes that 3 I'll give a quick concentrate on algorithms
STFC-RAL-CR03 R61: been developed for super devices. Yeah.
STFC-RAL-CR03 R61: But before that, the first 2
STFC-RAL-CR03 R61: that I've really been use very much positive physics already as well, essentially sets up a ising spin model. And you define your problems such that the ground state of the ising spin model is your your answer. Essentially. So, they're very well suited to optimization problems. Where, for example, I can set up some energy landscape. And I anneal
STFC-RAL-CR03 R61: I'm essentially I can. I can find that most of the use for audio about it. kind of confusing as well. So you can dial up your problem, Hamiltonian, from A, from a Hamiltonian. This is
STFC-RAL-CR03 R61: optimization problems. However, they are constructed from many, many noisy qubits which are very easy to control, and it's like you can't control them during the algorithm. You can't just let them be. And so they're not universal, very good. What they do. But we can't write a universal date set for these sorts of devices.
STFC-RAL-CR03 R61: And then there's a new kid on the block switch manipulate photons. So they benefit from the infinite fog. Space that's available from a photon.
STFC-RAL-CR03 R61: And these are known as continuous variable devices, because I can encode photon, and I can deform this photon in many ways maybe talk through photons and that's how we can get a universal gate operation
STFC-RAL-CR03 R61: with a heavy caveat at the minute. Everything in Gaussian.
STFC-RAL-CR03 R61: If we have non Gaussian operations and we have a universal gate set. But currently nonlinearities and optical material are not happening big enough, not strong enough to to give us these non Gaussian operations. But there are many measurement base approaches that can do this.
STFC-RAL-CR03 R61: And one Downside is also one of the main selling points of these devices is that they weekly interact with the environment. So from a coherence point of view that they're really good. You can set the photon off and it's probably gonna be in the state you set up when at the end when you measure it, but
STFC-RAL-CR03 R61: that's a downside trying to make them entangle them with a photon is is very different.
STFC-RAL-CR03 R61: However, we are trying to use these devices. Now simulate once Bill series. So so watch this space. I totally could tell you a little bit more about that. But they quite tricky teams a lot about quantum multi.
STFC-RAL-CR03 R61: But the the big pillow of quantum competing really, what's had the most kind of money and research thrown at it in 19 is a super looking computer which works on a qubit basis. So a 2 state system. Where I can flip a key bit between 0 and one and have a linear superposition of 0 and one.
STFC-RAL-CR03 R61: So we can model the qubit as a block sphere which top right corner. Once I get this working.
STFC-RAL-CR03 R61: And essentially, I can say that the state of that qubit is this vector on the surface of the box fit which is a linear superposition of these 2 basis states called the computational basis and 0 one. And I can define any State on on this on this box fit.
STFC-RAL-CR03 R61: and when I measure, I collapse that down to a 0 or one which I can project onto a password. So this is a single key bit. And when we apply many of these key bits together, we can have multiple Ga multiple qubit operations and single keyword operations. So, for example, in the bottom, right and corner here we have this rotation which can rotate this. And then I can couple to key bits together, using a C not operation.
STFC-RAL-CR03 R61: And these Senate operations essentially act by
STFC-RAL-CR03 R61: almost taking a condition of what the keep my my control keep it is in and then applying an operation. If that control keep, it is in the state. So here a a normal C not takes a keep it. That's in the one state, and if the control keep, it's in the one state I flip the target state. Otherwise I leave the target state B,
STFC-RAL-CR03 R61: and so
STFC-RAL-CR03 R61: these are very powerful devices are highly controllable. I can. Now, I have this gate set. I can control the key bits as the algorithm goes along. However, I only have a very small amount of qubits, and these key bits are are quite noisy, and it's these noise effects, which really at least be coherent in the devices, and that's the real thing. It's holding quite a minute.
STFC-RAL-CR03 R61: With these sorts of devices. I can write these circuit diagrams, and I'll be using circuit diagrams throughout the talk. So just to give a quick introduction and to to what they are. But essentially here I have a 4 key bit system. So these horizontal lines are individual key bits. These boxes are single gate operations, and then these.
STFC-RAL-CR03 R61: That's for lines of control. So for example, here I control from the first qubit, and I update the third qubit and then, for example, that that carries along. And here I have it double control to control and update it for.
STFC-RAL-CR03 R61: And so these circuit diagrams are really useful. And I'll use space on. But essentially, these devices are are what Ibm and Google are aiming to use. And we can achieve a universal
STFC-RAL-CR03 R61: computational method using these devices.
STFC-RAL-CR03 R61: So that was a little bit of a whistle stop touring to the ideals of quantum computing. But really, when you get to use them, we're in this noisy intermediate scale quantum era, according to John Prescott.
STFC-RAL-CR03 R61: and that means essentially that we have no continuous quantum error correction.
STFC-RAL-CR03 R61: So these devices are very prone to errors from progress effects as well as from environmental.
STFC-RAL-CR03 R61: And so we try our best to to categorize these errors and the main 4 which I'll talk about later in in when it comes to actually designing algorithms. Come from these multi qubit gate operations. So this C not operation where I'm applying essentially also to to Quebec, is very prone to high errors in comparison to single gate operations, where I'm just posting a single qubit.
STFC-RAL-CR03 R61: and then
STFC-RAL-CR03 R61: almost extension of this, we have these things with swap. So if I want to apply a conditional
STFC-RAL-CR03 R61: 2 key operation across 2 key bits, I need those 2 key, this 3 next to each other, and so in the architecture I have to swap the States to the key bits, which in their turn take 3 of these senior operations. So the errors become very large, though cumulatively large.
STFC-RAL-CR03 R61: And so these multi key operations are bringing down. They associate error with these operations is very important to the Department of Front.
STFC-RAL-CR03 R61: and then more on a hardware point of view. There is the so-called T. One Times, which you're a CEO imported when it comes to the which is the time it takes for Cuba to to decay from exosital state back to its ground states.
STFC-RAL-CR03 R61: And so if I, my algorithm and leave it alone. And my algorithm is longer than that. It's t one time the chances are that the key bits not really and safe. I want it to be in and so
STFC-RAL-CR03 R61: I have to take this into account when I'm designing algorithms. If I want to get high fidelity resource back in.
STFC-RAL-CR03 R61: and finally to say that
STFC-RAL-CR03 R61: kind of ties into t one time, if we have really really long circuit desk, that that are longer than the T one time to these cubits. The chances are that I'm just making noise at the end of the algorithm. I'm not actually gonna get anything useful. And so
STFC-RAL-CR03 R61: there are many challenges into divide deciding algorithms which also makes it very exciting. So computers we always have to some extent Internet resources. And we don't need to be very good architects, and so really forces you to to write efficient algorithms that can do to what you need.
So
STFC-RAL-CR03 R61: the way that we, we combat these errors comes from something called transfer.
STFC-RAL-CR03 R61: Essentially, we can take into account that we have to take into account the hardware of the device, and so that we know the qubit mapping which qubits can talk to which qubits and so on. So there's a real and study of how we can put these average onto the device. And we'll we'll talk about that later on when I show you an example with the partnership.
STFC-RAL-CR03 R61: So that was a wish to stop touring to to the overall bunch of users. So I usually stop here. If there's any questions before I move on about how we use these devices? If not, I'll go into showing you how many.
STFC-RAL-CR03 R61: since you talked about times. What are the sort of characteristic times you're talking about for
STFC-RAL-CR03 R61: being able to keep things in the state. Yeah. So we're talking a milliseconds, I think, for for t one times. So it depends on the the architecture entirely the device we're using. I think the T one time was 100 ms or something.
STFC-RAL-CR03 R61: and the algorithm with longer than that. So let's see, I think most time it it changes and Ibm off. So really tell you exactly what they're doing. But in the
STFC-RAL-CR03 R61: but it's available on, they've just released any assistance to which I thought about later. So that may have all changed. in la.
STFC-RAL-CR03 R61: okay, but no more questions I go to to and showing you sort of quantum algorithms which we can utilize in part considers. So one I'd like to to emphasize is the quantum war.
STFC-RAL-CR03 R61: So I moved to the right.
STFC-RAL-CR03 R61: If I do this for a hundred point flips or a hundred steps in my wall.
STFC-RAL-CR03 R61: and I do that, walk a million times and measure the final position of the walker. I get what we all expect happen I get Gaussian. So we see this with accounting board. You drop lots of full bearings through through distribution.
STFC-RAL-CR03 R61: Now, if I move to the
STFC-RAL-CR03 R61: I move my walk into position.
STFC-RAL-CR03 R61: and if I do this many, many times I can express it at the hill, so I have all of the
STFC-RAL-CR03 R61: decisions on my number line augmented by this coin operation.
STFC-RAL-CR03 R61: and so my walker will move through this
STFC-RAL-CR03 R61: single underlying difference between possible walk and a classical walk.
STFC-RAL-CR03 R61: And the once walk isn't actually random. It's a pretty unitary operation. A task or random walk would require measurement. But here we're assuming that I keep the water informed throughout. I don't measure any time. I only measure the final position.
STFC-RAL-CR03 R61: So I do. Exactly the same might be 100 once and point flips. And I measure, and then I do it 1 million times, and I get a distribution that's vastly different from classical.
STFC-RAL-CR03 R61: and actually the probability of ending when you began. It's almost 0, and you have a higher probability of ending quite far away.
STFC-RAL-CR03 R61: Actually, you can show that the quantum walk is almost ballistic movement in in both directions.
STFC-RAL-CR03 R61: And so they, if you do some tricks with working out the Asian. You can show.
STFC-RAL-CR03 R61: Actually, the spread of the quantum walk is key faster than a class walk. So we can. We can search this from space and be faster. And so it's starting to hint at speed of if we apply and search algorithms to search operations.
STFC-RAL-CR03 R61: So this is a gate wise going back to
STFC-RAL-CR03 R61: grows the depth of the service very well suited to to nest devices, and you can see here that I have the
STFC-RAL-CR03 R61: point. Operation. Single operation doesn't necessarily need to be hard on 1 point. But that's the point we just find here puts into 50 50 super position.
STFC-RAL-CR03 R61: And then I have an increment operation.
STFC-RAL-CR03 R61: And so if we work this out essentially, if this is in the one state, then in binary, essentially, I increment the number encoded on the position space.
STFC-RAL-CR03 R61: and then I have a decent operation. So this is in the 0 state. I id commend the the number in line. And this is a single offer, a single step in the possible. So for for 100 steps, I apply this algorithm under time.
STFC-RAL-CR03 R61: and it just creates any
STFC-RAL-CR03 R61: so universal competition method themselves
STFC-RAL-CR03 R61: approving a CEO. This is a bit more difficult just looking at it.
STFC-RAL-CR03 R61: But Zaghari
STFC-RAL-CR03 R61: once have been shown. So there's a type of quantization of Monte Carlo which has been shown to to have a speed up when put into the quantum more and framework. And so this stops to ring alarm bells and particles who love a mark off chain. Monte Carlo. If we can start to speed up these sort of algorithms then that would be and we'll see how we can apply that to to pop chat.
STFC-RAL-CR03 R61: And so yeah, so the. It's been proven under the condition that these algorithms are reversible. And they do. And
STFC-RAL-CR03 R61: so an interesting extension of a quantum walk is to allow the walk to have memory. And so memories are not very
STFC-RAL-CR03 R61: good name for this sort of thing. We don't do any form of measurement and put it onto Qram or anything like that. This is mainly just allowing us to essentially swap states in system that allow us to have arbitrary dynamics. And this is so memory was coined a long time ago. But yeah, there's no QR,
STFC-RAL-CR03 R61: so essentially, we can augment our Hilbert space a step further and allow our walker to move in a memory space as well as a position and coin space.
STFC-RAL-CR03 R61: And this, as I said, allows us to have obviously dynamics. And by, for example, remembering a coin operation or a position that the walker has been in.
STFC-RAL-CR03 R61: And so actually, we can regain classical dynamics. So we can regain the randomness of a classical random walk in full unitary evolution.
STFC-RAL-CR03 R61: So this is very advantageous, for when you want to, for example, couple that quantum, walk into a fully quantum system that you don't want to collapse any of the wave functions. And and
STFC-RAL-CR03 R61: however, they're very tight conditions on when advantage comes about, and whether or not we can use these to really get us to speed up. That we are aiming them to get for 400
STFC-RAL-CR03 R61: they've already been used and we use doing this paper here
STFC-RAL-CR03 R61: to essentially improve a very simple part and shower and the the show today is actually an improvement on this paper. But essentially by reframing our algorithm in an algorithm that quantum computers naturally, understand. For example, the wall.
STFC-RAL-CR03 R61: we were able to simulate only 16 times the the shower depth of the problem shower using half the amount of qubits. And so really, we're seeing how these
STFC-RAL-CR03 R61: by thinking differently and and using kind of quantum architectures already, we can make very efficient average.
STFC-RAL-CR03 R61: So why are we interested in in physics. I'll talk about higher physics. But particle physics on the whole.
STFC-RAL-CR03 R61: I'll give the the use case, which is event event generation. So we're colliding protons together at some alarming rate, at some alarming energy.
STFC-RAL-CR03 R61: And essentially they make a big mess of order, 1,000 particles in the in the detector
STFC-RAL-CR03 R61: and the description of these events is highly complex. And so you see, on the drive, this is the as you can see, it's very complicated. And this is actually a massively dial down interaction between 2 protons and you can see you. We can break it down to many release.
STFC-RAL-CR03 R61: Once Carla generated in our most successful approach to simulating such a such a collision event. And they explored the factorization PC, so we can take this immensely complex system and essentially break it down into 4 steps.
STFC-RAL-CR03 R61: And so the first step is obviously the part and then see function where we have their workout. What the hell is in these protons? They fly towards each other
STFC-RAL-CR03 R61: and hopefully, give or take a few initial state radiation showers. We have 2 of these come in from the protons, snap each other, make something new in the middle, the aim for all of us, and that new thing for the charge. And so
STFC-RAL-CR03 R61: from this hard process which is 11, which is extremely high energy, we've got to get down to this high multiplicity system of hypnotization, which is relatively low energy. And the way we do it is by radiating and essentially in the part and shower. So we have this problem shower which we can essentially pull away for the energy scale.
STFC-RAL-CR03 R61: And these papers I've linked here are quantum computing
STFC-RAL-CR03 R61: algorithms which attempt to do each of these steps, and we'll be talking about the ones that are right for me.
STFC-RAL-CR03 R61: So this is all well and good. But yeah, how long does it take to do this. And in fact, actually, if you look at Atlases CTO hours which I think is 3 billion, which I think I don't know. Correct me if I'm wrong, but I think it's going to increase by factor of 10 this year CPU hours for the simulation 15 of that is taking on the hard process and and the button.
STFC-RAL-CR03 R61: And so any improvement we can do in these simulations, any speed of could be really a beneficial to it as we move to an era of higher, more.
STFC-RAL-CR03 R61: And guessing. Tomorrow, we should put online this algorithm. But we have to start thinking about the, for example, and showers full of lives and kitchen.
STFC-RAL-CR03 R61: So along with the face license, so improving the hard process and the bottom.
STFC-RAL-CR03 R61: So just to give a quick overview to for patent showers.
STFC-RAL-CR03 R61: As I said, it's what we radiate these additional parts to get this down from the hard process to the hard hyponization process. And this affects is
STFC-RAL-CR03 R61: And so the cleaning mode is very nice. We have a Parthen comes along parallel, and we split the momentum between these 2 parts. With this factor that
STFC-RAL-CR03 R61: I'm these are very hot showers.
STFC-RAL-CR03 R61: And so that
STFC-RAL-CR03 R61: quantum algorithms before the one I about show you focus completely on the cleaning limit and didn't take into account any specs come in from the soft mode where we produce Parton. We're banishing 4 min.
STFC-RAL-CR03 R61: And so this only allows after factorization.
STFC-RAL-CR03 R61: And so we have to take into account and deal with this partial factorization. But, luckily for us, the leading terms in the soft limit include the clinic limit. So it's a good place to start from shadow development.
STFC-RAL-CR03 R61: which we then split we do that.
STFC-RAL-CR03 R61: and so you might have to. You might as well repeat this. But essentially it allows for experience to be taken very straightforwardly. So we can essentially have symmetric diagrams. And also mentioned translation is done by essentially Rico sharing from different.
STFC-RAL-CR03 R61: I thought
STFC-RAL-CR03 R61: so I have the mattress. I'm gonna put a horrific and
STFC-RAL-CR03 R61: equation on the board at least, put in the purple box. So this is the master equation of a box and it's a recursive. So essentially so, it's a regressive equation. So essentially, we have the first term here, which is and that is the probability that my part on traverses from this virtual.
STFC-RAL-CR03 R61: And then second term is essentially my exclusive decay. Probability, which says that my apartment goes from T to some other.
STFC-RAL-CR03 R61: so it's easy to see from 2 virtualities and missing one or more platforms. And then, after we have a message one. We record that
STFC-RAL-CR03 R61: that's where it gets information.
STFC-RAL-CR03 R61: And this as I said, the non emission probability is it's detected by any limit we can essentially just. And then time, device, fishing function. Essentially, we have a shower.
STFC-RAL-CR03 R61: And we have this ability which we have to deal with.
STFC-RAL-CR03 R61: And these parameters at C and T.
STFC-RAL-CR03 R61: Our face based variables, and we have a choice on one how to define these face based variables but most all current implementations of devices. Continuous variables and, as I said before, the tonic devices are a continuous variable device but super looking continuous variable is.
STFC-RAL-CR03 R61: and so is this an air on the coffin? For our quantum shower? Luckily, the answer is no and in this paper we showed you can take a model of discrete Pcd, very short eye review. And you can build a problem shower on a discretized Qcd Facebook.
STFC-RAL-CR03 R61: So just through some more maps. We have to make several apps rotations in order to discretize our Qcd system so that we can put a problem shower onto a problem device.
STFC-RAL-CR03 R61: And so the first choice we made is that we parameterize our face space. We use our face space parameterization to be the glue on the transfer cement, the rapidity, and by doing this we restrict our emissions of the gluons to a triangular face is trying to face here.
STFC-RAL-CR03 R61: And essentially, if I modeling out these noses
STFC-RAL-CR03 R61: and I gave her a talk
STFC-RAL-CR03 R61: some people that the loan claims to and call them noses for the whole call. But this is officially known as the secondary London from the primary type of update Conference before. So we have this primary lung plane here, and we fall out these noses, which is secondary.
STFC-RAL-CR03 R61: By making this parameterization our inclusive portability becomes a little bit more simple from the previous. So essentially, we now have this constant CR, 4 x over pi d capita, t. One. So things are looking good and we've now defined Kappa here to be
STFC-RAL-CR03 R61: related to doing transverse momentum. And the minute it's a molecule master. And so this high L, essentially, it's a they're not drawn. It's an equal after triangle. Essentially.
STFC-RAL-CR03 R61: No, it's not only that triangle, the height and the base are the same. So
STFC-RAL-CR03 R61: to get onto.
STFC-RAL-CR03 R61: And so if we ignore
STFC-RAL-CR03 R61: gluons split into 2 box, which is actually not a bad approximation at high energies. And we examine only the the transverse momentum dependent. When we go. S, we see that actually to first order. It's just a constant times one over Kappa, where now we've defined a lambda here, Lambda, Qcd.
STFC-RAL-CR03 R61: And and say, that goes up by BC.
STFC-RAL-CR03 R61: And so this leads for our increases to pay probability, and Dp to to take a really really simple form.
STFC-RAL-CR03 R61: and it's just d kappa by Kappa and dy by Delta YG, where, when we look only at Gcg splittings does. YG. 11, 6.
STFC-RAL-CR03 R61: And then, if we interpret this really coupling as again lost equation. we see that actually gluons that are produced within
STFC-RAL-CR03 R61: this rapidity range 11, 6 are actually reabsorbed into a single coherent gluon.
STFC-RAL-CR03 R61: and so we can start, slice up our face space and into these slices of Delta YG.
STFC-RAL-CR03 R61: And so, if I am at 2 glue ones in this space, I can just model them as a single, very nice we have a. But we still have continuous kappa.
STFC-RAL-CR03 R61: So to start the fully discretized system, we have to go back to this idea of folding out these noses.
STFC-RAL-CR03 R61: and if we look at
STFC-RAL-CR03 R61: the original triangle, the height is l, and the base is L. Then if I fold out from a height little L, then the base of this fold will be L by 2,
STFC-RAL-CR03 R61: and if I do a bit of rearranging, I show that actually, then, because I've discretized through the rapidity span on the on the base of this triangle, this fold, then actually the height of this triangle also has to be and discretized, and this time into into slices of 2 does watch it
STFC-RAL-CR03 R61: so my face base now, is fully just dive into these tiles that are dud YG by 2 dot YG and so that I can select a glue on any glue on in this tile I can make a coherent glue on, and I just for ease. Plant that coherent blue one in the center of these tiles. And I'll deal with the fact that I need to smear that glue on a little bit hmr.
STFC-RAL-CR03 R61: and so this is hard to look good and something we can put onto a quantum computer. But then we went a little bit step further. So we weren't going to look at the
STFC-RAL-CR03 R61: the pseudocode. But if we put it into the non emission probability, we see that actually, the probability of selecting
STFC-RAL-CR03 R61: a single tile here in this slice is one over the number of slices.
STFC-RAL-CR03 R61: Sorry one over the number of tiles in this slice, and we can treat each slice individually. So I can just go here. Probability selecting this one is obviously only percent here, 50 50 here, the third each.
STFC-RAL-CR03 R61: and then a quarter to reach, and so on. And so now I can sample from this face. It's really simply just fires, and she's living a coin at each point on the baseline. So I use the word coins to give a hint that what sort of algorithm will use.
STFC-RAL-CR03 R61: So we then take it one step further. and realize that actually to and
STFC-RAL-CR03 R61: regain all the kinematics of the pardon shower. All you need to know is the growth structure, the baseline of this of this nose and this this lawn plane growth.
STFC-RAL-CR03 R61: And because We can only fold up by hour by 2.
STFC-RAL-CR03 R61: This grove is
STFC-RAL-CR03 R61: constrained within an area smaller than the original triangle.
STFC-RAL-CR03 R61: And so then we start to look good. So essentially, we can build this lattice on this 2 dimensional lattice on this area. That's less than our original triangle, and we can develop a 2 dimensional quantum walk or 2 dimensional random walk, which was sample from our system. So I go. I start in the left here.
STFC-RAL-CR03 R61: and I hop along to the next slice. I flip a coin here. It's 50 50. If I select that I'm going to fold out. I step out into the fold and I step back, and then I step to the next slice, and I throw another coin, and here I didn't succeed. So I carry on. I flip through another coin, and I see, actually, I'm gonna emit from the top slice, so I fold all the way out and come all the way back.
STFC-RAL-CR03 R61: and I keep doing that. And then I apply that recursively for each of the folds that I've developed as I've gone along.
STFC-RAL-CR03 R61: And so we can put this absolutely even simpler if I say that I rotate my my space every time I fit the coin. Then I can build a one dimensional control, which is what I've done essentially in this algorithm. So we have a single coin operation which is on the baseline. I always do a baseline
STFC-RAL-CR03 R61: it, and this Lander is essentially measuring the distance that the wall takes.
STFC-RAL-CR03 R61: I then decide whether or not I'm gonna step out into the into the fold with this shift operation that controls from my point operation for some bookkeeping. And
STFC-RAL-CR03 R61: I essentially
STFC-RAL-CR03 R61: record where the the glue on. If there has been a glue on emitted then I record the new one. And then finally, I give my algorithm the chance to remember whether or not
STFC-RAL-CR03 R61: there has been a glue, and I don't always use this, but if I want to, I can use it. and then I just measure the baseline and the number of blue ones, and I can reconstruct all the kinematics from a one dimensional quantum wall.
STFC-RAL-CR03 R61: So we we looked at doing this for let data. And actually, for let data, there are only 24 unique pro structures, if you choose.
STFC-RAL-CR03 R61: sensible values of PCB, Ecd, we see that only 24 unique growth stretches. And so these are all the 24 gross riches. And actually, you can think well. Now we only have transport. Why don't we just enumerate them on a classical device and go through them really quickly? And in fact, actually, yes, you can. We saw that by thinking computer, we massively set up a classic library
STFC-RAL-CR03 R61: which is exciting. But but we wanted to see it once. Video,
STFC-RAL-CR03 R61: so, yeah, so these are our growth switches. So you can see, A is where there has been no blue ones produced. And then X is where we produce many, many blue ones.
STFC-RAL-CR03 R61: and I get a lot sick from my my message branch for the next plot. But I'd like to say that we made this plot first, which took a lot longer than the next plot. So the the lettering is not perhaps the best, and to choose when you come to see the the results.
STFC-RAL-CR03 R61: So then, once we generate to that growth device we then handle essentially 50 to do hybridization. And the way we keep that just to to to deal with the. And then essentially, we read off the dipole masses from our dials and
STFC-RAL-CR03 R61: from these from the grove and then we generate uniformly distributed can go.
STFC-RAL-CR03 R61: And here we apply this mapping. But in essence you can apply any momentum mapping and produce a a branching event.
STFC-RAL-CR03 R61: and so then we run it. As you can see. Now, we should really put in where he is. But fun. So we ran it on a quantum simulator, which is where we have these black dots.
STFC-RAL-CR03 R61: And essentially, we, we get bang on with what we expect classically, which is good news. But then we run it on the Rbm ibm Rgs device, which is a 27 qubit NIST device. And, as you can see. Actually, it's quite noisy.
STFC-RAL-CR03 R61: And so if you think back to the beginning, when I mentioned.
STFC-RAL-CR03 R61: you can see that there seems to be some pattern between. Each one, it seems to oscillate up and down, especially towards the end, between being slightly over and then being slightly under
STFC-RAL-CR03 R61: and that's because the first glue on. If we go back to these, the first blue on the left hand side, and essentially we flip a a qubit, and then we leave it alone at the start of the app, and, as you can see, every one of them has alternating whether or not it has the first glue on or not.
STFC-RAL-CR03 R61: And so. after
STFC-RAL-CR03 R61: pulling our hair out for quite some time, we realize that actually, if we pass it with the came back to its ground state most of the time. And so
STFC-RAL-CR03 R61: we have this slight enhancement in in groceries that don't have this glue on emitted and
STFC-RAL-CR03 R61: the deficit in in one city.
STFC-RAL-CR03 R61: But we ran essentially for producing a desk in lab
STFC-RAL-CR03 R61: and then as I said, the main source of errors is
STFC-RAL-CR03 R61: But we thought, Okay, well, we've got this farm. We spent some money to run it on a quantum device. We may as well see what happens and actually, 50 is pretty good at dealing with with noise. It deals with Monte Carlo data. And these inputs are correlated. So it. It dealt with this this noise pretty well.
STFC-RAL-CR03 R61: as you can see, it's still not exact.
STFC-RAL-CR03 R61: But we get a pretty good you know. Definition of you know that we follow the data pretty well.
STFC-RAL-CR03 R61: And this Dqc shower is the classical out analog of the quantum shower. So we do it in exactly the same way. But we just showed. If we put through this, obviously, we'll see. It just goes through all the data points. So it probably wasn't a fair comparison. But this is a live to live comparison.
STFC-RAL-CR03 R61: And we get an encouraging data description. The best time I, quantum computers been used to generate realistic shower data that's comparable to to real
STFC-RAL-CR03 R61: live data as well. Yeah.
STFC-RAL-CR03 R61: so are there any questions about the same algorithm
STFC-RAL-CR03 R61: device. So we see the error. So we enumerate all of we don't generate
STFC-RAL-CR03 R61: in the classical algorithm. We don't generate the growth. We just give them a wait and then select.
STFC-RAL-CR03 R61: Okay? So
STFC-RAL-CR03 R61: we also applied another quantum primitive algorithm, essentially problem. And and
STFC-RAL-CR03 R61: this is this is in collaboration with,
STFC-RAL-CR03 R61: okay, it's quite a pefy.
STFC-RAL-CR03 R61: Okay? So so made a joke. My experimental friends made a joke that as a theorist act to explain track finding when I went to Bristol to some of the leading months in track finding but anyway of charge passports through the through the track. Essentially. So we need to identify these charge particles.
STFC-RAL-CR03 R61: And we use highly granular detectors to do this silicon detectors which can measure of the charge as it goes through through the system.
STFC-RAL-CR03 R61: And memory. I've been shown to be very useful, especially, for example, in experiments such as Cdf firm.
STFC-RAL-CR03 R61: However, as we move to to more highly granular detectors these are gonna become ineffective, essentially. But the side of your am chip is gonna be enormous. So the idea is that maybe we could improve this using a quantum computer which essentially has an exponentially growing help space which we can encode
STFC-RAL-CR03 R61: information on them.
STFC-RAL-CR03 R61: So
STFC-RAL-CR03 R61: this image on the left-hand side shows a toy trucker. We go a toy trucker, and we try to apply a quantum template mapping. So a quantum version of associate memory but slightly enhanced, using the Grover apple
STFC-RAL-CR03 R61: to try and identify tracks that will lead the this sort of hit pass in the United States.
STFC-RAL-CR03 R61: So we do this by utilizing, as I said, another quantum primitive, known as the quantum amplitude, amplification
STFC-RAL-CR03 R61: and essentially the aim is to identify a state within a day database. That's a winner. So we have a a state that we're looking for in this database, and we want to apply quantum algorithm to a superposition of this of our database that will always return a very high probability the state we're looking for.
STFC-RAL-CR03 R61: And so the way we can, we can imagine this is, we can imagine it. Yeah, geometrically. So we can say, okay, in our Y plane.
STFC-RAL-CR03 R61: we have our winning state. This is the state that we want to find. And our explain here is a superposition of our
STFC-RAL-CR03 R61: and our database without the winning space. So we want to make them orthogonal to each other. Attention.
STFC-RAL-CR03 R61: And so we can encode our database onto the system. And
STFC-RAL-CR03 R61: here you go. This is a
STFC-RAL-CR03 R61: each of our elements in our database. N is encoded in some equal superposition.
STFC-RAL-CR03 R61: And then, essentially, I need to work out a way of making this vector, become this vector.
STFC-RAL-CR03 R61: and so
STFC-RAL-CR03 R61: I can write a constant routine called oracle, which will mark my interesting state. So here we have a function F of X, which is one. If X is equal to our mark, state our winning state. So I should change that to a W. So if this X is equal to our winning state, then essentially, we apply a negative phase to the state. So our system is now.
STFC-RAL-CR03 R61: I completely equal to position. One of them has negative face. Now, if I measure now, there's no difference. Obviously II can't measure this phase. So I need now need to apply something which allows me to amplify the amplitude of this month as this diffuser takes this the
STFC-RAL-CR03 R61: the form here, where essentially idea, a dagger. This is a phase
STFC-RAL-CR03 R61: flip on the 0 state and a 9, and apply a backpack.
STFC-RAL-CR03 R61: And so once I apply the oracle, I can mark a state essentially reflected around the S front.
STFC-RAL-CR03 R61: and then the diffuser geometrically. Well, now.
STFC-RAL-CR03 R61: allow me using this a dia s. 0 a to make a flip around the essence.
STFC-RAL-CR03 R61: And so now, I look like this user and are equal to the S state. Geometrically, I've rotated essentially towards the winning state. And if I do this many times iteratively, then essentially, this red state here is going to get closer and closer to the W.
STFC-RAL-CR03 R61: And as a optimum amount of time that you do that, and that is given here by the the floor of a 5 by 4 group N over M. Where N is the number of mark states in in my system. So if I have 5 target states in the system, then it will affect how many times on each other? 5.
STFC-RAL-CR03 R61: And so we see that actually, from sort of databases this quantum ampute identification gives us a pographic speed of polynomial speed up over classical algorithms which would have to search for each of the database elements one by one. And so that's how we would do it. For example, if we had a template
STFC-RAL-CR03 R61: different hits in our in our tracker, we'd have to look through one by one essentially, to to find
STFC-RAL-CR03 R61: preparation for track.
STFC-RAL-CR03 R61: I then apply this article, and how would I, for example, mark this? And so.
STFC-RAL-CR03 R61: if we look in the bottom right corner here. And and I say, Okay, well, my, what I want my 1 one state to be marked. Let's say that corresponds to some pattern in my pattern bank
STFC-RAL-CR03 R61: I control from the one state on the first, keep it and flip the phase, and the second keep it so. So, for example, here. So if it's 0 0. I do nothing to it, but if it's 1 one, I flip the face essentially.
STFC-RAL-CR03 R61: And so when I come to the diffuser, then now I have a full superposition for the 1 one State. As an active phase I applied essentially the inverse of State preparation.
STFC-RAL-CR03 R61: which will give us a another situation for which the 0 says, I identify, and I can return it back so month monthly, you can work, work your way through and realize that by this point we have enhanced the the amplitude of our our target state.
STFC-RAL-CR03 R61: So this is fine and this I suggested.
STFC-RAL-CR03 R61: essentially as as a way to do back in the ages of ways to do. Associative memory searches on a device, however, for tracking this isn't. We want to essentially hand it hit pattern online and get out something that will be outside. This is an interesting pattern.
STFC-RAL-CR03 R61: So we apply quantum template matching. So I forward my system by applying another set of key bits which mirrors that keep it to my template. So I have now other data, but add a template. Right? So
STFC-RAL-CR03 R61: I encode on the day to register my online data from the device and on my template register I have my, all my possible hit patterns my physical hit patterns, I'm allowed.
STFC-RAL-CR03 R61: I then have this
STFC-RAL-CR03 R61: article now, which is slightly different, so I can control from the state of my data. And I flip all the states corresponding to ones in the data, in the template register. So if we think about it, okay, well, if the if the data in the template register are the same.
STFC-RAL-CR03 R61: then this will make all of the qubits in my Templar to 0. So if I then do a phase flip on the 0 state
STFC-RAL-CR03 R61: then I've marked my my state I'm interested in, and then I flip them all back so that we had before what we wanted, but with the phase now on our market. And then I applied to the user,
STFC-RAL-CR03 R61: and I do this, yeah for the optimal t times and I should get back with my probability.
STFC-RAL-CR03 R61: the state that I was looking for.
STFC-RAL-CR03 R61: Okay. So here, for example, we have this diffusing operation again and we use this template register and dates register now to see.
STFC-RAL-CR03 R61: So we did this for our toy tracker, and we got some really fun plots out, but it's actually more interesting than it looks. Essentially, we had a initial superposition of equal probability of all of these physical tracks in our database. So we
STFC-RAL-CR03 R61: made some just for ease of encoding. We made some assumptions that the track couldn't be to curve and we used
STFC-RAL-CR03 R61: certain momenta ranges as well.
STFC-RAL-CR03 R61: And but essentially, we had 15 possible tracks that could go through this toy detector. And we see that okay for this track. We've identified it as being the one state which was just a set of zeros after this track. Okay, we can see this is the fifth track, and so we can return with high probability the correct match track.
STFC-RAL-CR03 R61: So this is oh, well, I good. What happens if I hand it data, for example, from the detector where one of the tracking modules is decided, not fire. But I now have some partial track data.
STFC-RAL-CR03 R61: and I am chip would break down this one to be, because, you know, it can't say, Oh, well, it could be that one. It could be this one. But constant computer allows us to to deal with missing.
STFC-RAL-CR03 R61: So if we don't include
STFC-RAL-CR03 R61: this part of the bit string, our cubit bit string in our oracle, then, essentially, we can allow for the 2 States to be measured at the same time.
STFC-RAL-CR03 R61: So here, for example.
STFC-RAL-CR03 R61: we miss this layer here, this layer in the fire. And these tracks all possible, essentially. And these tracks correspond to 8 and 9.
STFC-RAL-CR03 R61: And so the quantum computer can give you a track back when you have incomplete data which we can also design the system. So should it do this randomly. If you don't get your answer from looking at the complete data. You can randomly select Cubas not to measure or not to include in the oracle, and this couldn't lead you to tracks which are which are possible where you're missing data.
STFC-RAL-CR03 R61: So this is the quantum template matching algorithm we we design and essentially has a this is a quantum speed up of a polynomial speed up of how you would perform memory algorithms
STFC-RAL-CR03 R61: So any questions about that, if not, we can come to them at the end.
STFC-RAL-CR03 R61: So what next? 4 kinds of using impact builders?
STFC-RAL-CR03 R61: So I was talking to Avon actually, earlier about the effort in the Uk compared to efforts elsewhere. So most of the most of the effort in the Uk is focus on the theoretical science and developing Hamiltonian simulation, which is what Feynman suggested and hinted to back into the eighties.
STFC-RAL-CR03 R61: But there are many a a applications involved with this where we can start to see maybe this speeder will be useful. So there's a we really need a dedicated research effort in the Uk, and just this sort of
STFC-RAL-CR03 R61: algorithmic design. And the main hubs in Europe tends to be in Germany and obviously in Cern has a quantum technology in initiative and the Uk. Is somewhat lagging behind. And so at the moment we're very theory based. But it'd be nice to see a few more applications, especially from a quantum machine learning point of view where this could be really useful in the near term.
STFC-RAL-CR03 R61: but in terms of where we going,
STFC-RAL-CR03 R61: and what's going to be available to us?
STFC-RAL-CR03 R61: There are 3, count 3.
STFC-RAL-CR03 R61: The first time people want more qubits, and so just keep plowing as more qubits, but this becomes at some point when the errors in in very large queue systems become too large. This will just become an either. We won't be able to control. This will get completely deeper here resource at the end.
STFC-RAL-CR03 R61: So so if we're going to go for more qubits, we're going to need better technology. We need more technology. That is is fault tolerant. And there's a huge effort from Ibm and Google to make these cubits very fault tolerant.
STFC-RAL-CR03 R61: At the same time, it's playing out many, many keepers. I think the the amount of keepers you have makes Ibm more headlines than at the 120'clock. But in my opinion, we're kind of stuck with these noisy devices for some time.
STFC-RAL-CR03 R61: So if we want to make realistic algorithms, we're gonna have to be better at designing these these devices, and the research effort in the minute really is preliminary trying to build a state for which we can, we can start to build practical algorithms on these devices and using primitives that a quantum computer understands. For example, a quantum walk or the quantum phase estimation is a real step into how we can start to build more realistic.
STFC-RAL-CR03 R61: Now, the bottom right here
STFC-RAL-CR03 R61: is now slightly out of date. Ibm have now released their 1,000 qubit device in their system to
STFC-RAL-CR03 R61: which is shining than any of their devices. And they use more dry eyes this time to make it look better. But if you go online they release everything. But what I'm really excited about actually from Ibm is that they are now moving away from essentially fabricating a single chip looking at spreading Cuba chips together.
STFC-RAL-CR03 R61: And so essentially, that system to is a modular computer where you know, you have a which is 1, 2, 7, and then you buy another one, and you can make. And that's, I think, gonna be a very powerful path to way. We're gonna move to fault tolerant more fault, tolerant devices with with more, instead of trying to make a chip itself that has a thousand queues on
STFC-RAL-CR03 R61: which is the quantum
STFC-RAL-CR03 R61: programming language. And so that should be more stable. Now for people to learn and get into the field. And with previous systems, you'd set the Ph up on doing
STFC-RAL-CR03 R61: 1, 2, and then 50.1 3 comes down. It's completely different. So hopefully, now there'll be a learning tool. Hopefully, we'll see more.
STFC-RAL-CR03 R61: But just to summarize.
STFC-RAL-CR03 R61: Hi, this is really on the edge of this computational frontier where we have new. We have the the hailing online, which is, gonna give us on Friday to map data. And, as BBC told us few days ago, Fcc is coming but certain members aren't very happy about it.
STFC-RAL-CR03 R61: And then, whatever happens in the future, we're gonna need new confusing applications because we can't deal with the amount of data that's gonna be produced.
STFC-RAL-CR03 R61: And so on to computing potentially offers at
STFC-RAL-CR03 R61: a way to combat these these conversational kind of objects.
STFC-RAL-CR03 R61: So in this talk, I I've shown you the first real live next device, and also I've shown you a look at using Qa. And
STFC-RAL-CR03 R61: to employ a novel oracle which will allow us to do practical argument.
STFC-RAL-CR03 R61: That's it. Any questions.