STFC-RAL-CR03 R61: Thank you. Good morning, everyone. Welcome to this PPD and PCC joint seminar, titled, Leveraging Quantum Hardware for Fundamental Physics.
STFC-RAL-CR03 R61: It is our pleasure to introduce today's speaker, Jack Araz. Dr. Arraz is a Presidential Fellow at City St. George University of London, and an Honorary Senior Research Fellow at UCL.
STFC-RAL-CR03 R61: His research spans collider phenomenology, advanced computational methods, and more recently, the interface between quantum information science and high-energy physics.
STFC-RAL-CR03 R61: His work focuses on extracting maximal physics insights from LFC data, particularly through gentrification frameworks.
STFC-RAL-CR03 R61: Detector simulations and statistically robust inference techniques.
STFC-RAL-CR03 R61: He has made significant contributions to tools such as Metaanalysis 5 and to the broader effort of preserving and reusing experimental analysis in high-energy physics.
STFC-RAL-CR03 R61: More recently, his research has expanded into quantum computing and tensor network methods, exploring how quantum and quantum-fired techniques can enhance data
STFC-RAL-CR03 R61: Analysis, anomaly detection, and simulation in particle physics.
STFC-RAL-CR03 R61: Dr. Braj has…
STFC-RAL-CR03 R61: an extensive publication record across collateral physics, machine learning applications, and quantum simulations, and is actively involved in shaping modern data-driven approaches to physics, beyond, standard model.
STFC-RAL-CR03 R61: Today, we will focus on, the seminar titled Leveraging Quantum Hardware for Fundamental Physics, so please join me in welcoming Del.
STFC-RAL-CR03 R61: I'm blushing.
STFC-RAL-CR03 R61: Thanks a lot for having me. It's really nice to be here. It's a beautiful weather today. It was beautiful to bike over here from the train station.
STFC-RAL-CR03 R61: So, I'm gonna talk about how can we use
STFC-RAL-CR03 R61: because Bridge wanted me to focus on a particular paper, I'm going to talk about how we can use quantum hardware units so that we can simulate quantum… we can simulate particle physics experiments, or any kind of collider experiments in the future, hopefully.
STFC-RAL-CR03 R61: I added a lot of introductory slides, because I thought there would be PhD students and everything, but I can skip them quite fast. So.
STFC-RAL-CR03 R61: what I'm going to talk about is I'm going to introduce, first of all, digital quantum computing, how does the quantum computer works, then I'm going to introduce how stimulating fundamental works in this framework, and then I'm going to move on to Hybrid's quantum system. This is not classical and quantum, this is
STFC-RAL-CR03 R61: Q mode and qubit working together, and then I'm going to talk about quantum optimal control. Basically, how can we use AI to tune the quantum hardware to get it
STFC-RAL-CR03 R61: Get it specifically tuned for our simulation work, and hopefully get it work in a nearer time than 30 years from now.
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: Let me quickly talk about, how does the quantum computer work? So, any operation in a quantum computer, we write it as a… basically a traditional circuit.
STFC-RAL-CR03 R61: circuit goes from left to right, where we start from an initial state, and we manipulate this initial state, which is a zero-bit state, qubit state, I should say. We manipulate this with single qubit gates. These are unitary operators, poly matrices, basically a C2 generators, right?
STFC-RAL-CR03 R61: So we can manipulate this on a… if you look at the block sphere, we can manipulate a random vector on a block sphere.
STFC-RAL-CR03 R61: We're using these operators to map this into different positions in the block sphere. And more importantly, we can, of course, rotate these vectors wherever we want to be able to span any vector space in this block sphere, or multidimensional block sphere, for that matter.
STFC-RAL-CR03 R61: So, the next, third, third component of this is, of course, two-qubit gates, which is basically creating these entanglements that we are looking for. Here, I'm showing you the CNOT gates, where
STFC-RAL-CR03 R61: If it checks the first qubit, for example, it checks if it's 1 or 0. If it's 1, it flips the other one as well. If it's 0, it doesn't do anything.
STFC-RAL-CR03 R61: So, how does it work? If I look into a 00 state, for instance, apply CNOT get, and ask what is going to be the probability of my state at the end, I will get 0, because there's nothing to flip.
STFC-RAL-CR03 R61: But if I rotate this 90 degrees to get 50% chance of having 0, 0, and 1, I start to get now the second qubit is flipping as well because of this seam update.
STFC-RAL-CR03 R61: And then, what I do is, of course, I need to do my measurements. I can choose a Hamiltonian that describes my model, whatever I want to study, and I calculate the expectation value by sampling from this quantum computer, and hopefully get
STFC-RAL-CR03 R61: Minimal noisy results.
STFC-RAL-CR03 R61: So… what can I do in terms of simulation?
STFC-RAL-CR03 R61: Of course, there are lots of ways that we can simulate. What I'm interested mostly is simulation of many-body systems. For example, we can do converse manner systems, quantum manybody systems.
STFC-RAL-CR03 R61: chemistry. In chemistry, they're simulating the molecular structure of certain interesting molecules. That is really hard to simulate with classical computers, but what I'm currently interested in, simulating QCD, hopefully one day.
STFC-RAL-CR03 R61: How does the… Proton structured with quartz and gallons.
STFC-RAL-CR03 R61: Of course, there are lots of different ways that we can do this with, for example, exact diagonalization.
STFC-RAL-CR03 R61: The problem with exact normalization is
STFC-RAL-CR03 R61: We cannot do so many atoms, so many quads, so many balloons at the same time. We have limited ramp, so we cannot ramp them into one thing. We can go away from this with Monte Carlo methods, when Monte Carlo has certain limitations that I will go into, then to go beyond those limitations, we describe tensor methods.
STFC-RAL-CR03 R61: to solve them. But, of course, they will come with their own challenges. So, let me, let me go through, step by step, what these challenges are, and what's the problem with simulating QC.
STFC-RAL-CR03 R61: We… really know well how QCD works. Perturbation theory works perfectly, there's no problem.
STFC-RAL-CR03 R61: The problem comes when you go to low energy, where perturbation theory basically fails. So we, in the 70s, I'm saying we, but I wasn't alive in the 70s, Cohen and Sutskin invented this lattice QCD framework
STFC-RAL-CR03 R61: where they describe… discretize the Euclidean lattice space to be able to represent… to be able to compute anything that we can on the side of QCE.
STFC-RAL-CR03 R61: The problem in the Lattice QCD framework is there's something called sine problem.
STFC-RAL-CR03 R61: where if you have this chemical potential type of complex term, what you get… you start to get noise in the noise is not required. Integrability becomes really challenging. For example, if I don't have this term, if I just have the action expectation value of that action, it's quite simply
STFC-RAL-CR03 R61: integrating, let's say, a Gaussian distribution. It's really easy to integrate.
STFC-RAL-CR03 R61: But if I have, for example, a time evolution or a chemical potential like this, my distribution becomes very oscillatory, so it's getting really hard to integrate. You need to get nitty-gritty to be able to… so the lattice spacing needs to be very, very fine-grained.
STFC-RAL-CR03 R61: To be able to integrate this entire thing.
STFC-RAL-CR03 R61: The problem is, we don't have that computational power, so it becomes really challenging to do.
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: we have this workspace. We can do, for example, we can calculate everything with the perturbative field theory, we can do a lot of things with lattice QTE as well. What are the specifics that I'm thinking about, that… that we cannot do? For example, the main things is parton distribution function. How does the momentum of the proton distributed among quads and globes?
STFC-RAL-CR03 R61: Me…
STFC-RAL-CR03 R61: kind of extract this information, but since we have to project this into a light cone, it's really hard to… because it really becomes hard to compute on a lattice QCD, or even tensor network methods that I'm gonna show a bit about. And lastly, the final part of this collider event.
STFC-RAL-CR03 R61: How does the, the…
STFC-RAL-CR03 R61: quarks and glooms that we observe becomes the mesons and hard loans that we observe in the LSE fragmentation functions. It's really hard because it's…
STFC-RAL-CR03 R61: Basically, an evolution function, it's time and observed.
STFC-RAL-CR03 R61: So with lattice QCD, you cannot access this time-dependent observables because of the term that I showed you. It's really hard… becomes really hard to integrate. With the Lamatt method, we can basically, by assuming that PDF plug momentum is really high, you can kind of extract PDFs.
STFC-RAL-CR03 R61: But fragmentation functions are really challenging to do, so it becomes very computational and costly. So the question that I want to achieve with quantum computers in the future, hopefully, how can we simulate time-dependent, non-protective phenomena? Not to replace lattice QCD or any current methods, they are really good at certain regimes.
STFC-RAL-CR03 R61: But how can we resolve things in the regimes that we cannot compute anything at the moment?
STFC-RAL-CR03 R61: So… What about PDF? Why, why I'm so interested in PDF?
STFC-RAL-CR03 R61: When I was young, I thought supersymmetry was a thing to save us all, so I was working on Gleno production, and as you can see here.
STFC-RAL-CR03 R61: When you calculate the cross-section of the gluino production, we kind of understand the scale uncertainties, and they are pretty much the same throughout mass evolution of the glueno.
STFC-RAL-CR03 R61: But, as you can see, PDF distribution gets really tricky because we don't have enough data to be able to fit, in these regimes where energy is quite high. We're up to have, like.
STFC-RAL-CR03 R61: 100% uncertainty there. So, having an access to our first principle calculation will enable this to… to be shrimp. Of course, there's going to be theoretical uncertainties, but we will have… we will have much better understanding of how to… how to
STFC-RAL-CR03 R61: constrain these uncertainties. So, using tensor network methods, we are actually right now working on how to compute this thing, and the problem comes with this matrix element. As you can see, there are two time evolution type of operators which boost your matrix element onto a life cone.
STFC-RAL-CR03 R61: which creates these issues into LatticeQCD framework or any other framework, and it's quite large. For example, if you want to calculate the pester network with a single flavor, you can get nice distributions, but you can see that already.
STFC-RAL-CR03 R61: With, with single flavor physics.
STFC-RAL-CR03 R61: I'm going beyond momentum fraction 1, which is because of the size of my lattice. I require a long, very large lattice to be able to simulate this properly, so that my quark doesn't have more momentum than my proton, which doesn't make sense.
STFC-RAL-CR03 R61: So there's a lot of resources that is required to be able to simulate tree flavor physics in terms of CCB.
STFC-RAL-CR03 R61: So that's what we want to achieve with quantum computers overall.
STFC-RAL-CR03 R61: So, of course, there are different methods. We want to eventually come to fault-tolerant quantum computers, but currently, if you look at this chart, this is basically showing you the representability of certain different methods with respect to energy scale and the dimensionality of space.
STFC-RAL-CR03 R61: Unfortunately, current quantum computers are quite limited, but of course, we need to find a way to enable this simulation in the future when these methods are going to be available.
STFC-RAL-CR03 R61: So faster networks can enable you to go a little bit further, but you cannot go two-dimensional or three-dimensional. Two-dimensional, it's possible, but it's very limited. Two-dimensional, it becomes really hard. Also, you need to find a way to embed the Hamiltonian in a really smart way to be able to
STFC-RAL-CR03 R61: efficiently calculate these, methods, especially if you go to a two-flavor, three-flavor physics, it becomes really complicated, even if you're working on a very simple Hamiltonian.
STFC-RAL-CR03 R61: I am currently arguing that maybe neural networks can bridge the gap between today's tensor network, limited tensor networks, and maybe tomorrow's quantum computers. I'm not going to talk about that today, but today I want to talk about how can we use
STFC-RAL-CR03 R61: current quantum hardware resources, what type of hardware resources we can use to basically simulate standard with these, magnets.
STFC-RAL-CR03 R61: So, of course, QCD, eventually, when we want to simulate it, it's a very complex object.
STFC-RAL-CR03 R61: It has… I'm dividing it into three main categories. First category is basically just fermionic, second category is just gauge fields or photons, whatever you want. And the third category, gauge fields interacting with the fermions, right?
STFC-RAL-CR03 R61: So we have… the combination of these three will become our QCD. So the first category can be easily
STFC-RAL-CR03 R61: easily, simulated on a quantum computer, because I can simulate fermions as a qubit, degrees of freedom match. So, okay, that's… that's nice. But the problem becomes, how about gauge speeds? These are inf… this has infinite degrees of freedom, okay? You can argue that I can map these,
STFC-RAL-CR03 R61: the infinite degrees of freedom into a discrete group, and I can cut off the… truncate, basically, the space, and maybe simulate them into a few qubits. Sure, but then you're introducing some truncation errors.
STFC-RAL-CR03 R61: Same goes for the third category, where we have the different qubits and gauge fields, or fermions and gauge fields, so either I have to truncate gauge fields to be able to play around with the interaction, or I need to find a different method.
STFC-RAL-CR03 R61: So, different method comes from the continuous variable quantum computers, where I can use, for example, photonics can be used to describe all the photonic interactions and gauge field theories. I can embed them all there pretty nicely, but the problem is.
STFC-RAL-CR03 R61: a photon doesn't interact with superconducted qubits, so how can I create
STFC-RAL-CR03 R61: method that can interact qubits and humans. That's what I'm going to talk about a little bit today.
STFC-RAL-CR03 R61: So, qubits, as we've already seen, can be achieved with the superconducting circuits called atoms, straton topological qubits, and these are digitally realized, very well known, and we can represent this as your circuit description that I showed you before.
STFC-RAL-CR03 R61: And Q modes are pretty much the same. We can realize them with photonics, trapped ions, and again, superconducting circuits.
STFC-RAL-CR03 R61: Why superconducting circuits can achieve Q modes, I will get into that later in the talk.
STFC-RAL-CR03 R61: And these are basically represent infinite-dimensional Hilbert space, which is very much suitable for representing gauge fields, if you want to represent the entire structure of the gauge field without truncation, hopefully.
STFC-RAL-CR03 R61: They can be gate-based as well. We have certain operators that we can digitize and operate on these Q modes in the photonics and in the trap dialog, any hardware that you want.
STFC-RAL-CR03 R61: So the gates that I'm gonna talk about today, we can represent them as, just like before, instead of now representing them in a block square, we can represent them in a… as a Wigner function, where we can displace these Wigner functions, we can squeeze this… this wave packet.
STFC-RAL-CR03 R61: There's non-Gaussian gates I'm not gonna talk about, but we can basically agree with non-Gaussian gates, although this is really hard to realize in a quantum computer. We can, of course, rotate, and as, just like in CNOT gate, we can entangle two different
STFC-RAL-CR03 R61: Sorry, two different key modes with a beam splitter, for example.
STFC-RAL-CR03 R61: So, how about hybrid system? How can we realize a qubit and Q mode interacting with each other? Because I don't want to truncate my gauge field to put it on a quantum computer. How can I realize such a hardware?
STFC-RAL-CR03 R61: So, trapped ions are really ideal interface to be able to achieve this. We've been working on this quite a while. So, basically, trapped ions has ions that I can use as a qubit. Quantum already has developed this technology. You can split this spin of an ion, and you have a beautiful qubit, and it has a very long coherence time and everything.
STFC-RAL-CR03 R61: It's really safe.
STFC-RAL-CR03 R61: But I can do something else. If I just use the collective mode of these ions, I can create a quantum harmonic oscillator inside the quantum computer. Now I have both Q modes and qubits at the same time.
STFC-RAL-CR03 R61: Of course, there are some challenges. I have to tune the laser in a certain way, and I have to sacrifice a couple of qubits inside my quantum hardware to be able to control this cube mode.
STFC-RAL-CR03 R61: But at the end of the day, I can achieve. And in the paper, I believe we calculated that if we want up to 8 modes inside our oscillation.
STFC-RAL-CR03 R61: I believe that 3 qubits, sacrificing 3 qubits, is enough to get a really decent fidelity.
STFC-RAL-CR03 R61: For, for our item trap system.
STFC-RAL-CR03 R61: So, I'm showing you here a variety of gates that we can realize in a very high fidelity. There are qubit gates, Q-mode gates. We already know these were possible because you can realize Q modes or qubits separately. What I'm interested in, what is really important, is the hybrid gates.
STFC-RAL-CR03 R61: So I can realize qubits interacting with cubes at the same time as a red sideband or a blue sideband. They're also introducing a non-Gaussianity through this gate, so it can bring different features into this. And we can realize
STFC-RAL-CR03 R61: These gates with a really high fidelity for a certain structure that we worked on.
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: Let me walk you through an example that we studied, because we wanted to understand how can we use these in a real, real scenario.
STFC-RAL-CR03 R61: So we looked at James Cummings-Hubbard model. This is a very, very simple, condensed matter model, which is very widely known, and it has all this structure, all the
STFC-RAL-CR03 R61: pieces, bits and pieces that I'm interested in. It has qubits interactions, it has a fermionic interaction, it has some, cumorph photonic interactions, so it's basically displaying how this photon interacts with an electron.
STFC-RAL-CR03 R61: And if you look at this last term, I have both Q modes interacting with Q bits.
STFC-RAL-CR03 R61: So, using the gate set that I introduced earlier, I can basically create a digital quantum computer that maps this entire Hamiltonian onto my quantum computer as a filter step, for example, this single thing.
STFC-RAL-CR03 R61: shows you a single charge for this particular Hamilton.
STFC-RAL-CR03 R61: So, we took this concept and put it on the quantity hardware, and tried to simulate, try to work out how to simulate this time evolution. For example, I fixed
STFC-RAL-CR03 R61: random initial state with the random parameters on the Hamiltonian, and we can simulate this, this oscillation between qubits and cumulates. As you can see, these Bs are bits.
STFC-RAL-CR03 R61: in each site, and M is describing new mode, and this is the time evolution, with respect to these fixed parameters. So time evolution, we can work out. This is pretty easy. This is shorter steps, basically, shorter evolution.
STFC-RAL-CR03 R61: How about preparing a steak?
STFC-RAL-CR03 R61: can we use, for example, a DQE type of method using the same architecture,
STFC-RAL-CR03 R61: instead of having this time evolution, fixed parameters, how can I map these into a trainable parameter so that I can basically treat this as a VP procedure, so that I can prepare my ground state, or in the future, prepare my proton state, hopefully?
STFC-RAL-CR03 R61: So it's basically the same idea as how you would do in a regular superconducting quantum computer, where my gate is basically a stack of these gates.
STFC-RAL-CR03 R61: And I'm optimizing this entire circuit with respect to expectation value of my Hamiltonian, and trying to do the gradient descent to find the global minima, and it turns out we are able to map between… with various, kappa and delta values. You can map it to a… oops, oops.
STFC-RAL-CR03 R61: But you would say, oh, you are not able to get any fidelity, any reliable fidelity in this middle region over here.
STFC-RAL-CR03 R61: The reason for that is my first excited state, it becomes degenerate with my ground state, so I'm not able to differentiate them anymore. That's why I don't have any fidelity here. But we also looked into, for example, looking into first,
STFC-RAL-CR03 R61: first, not first, second state, the fixed quantum number ground state, and in that case, there's no degeneracy, so we can differentiate that perfectly in all the entirety of the…
STFC-RAL-CR03 R61: So, that's great, we… that means we have the ability to prepare a state, we have the ability to do the time evolution.
STFC-RAL-CR03 R61: And we can, we can… sorry.
STFC-RAL-CR03 R61: We can choose an interesting parameter, for example, two-body correlations that I'm interested in to measure in the particle collision event, and do the entire chain of simulations. Perfect. What's lacking? What else is missing?
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: The problem is, there is limited coherence time in my current quantum computers, and I cannot go beyond that. If I want to simulate the time evolution, I have to charitarize this, and
STFC-RAL-CR03 R61: for a decent, time evolution, I need to simulate multiple
STFC-RAL-CR03 R61: probably thousands of throttle steps to be able to achieve any.
STFC-RAL-CR03 R61: The problem is, my coherence time and current, I believe, last time I checked, it's, in IBM, it's 50 to 100 millimicroseconds.
STFC-RAL-CR03 R61: But the problem is, single qubit gates takes, like, 71 nanoseconds, and the 2-qubit gates, which is huge, takes 600 nanoseconds. So there's a very much limited time frame that I need to prepare my state, timable my state, and then measure something.
STFC-RAL-CR03 R61: It's really limited. So how can I go beyond? You might say that, okay, why don't you use machine learning to do this VQE thing, and maybe you can shrink this time to do everything more efficiently. Sure, we can try, but there's a problem there, too.
STFC-RAL-CR03 R61: If you increase the size of the Hilbert space, what you end up getting is a barren plotter, something called barren plotter. You're losing the gradient, so you are not able to optimize your system anymore for large lattices or very deep circuits.
STFC-RAL-CR03 R61: So you ended up with this barren plateau that you cannot move anywhere. So, what can I do? What is the… what is the solution to this?
STFC-RAL-CR03 R61: Yeah, how can we go beyond this continuity? So, the main issue is there are commercially available gates that I have to use to be able to run anything on my quantum computer.
STFC-RAL-CR03 R61: What if I don't? What if I just create my own gates?
STFC-RAL-CR03 R61: according to my own taste, because if, for example, I want to go here on this block sphere, I have to take this two-step operation to be able to get there. It's already
STFC-RAL-CR03 R61: to spend 60 nanoseconds wasted of time. How… what if I can just go from here to here directly? But there's no direct way to go there, because there's no gate available?
STFC-RAL-CR03 R61: how can I use AI to train my quantum computer to directly go there without using available gates? So it turns out
STFC-RAL-CR03 R61: I can use the pulses that they use to create these gates. So, in order to create this gate, for example, in IBM, they have a Josephson Junction, they tune the electricity signals going into Josephson Junction to be able to get a certain fidelity gate set that's available to you.
STFC-RAL-CR03 R61: What if I directly use these pulses inside the quantum hardware and tune my
STFC-RAL-CR03 R61: gate evolution for a single… for a certain duration, pulse duration, and directly get what I'm looking for, instead of applying this multiple gates billion times, and hopefully
STFC-RAL-CR03 R61: Maybe if I tune this in a really good manner, it's basically giving me an ability to simulate everything much more coherent than a short time frame.
STFC-RAL-CR03 R61: So let me, let me try to go through how this works. So in a superconductive quantum computer, Josephson Junction is simulated by something called transmont Hamiltonian. This is basically an unharmonic quantum oscillator.
STFC-RAL-CR03 R61: So that's why I've said there's a queue mode inside your superconductive quantum computer as well. Underlying hardware is actually working as an unharmonic oscillator, where you have the 0-1 shift between transition between… between 0-1 state, there's a,
STFC-RAL-CR03 R61: Unharmonic… unharmonicity, to be able to split, second and third for any higher degrees, higher order.
STFC-RAL-CR03 R61: modes in your system, so that you don't leak into that, because it's really hard to measure those states in a superconducting hardware, as far as I know. So you want them to be separated enough
STFC-RAL-CR03 R61: So that you end up with the lowest 0-1 state. And then, of course, you have the qubit architecture, which qubits
STFC-RAL-CR03 R61: which physical qubits are actually talking to each other inside your quantum computer. So these parameters are pretty much fixed by the prediction, by IBM, for example.
STFC-RAL-CR03 R61: listed typical values for these in IBM quantum computers. You can access them from IBM's website.
STFC-RAL-CR03 R61: So, I need another term to be able to control this with these falses and everything inside my quantum arc.
STFC-RAL-CR03 R61: So this comes with the control Hamiltonian. Essentially, I have a pulse term here, basically giving you a certain range pulses, depending on your laser, you can tune it, but typically, these are between 20 to minus 22 to pulse 20 MHz.
STFC-RAL-CR03 R61: And there's the phase rate between qubits and Q modes that they are interacting here. So using this, basically, I can tune my pulse rate and the phase between these pulses for each pulses to be able to get
STFC-RAL-CR03 R61: A new gate that's designed particularly by me.
STFC-RAL-CR03 R61: I don't care what gates available in my quantum computer by tuning these parameters how many ever I want.
STFC-RAL-CR03 R61: I can create a new gate that basically solves my problem, hopefully for me.
STFC-RAL-CR03 R61: So, why this is really important? Because it's essentially gonna lead a shorter coherence time. It's not shorter coherence time, but shorter time execution time, so that I don't hit coherence limits
STFC-RAL-CR03 R61: during the quantum computation, and it has been shown that this method is free from local minima if you have a certain evolution time achieved, and so that it's maxed from Baron Plateaus, which I will, show you a little bit later.
STFC-RAL-CR03 R61: So, let me tell you about Schringer model, and how do we simulate Schrodinger model using these techniques. How can we prepare the ground state, for example, of the Schringer model?
STFC-RAL-CR03 R61: Using these pulses.
STFC-RAL-CR03 R61: So the Schumer model is basically 1 plus 1 dimensional U1 gauge theory that is coupled with Dirac fermions. You can see the Lagrangian here, and I have an extra chiral rotation here, just to make things a little bit more spicy.
STFC-RAL-CR03 R61: I can use staggered Fermion descriptization and Jordan-Wigner transformation to be able to map this to a Hamiltonian formalism that I can use it to embed on a quantum hardware.
STFC-RAL-CR03 R61: So the first, first, equation here is very simple. It's basically a Hopping term, Eisenhoppington term. It's very simple, just in the addition of this kind of rotation. Even the second term is, like, really similar to a mass term, for example. But the third term, since I'm implementing this gospel, I'm integrating out my gauge field to be able to simulate this.
STFC-RAL-CR03 R61: It becomes a bit messy.
STFC-RAL-CR03 R61: So this last term creates this non-local Hamiltonian effect, which becomes really challenging to be able to simulate in a classical computer because of this long-range interaction in my lattice.
STFC-RAL-CR03 R61: That's why we choose to… choose to work with… with the Schwinger model, because it's really challenging, especially when you have this kind of limitation kind of…
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: If I just take this model, take this Hamiltonian, convert this to a charter step, a single charter step in 4 qubits, just in 4 qubits, 4-site Hamiltonian, looks like this.
STFC-RAL-CR03 R61: It takes 11 microseconds to run on a quantum computer if I don't do any smart things, and I'm actually cheating here. As you can see, my qubits are jumping over here, where I need to introduce, actually, some swap operations here. I'm even avoiding this.
STFC-RAL-CR03 R61: I'm even avoiding those swap operations, just raw, assuming everything can talk to each other, I have 11 microsens. That means I can only run 9 short steps in my quantum computer, which means nothing. What can we do with this?
STFC-RAL-CR03 R61: So how can we… Improve this, this limitation.
STFC-RAL-CR03 R61: So what we did is, let's assume that my quantum computer is the same structure, just 4 qubits. I have a linear quantum computer that everything is talking to each other in that adjacent format, and I'm creating my Hamiltonian with using just pulses, right?
STFC-RAL-CR03 R61: Basically, again, just like in BQE, I'm optimizing to get the ground state expectation value of the Hamiltonian. So I'm diabolizing the Hamiltonian of the quantum computer.
STFC-RAL-CR03 R61: If we optimize this, what we get is basically I can execute the entire circuit with 180 nanoseconds, which is 61 times faster than single trotter step. And I cannot guarantee you that single trotter step will be enough
STFC-RAL-CR03 R61: to prepare the ground state of my Amazon, and probably I'll need to repeat this multiple times to be able to get the ground state, but with
STFC-RAL-CR03 R61: quantum optimal control, I can achieve much, much faster, 61 times faster than single structure step, and this is basically showing you my pulse profile inside my quantum computer, and I think, if I'm not mistaken, for each qubit, I have 100 different pulses.
STFC-RAL-CR03 R61: and single face for the Empire of Syracuse.
STFC-RAL-CR03 R61: I can't even overkill this, I can add more phases, I can add more pulses, etc.
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: how about my evolution structure look like? Because I told you that this can leak into higher energy states inside my simulation, then I lose the information, then I have to find a way to retrieve this information if I leak into, for example, second excited state or third state.
STFC-RAL-CR03 R61: If I look at my past evolution, I don't see anything leaking. I think I didn't add it in here, but there's a little bit of leakage to second site in
STFC-RAL-CR03 R61: some of the states in the middle, but at the end, it all dies out, and I can compare to my state to an exact diagonalization, of course. I can get exactly matching results with the exact diagonalization and prepared state in terms of eigenstate of my happenstance.
STFC-RAL-CR03 R61: Okay.
STFC-RAL-CR03 R61: So, this is… this was for only a quantum computer that is just adjacently, perfectly sit together next to each other. The problem is my Hamiltonian is not like that. My Hamiltonian is all to all correlated.
STFC-RAL-CR03 R61: or in a… in a different Hamiltonian, it might be my Hamiltonian as a, as a fairly popular commission.
STFC-RAL-CR03 R61: how can I integrate? Is there anything that I can improve in the architecture that will reflect my Hamiltonian structure? Would it actually affect the result? Can I make it faster by manipulating, actually, the hardware itself?
STFC-RAL-CR03 R61: What we did is basically, this is experimentally not possible, but what we tried to do is, what if my quantum circuit, quantum hardware is all to all connected?
STFC-RAL-CR03 R61: Does it improve anything? And it turns out that I can go 109 times faster than single throttle step. Again, just single throttle step.
STFC-RAL-CR03 R61: So it's really faster that if you implement the physical information that we have from the Hamiltonian, you realize that it's much more efficient to simulate the quantum computer. So imagine that embedding entire,
STFC-RAL-CR03 R61: periodic boundary conditions, you can have a quantum hardware with the periodic boundary condition already embedded in there, like their circular circuit structures.
STFC-RAL-CR03 R61: We can use that information in this structure, to be able to achieve much more efficient computation with this.
STFC-RAL-CR03 R61: Okay, so I have this infrastructure. How about in a real hardware? Can I… can I put this in a real hardware and get anything comparable to what I just showed you before?
STFC-RAL-CR03 R61: It turns out, the answer is no.
STFC-RAL-CR03 R61: If you go to a publicly available, not research-specific quantum hardware, you will see that anything around 1 microsecond even goes up to 2 microseconds, and this is the lean value with the uncertainty of the red one.
STFC-RAL-CR03 R61: So, I cannot achieve anything. So, what is the reason for that? It turns out there is a reason why these particular, quantum hardware is public.
STFC-RAL-CR03 R61: Because the coupling strength between each qubit are only 2MHz, and the state-of-the-art quantum hardware in, I think, Eagle processor, they are calling it, it's around 20 MHz each coupling between qubits. So…
STFC-RAL-CR03 R61: It makes a huge difference to have a higher value of
STFC-RAL-CR03 R61: of coupling between each physical qubit. So, we thought, okay, if that is the main concern, what if I can increase this, this, coupling strength to, I don't know, 30, 40, 50, maybe I will get infinite efficiency.
STFC-RAL-CR03 R61: Well, there's no free lunch, unfortunately. We try to increase the, coupling strength and see what is the effect of this coupling strength on the, on the, simulation, efficiency. So this is showing you the… that,
STFC-RAL-CR03 R61: minimum estimated time that you need to have on the pulse, and as you can see, when I decrease the coupling strength, it increases quite drastically, exponentially, actually, and also my uncertainty on the ground state also increases.
STFC-RAL-CR03 R61: if I increase… decrease this coupling strength, I start to hit a flathead at around 20 MHz, which is currently what we have in the quantum hardware. So there's no free lunch, there's a limitation, which is called, actually.
STFC-RAL-CR03 R61: quantum speeds in it, if I'm not quoting wrong, I hope.
STFC-RAL-CR03 R61: So there's a certain limitation that you can evolve an adiabetic state from state A to state B. There's a certain speed that you can achieve, and you cannot go beyond that. And we actually basically seen that effect by playing, the coupling strength as well.
STFC-RAL-CR03 R61: So, if this works, that's great. That means we basically cheated our life from the coroner's time, we solved the coroner's problem. What about the barren plateaus? Because I still need to optimize the circuit.
STFC-RAL-CR03 R61: how does it gonna work? If I cannot use VQE, I cannot use Quantum Optimal Control. So, is it a problem still?
STFC-RAL-CR03 R61: So what we looked into is, we basically sampled from a really uniform distribution of the parameters of the pulses and phases that are counted, and we calculate the variance for each sample. And what we get is basically, as you can see, the variance
STFC-RAL-CR03 R61: increases with the number of qubits and the pulse duration. So, when I increase the pulse duration, I give much more contribution to each pulse, so they are… the probability of having this… this barren plateau… Yeah, just…
STFC-RAL-CR03 R61: Where was I?
STFC-RAL-CR03 R61: So… so I have more time for this single pass to evolve inside the function, so I have… I… I can increase my variance, with the number of sites. That means that if I increase the number of qubits.
STFC-RAL-CR03 R61: I'm going away from Darren Plateau, and I can… if I… if I deepen to Darren Plateau, I can basically increase the concentration to get out of it as well. So there's much more control on… on the… on the… on the, diamond plateau issue over here as well.
STFC-RAL-CR03 R61: So, that's all I wanted to talk about. Let me conclude, let me summarize what I've talked, and tell you a little bit about what I'm planning to go beyond, beyond this.
STFC-RAL-CR03 R61: So I've talked about different methods, different quantum hardware, how can you use different quantum hardware to basically simulate fundamental physics, because we have different pieces in the standard model that we possibly want to simulate, but they might not be suitable to simulate just by qubits.
STFC-RAL-CR03 R61: maybe we want to, embed… extend this to use Q modes, and by using Eintrape quantum computers, this might be possible. Or there are,
STFC-RAL-CR03 R61: cavity interacting with superconducting qubits that gives you the ability to have this Q-mode-qubit interaction as well. I'm not expert on this in any shape or form, it's just…
STFC-RAL-CR03 R61: By what I read. So there are different technologies that we can use to be able to get this standard model simulated on a quantum computer much more efficiently, hopefully without much truncation.
STFC-RAL-CR03 R61: Of course, there has to be truncation because of the experimental limitations, but hopefully it's in a much more nicer way.
STFC-RAL-CR03 R61: And I talked about quantum optimal controls because of the hardware limitation, coherence time limitation in the hardware. You can use the quantum optimal control to basically engineer
STFC-RAL-CR03 R61: a specific computational structure for ourselves, for our, specific use, so that's QCD simulation, or whatever our Hamiltonian needs. So we can tune the hardware specifically for our needs.
STFC-RAL-CR03 R61: So where I want to go from there is basically my goal is hopefully one day to simulate PDFs and fragmentation functions more, more accurately. So I want to understand how can I use these separate systems to do some scattering, how can I use them to simulate PDF or,
STFC-RAL-CR03 R61: quantum link model, for example, if I implement quantum gauge fields as quantum links, instead of just integrating over them, I can represent gauge fields as Q modes and link them with the qubits, for example, fermions, on this hybrid system, so it's much more efficient without truncation.
STFC-RAL-CR03 R61: I want to understand how these hybrid systems will basically eventually evolve into QCD,
STFC-RAL-CR03 R61: And I'm looking into different methods beyond tensor networks and quantum computers, for example, neural quantum states, to be able to understand how can we actually achieve
STFC-RAL-CR03 R61: bridge between today's limited classical methodologies to tomorrow's, hopefully more able quantum computers.
STFC-RAL-CR03 R61: Thank you very much for listening, I thought I've been trying to…
STFC-RAL-CR03 R61: Very interesting, talk, questions from the room.
STFC-RAL-CR03 R61: So, I might have missed something, but when you're talking about the speedup, when you design these, like, custom gates.
STFC-RAL-CR03 R61: it seems surprising that it's, like, orders of magnitude improvement, not… because the individual gates, presumably formed a short composite.
STFC-RAL-CR03 R61: Obviously, you have a few discrete gigs.
STFC-RAL-CR03 R61: I need too many gates to be able to achieve the same result. So we looked into… looked into how can we… so the problem is, how can we prepare the ground state of fluid, right? So you… it's not that you still decompose in the gates, and you… you just…
STFC-RAL-CR03 R61: made kind of composite gates. It's that you go and… You're doing the entire evolution.
STFC-RAL-CR03 R61: Yes. Instead of… okay. So, I need too many gates to be able to achieve what I'm trying to achieve.
STFC-RAL-CR03 R61: So that it takes a long time to be able to do. So if I can shrink that even a little bit, I have a little bit more time to do time evolution, I have a little bit more time to do
STFC-RAL-CR03 R61: or measurements of different observables, for example, so I'm just trying to shrink that time as much as possible.
STFC-RAL-CR03 R61: Now, I have a PhD student actually working on how to do this, not just for ground state preparation or excited state preparation, how can we do this… use the same methodology called optimal control to… to compress the timing issue, for example.
STFC-RAL-CR03 R61: How can we shrink that part of the mission so that we can do the trauthorization in much more action?
STFC-RAL-CR03 R61: Is it for me? Yeah.
STFC-RAL-CR03 R61: Just, so, towards the end, when you came to, sort of, talking about taking your, custom gates and making them real.
STFC-RAL-CR03 R61: How exactly…
STFC-RAL-CR03 R61: do you go about this? Is there some sort of, like, low-level API available, which gives you more direct control over the pulses? There was. What? So now, according to U.S. government, it's a national security interest, so that's why it's actually really important for us to develop our own quantum computers here.
STFC-RAL-CR03 R61: So, there was something called Tiskit Dynamics Interface, so that you can use the pulses and design your own pulses into the inside quantum computer and actually submit this job into quantum hardware.
STFC-RAL-CR03 R61: they canceled this after we published. We were so lucky.
STFC-RAL-CR03 R61: But yeah, I think it is really important that we have access to our own content partners so that we can explore these capabilities.
STFC-RAL-CR03 R61: What changes do you have to do with the hardware to achieve this compression of gates?
STFC-RAL-CR03 R61: I don't need to change anything. So, there's, if…
STFC-RAL-CR03 R61: I don't want to change the architecture itself. Sure, that's fine, because it's harder to change the architecture when it's already there.
STFC-RAL-CR03 R61: as long as I have access to pulses that they use to create these circular gates, they already use them to create the gates. If I have the access to use them directly.
STFC-RAL-CR03 R61: I just do their job for them, for my purposes.
STFC-RAL-CR03 R61: So instead of having a keyboard, I have electronic signals to, like, my, I'm fine.
STFC-RAL-CR03 R61: Have you ever tried, or are you planning to eventually benchmark these gates relation things on the real quantum computers? For each one are you asking for? For hybrid one or quantum quantum computer?
STFC-RAL-CR03 R61: like, the real… Both of them. So… so for hybrid system, for Q2 model, we are actually working with Samia National Lab, so they are…
STFC-RAL-CR03 R61: They're… they have… they have experimenters who are experts on designing these trapped iron quantum systems, and they are currently working on how to make our simulations real… applied to their quantum systems.
STFC-RAL-CR03 R61: Basically, they are using quantum optimal control to be able to achieve the case that we propose to achieve. So yeah, we are… They already have a quantum circuits locally, right? They have, yes. They do have access to hardware and everything. We just want our gates in their machine.
STFC-RAL-CR03 R61: And can you apply it here in the UK? You know, the NQCC here has a program that's gonna allow
STFC-RAL-CR03 R61: implementing or doing any simulation benchmarking on regulatory, just basically hearing.
STFC-RAL-CR03 R61: basically database here in the UK or elsewhere as well. Well, I did that for, for, regular supercombatic projects that I'm working on, but I believe, so…
STFC-RAL-CR03 R61: I believe in QCC for IronTrack, for example, working with Quantum, and I think Quintinum only allows for qubits instead of
STFC-RAL-CR03 R61: having access to Cuba, as far as I know. So, I think the superconducting is Rigetti.
STFC-RAL-CR03 R61: That's what I'm very guessing.
STFC-RAL-CR03 R61: For ion traps.
STFC-RAL-CR03 R61: Yeah, for the IM partner, but there's, like, there's, like, an internal…
STFC-RAL-CR03 R61: internal hardware teams as well, which was… I guess, basically, there's, like, two modes of working with the NVCC. One is that there's this kind of platform where you access commercial offerings, where you probably don't get this low-level access. But there's also the internal research teams, where you probably have much smaller devices, but potentially a more meaningful collaboration on
STFC-RAL-CR03 R61: No, but there is also, in IBM, you mentioned IBM, you have… there is access also to Willow.
STFC-RAL-CR03 R61: the famous…
STFC-RAL-CR03 R61: the pen is checked. That's where, basically, probably the most. But I think maybe you don't have the still-level access. Yeah, we tried, well, when we were doing the paper, when we were writing, we were working with IBM, and we submitted there.
STFC-RAL-CR03 R61: But after… after we published, basically, they cut the access for the low level,
STFC-RAL-CR03 R61: Mr. I don't know if…
STFC-RAL-CR03 R61: it's possible through NQCC? Definitely possible, and the call for, basically, you could submit this application up to…
STFC-RAL-CR03 R61: It's probably soon the deadline for research, for academic research. Before, it was only open to industry, and not currently open to, academic researchers here in the UK. Yeah, yeah, I had a…
STFC-RAL-CR03 R61: I can definitely send you the link, or we showed you today. I did apply for a PDF project that we are working, but I didn't know that you have access to low-level pulses through MQCC.
STFC-RAL-CR03 R61: That would be really interesting.
STFC-RAL-CR03 R61: I think there is a possibility. And then, yeah, another question. Did you also explore other modalities, like, for quantum computers, quantum computers, and hardware? For example, the other modalities, having much more coherent sign, but much slower speed.
STFC-RAL-CR03 R61: gate speed.
STFC-RAL-CR03 R61: And these kind of things. For example, cold neutral atoms can give…
STFC-RAL-CR03 R61: Very long coherent time with the trade-off, basically.
STFC-RAL-CR03 R61: Basically, with the much lowering speed. It's improving, but, like, if there is any kind of, I am very interested in looking at it, but I've never worked on particularly natural, but I'm… yeah, because we don't know which hardware is gonna be perfect, right? So I'm really interested in getting two different targets. Because, yeah, the good thing also is, with these modalities, you haven't supplied
STFC-RAL-CR03 R61: You can… you can create icing chains and complex systems where you can basically have
STFC-RAL-CR03 R61: harmonic policy lectures and so on, so it's very interesting as well. Yeah.
STFC-RAL-CR03 R61: Any questions from Zoo?
Archana Radhakrishnan: Hi, I have a question. I was just wondering how, if you could expand a little bit on simulating scattering systems?
Archana Radhakrishnan: Using a quantum computer?
STFC-RAL-CR03 R61: That's, that's… that's something that I'm trying to learn at the moment.
STFC-RAL-CR03 R61: So, I… let me try to describe as much as I know. I'm… I'm… I'm learning, so I'm not expert by any means.
STFC-RAL-CR03 R61: So, what you need to do is, for example, you have the Hamiltonian, but you need to prepare the vape packet first to be able to put it on a quantum computer. And,
STFC-RAL-CR03 R61: I think for the fermionic models, you need to do some sort of
STFC-RAL-CR03 R61: Or level transformation to be able to
STFC-RAL-CR03 R61: do this, embed this wave packet on a fermionic lattice, for example. It's much more easier if you have a scalar field theory, because then you can describe your wave packet much easily, but with fermions, it's a bit more trickier.
STFC-RAL-CR03 R61: But then, then you can basically evolve this in time once you've… embed your obey. Sorry.
STFC-RAL-CR03 R61: Once you embed your wave packet, you can evolve this in time and observe how they collide and everything.
STFC-RAL-CR03 R61: But this is basically the extent of timeout.
Archana Radhakrishnan: Wow.
Archana Radhakrishnan: Thank you.
STFC-RAL-CR03 R61: Thank you.
STFC-RAL-CR03 R61: I need the question from Zoom?
STFC-RAL-CR03 R61: our room.
STFC-RAL-CR03 R61: Not that I can ask. In terms of scale, I mean, particularly, how do you see the hybrid approach scaling for a really realistic?
STFC-RAL-CR03 R61: gauge story, particularly non-Amerian QCD,
STFC-RAL-CR03 R61: That's a great point. That's a very hot point. So, the… I think, currently, there's… I don't remember the numbers, we have the numbers in the paper, but the problem is.
STFC-RAL-CR03 R61: you can put only so many ions inside an ion trap, depending on your technology, so you need to sacrifice some of the ions to control the nodes, and then you have the modes and everything, so…
STFC-RAL-CR03 R61: there are different limitations on that being able to achieve, so I think…
STFC-RAL-CR03 R61: It needs to be evolved a lot.
STFC-RAL-CR03 R61: I don't have the exact numbers, but…
STFC-RAL-CR03 R61: I think currently, as far as I know, it's much more limited compared to a larger size, also, because right now we have, I mean, thousands of qubits. I don't think we can have
STFC-RAL-CR03 R61: that many qubits and cube numbers from a hinging trap. I mean, we can have in qubits, I believe, in a hiding trap, but not
STFC-RAL-CR03 R61: Qbits are cumuled at the same time, that many qubits are cumuled at the same time.
STFC-RAL-CR03 R61: And I'm then following up,
STFC-RAL-CR03 R61: Particularly the algorithm work which you did, our transferabilities from Minecraft versus other hardware platforms.
STFC-RAL-CR03 R61: Gate structures are very much transferable, depending on the… on the technology. For example, if you want to use superconductive quantum computers, you cannot use the same gate setter, of course, then you need to truncate your gauge field or integrate over your gauge field.
STFC-RAL-CR03 R61: So that's, that's two different solutions that you know, that you can do.
STFC-RAL-CR03 R61: If you have, for example, this cavity interacting with the superconducting qubits, that gives you another environment. I don't know much about it, but that gives you another environment to do cubes and qubits at the same time, for example.
STFC-RAL-CR03 R61: So…
STFC-RAL-CR03 R61: they have a similar, dataset to how we thought that you can map directly. You need to…
STFC-RAL-CR03 R61: change some of the operations, but at the end of the day, you can get similar, things. So…
STFC-RAL-CR03 R61: There's one more thing that I've heard about photonic quantum computers, but this is just what I heard. Apparently, you can use the polarity of
STFC-RAL-CR03 R61: of photon to make it look like a qubit, and then photon is a Q model. I don't know how they would interact, but maybe that's a possibility too, but
STFC-RAL-CR03 R61: Hopefully it doesn't impact it.
STFC-RAL-CR03 R61: I don't know, I don't know how to… I'll do it.
STFC-RAL-CR03 R61: I'm particularly happy to see our colleagues from NQCC here, and that sort of gives us a great comfort
STFC-RAL-CR03 R61: Engaging more with our analytics and,
STFC-RAL-CR03 R61: And, this seminar is an example. So, let's thank our speakers again.
STFC-RAL-CR03 R61: And thank you very much. Please be free to join us for lunch, and we'll have some follow-up seminars as well in the PQD and QCC seminar series in the coming weeks, so we'll keep you updated on this. Thank you very much.