Okay so it's a very happy to be here, had these excellent discussions and I see some familiar faces.
I'm very happy to be here.
So today I'll be telling you about why would you like to use quantum computers to simulate chemistry and the progress in a colloquium format?
Not too many details. I'm happy to answer details at the end over the last ten years on this subject.
And sorry, I just got the new clicker as well.
So let's just think, first of all, simulation in general and I just want to make the argument that as soon as humans have had technology,
they have been able to simulate their surrounding world in particular.
The ancient Greeks had a classical technology.
They were able to put gears together and they built this device.
That fascinates me. This is antiquity, right. And, you know, around 200 BCE,
they built this device that actually can predict the movement of the planets and even the next Olympia
that needs an arrangement of gears that we build to try to understand the movement of classical objects.
All right. And it is this classical technology that started with the gears and ended up with computing
that allowed us to have pretty much the physical the physical world that we live on,
actually. Peter Gleason One of my colleagues in the history of Science Department, and he's also Professor of physics,
wrote this very beautiful book called Image and Logic about the emergence of computing
as a further leg of science and has a beautiful chapter in which he says the following.
He says that without computer simulation, the material culture of today, for example,
my beloved iPhone or my laptop or my cell phone wouldn't exist, not even my computer.
So in some sense now physical reality is inseparable from the virtual counterparts.
And again, we're very good at designing bridges and rockets and classical computers,
but we are still perhaps not as powerful at simulating the quantum world, quantum devices, even molecules.
And that's why we perhaps want to do the same thing that we did with classical technology.
Well, now using quantum technology in other worlds, using quantum technology to simulate the quantum world.
So in particular, the field that interests me the most. I mean, the original title said Chemistry and Materials.
And it is because in my group we are also thinking about quantum simulators for periodic systems and in general materials is to actually discover,
for example, molecules. So many, many people always ask themselves the question, perhaps I'm partially responsible for this law that is going around,
that if you ever have a quantum computer, it will be used to do chemistry.
Okay. And I always am forced to answer this.
And one of the ways to answer it is just thinking about what will be the most useful to humanity applications of a quantum device if we ever have it.
And you might argue perhaps it's cryptography if you work at the NSA.
What? I will argue that, for example, just the fine chemicals market,
the market of drugs and perfumes and glues and all sorts of chemicals that are expensive with respect to their weight is $3 trillion.
So if you have a quantum computer and you impact the design of of molecules, then you can you can enter this market.
And of course, classical computers do a lot. And in my group we discover molecules is a big thing that we do.
In particular, we have a scorpion. We make sure here this is not a chemistry seminar.
But in this paper here, what we do is use the computer to simulate what we believe is the world's cheapest battery.
Now, battery made of Quinones, which are basically these molecules that plants use to in their electron transfer chain.
And we hack them or modify them with a computer to make them very, very good batteries, way cheaper than lithium batteries.
And these batteries can be employed, for example, in these tanks here,
coupled with solar cells, although this company, Volt, is already it's already bankrupt.
And the reason renewable dismantled is because this is these tanks are actually filled with metals and the molecules that we decided are metal free,
way cheaper than the chromium that these guys were putting in these tanks. Okay.
So I'm very excited about applications like these. But of course, if you say, well, I want to be more fundamental, of course,
this fundamental questions like I love this picture of of a process experiment of scanning a sealed tape and paint a scene on a surface.
And the reason I like it, of course, is because you can pretty much see the conjugate,
the electron cloud by this very, very delicate probe of this molecule in a solid phase.
But also because Pantheon is a very strongly correlated molecule that has to be studied with powerful metal,
such as density matrix or meditation group theory.
You have to follow the best that we have with classical computers to understand electronic structure of the system.
And, and we can do this the matrix normalisation group theory because it's a linear molecule.
So flat Polynesians in an infinite limit, they are called graphene.
And I'm in the physics department and I know that everybody is in love with graphene in these departments, with the chemists.
We just call it infinite polyethylene, I guess.
But, you know, graphene is basically an example of a system that is very interesting to simulate also with a simulator.
So that's the target that I'm talking about. I'm arguing the quantum computers will be perhaps first employed to do this.
And that's the subject of this talk. So now let's use them, see to see ourselves first and think, why do we really need them?
Right. So this is my former advisor, Martin Catherwood on the UC Berkeley wrote this paper where he actually was pretty good,
by the way, at extrapolating what will happen from different electronic structure methods.
And it doesn't matter if you don't know this acronyms, but they are very popular chemistry methods for simulating molecules.
What will be the power of those methods as we keep growing larger and larger supercomputers that use the same power as a small city?
Okay. So if you go to one of the largest computers of today and we're already hearing this line on the plot of his paper,
we perhaps can do with this the functional theory, a 10,000 or maybe even a hundred thousand atom simulation.
The problem, of course, is that for different properties, for example, charge transfer states, definitely we have errors of order 80 or larger.
And if you think about chemistry being at room temperature density, functional theory is not a predictive theory.
Yet of course I use it to predict that battery. Okay.
So obviously it's useful, but it's not. A predictive simulator is not a simulator that you can always rely on.
You have to calibrate it and you have to do a lot of work to understand it.
Now, if you think about exact solutions, those exact solutions have been proposed for a long time.
I mean exact organisation,
that's what it's called in physics of full configuration interaction which is called in chemistry is a very fine method within a basis.
I can exactly that. I'm going to lay out a huge matrix and get the answer.
The problem is that by the time the grandchildren of my children die,
I won't be able to simulate, even with the largest computers in the world, ten atoms.
So it's quite boring, you know,
like I won't be able to really make predictive chemistry if we don't change the paradigm and switch from classical computing to quantum computing.
So that's hopefully the argument that in matters to do what we're doing.
So the current paradigm looks like this. So I take a molecule, this is acetone.
I make them all the time independent, showing an equation and a muppet to a classical computer.
Okay. By the way, this is the exact computer that was used by SF Boys for the first time here in the England for
the first time to simulate an arbitrary molecule using a computer and then get the number,
for example, that the energy is roughly 192 cartridge.
If you think about it in terms of information, what we did is we took a quantum system which is intrinsically quantum mechanical.
The firm unique motion of the electrons in the potential of these nuclei or even the quantum nuclei as well,
and converted it to quantum, although of course, it's quantum information.
But then we committed the scene of cramming this quantum information in this very inefficient yet powerful classical information processor.
Okay. And finally, we obtained a classical information that's important.
We're not after understanding every detail about the molecules we went after understanding some macroscopic property like an energy at a moment,
the quadrupole moment, etc. And observable that I can enumerate with a polynomial number of numbers.
Even the electron density is okay. What is not okay is to go after, for example, the entire full wave function.
Because for those of you that know about it, it is akin to doing quantum tomography, which would be inefficient.
So Richard Feynman in 1982 published this paper that is listed here in the talk that I was surprised to know is his most cited paper,
the paper what he thinks about how to simulate physics with computers.
So that paper is more cited than than than his QED work and all the works by Feynman.
And what he proposed is very simple, and I can summarise it here in this a few equations.
If I have the wave function of a molecule or a material or a system, I want to study.
I want to first have to come up with a map, with a mapping.
I first come up with a mapping that takes that wave function to the wave function of the quantum computer.
And then let's imagine that we're interested in simulating the time evolution.
This is the unitary term evolution operator which is generated by the exponential of the Hamiltonian.
Well, you would have to have an uncontrollable quantum system, emulate the time evolution.
Right. And that the simple system, that simple, simple idea tells you that if I want to evaluate an observable on this right hand side.
Within the bases that I explained to them is this to me will be indistinguishable from a residual on this left hand side.
Therefore, achieving the idea of quantum simulation. In other words,
if I have this asset on molecule and I am looking at this circle with a rotating arrow
which is representing the rotating phase associated with the particular low energy,
I can state that I'm a state of this molecule that rotates at a speed proportional to its energy,
and I can build an apparatus like this one that actually has the same time evolution.
Then in principle, I achieve the goal. I can, for example, extract the energy out of that system and design a battery.
Okay, so that's kind of like the goal. So now what we need is we map a quantum system to another quantum system, which is quantum information, right?
And then we can actually map it to a quantum information processor and then get the same energy.
Okay. So that's kind of like the high level picture of this whole.
Well. It's like you wouldn't be here. Oh, yeah. So now.
This is not exactly that. I read what a museum in Japan asked me the following question.
Me and my student, James Whitfield, they asked us, you know, just imagine that there is a Moore's Law for qubits.
Okay. When will the qubits will be a classical computer?
And of course, we don't know. I mean, it depends on my experimental colleagues here.
I'm going to knock on and so on and say when you have your fourth and source ready and, you know, it's it's beyond my control.
But what I can say is the following what is true?
And I can tell my chemistry colleagues or anybody that the simulation is that because these algorithms are polynomials scaling,
no matter what is a polynomial power, which is basically the slope of this here.
And I just started here this random this cube here. All right.
Eventually, this here will cross copper cluster, which is a very powerful metal, and just disappeared from the face of existence.
So if you're a scholar of the copper cluster metal, you could retire or study using quantum computers.
Right? And then it then it will do secondary perturbation theory.
Maybe one day we get away with DFT, because I argue that if you have a quantum computer, that sort of things.
Exactly. Obviously, you will not want to do these methods.
Okay. So this will be a predictive or an explanatory simulation of matter.
And the other argument, I think this is a word of the year of the quantum computing people.
I cannot believe how many times I have heard my quantum computing colleagues call talk about quantum supremacy.
And if you haven't heard about this, you hang out with the quantum computing people and they will be telling you what quantum supremacy.
All our community, the community that I live on in quantum computing is really thinking about the moment.
What a quantum salivating about the moment when a quantum computer will be faster than a classical one.
Okay. I argue that simulation of chemistry perhaps is also an experiment that can that can be one of the first ones to do quantum supremacy,
if not the first one. Okay. And that will be exactly the moment where we just crosses the exact line.
So we don't we don't need to go very far to achieve quantum supremacy.
So there's a little animation problem, but I won't try to tell anybody here that doesn't know what is a quantum computer?
What is it in three slides? So those of you that know forgive me and those of you that don't know also forgive me because it might be too stupid.
But let's start with the classical bit. Right.
There's currently no current of Magnetisation or no Magnetisation or up or down any type of amount of one of ones and zeros.
That will be basically classical information. Quantum information is a generalisation to the fact that I might have two states, for example,
around an excited state or superconducting current going to the left or to the right,
or a particular hyper fine state of anatomy or whatever I want to use as as as a place to store information.
But what I can do in quantum mechanics that I cannot do in classical mechanics is actually generate the superposition.
A very cool way of visualising this is already alluded to here is basically this idea of a block sphere.
The only thing I did is I took these two complex numbers and factories them in this way because I assume this wave function
is normalised so I can factories them as a little point in the sphere where C2 is in the top and one is in the bottom.
And my cubit, for example, will be in a superposition between zero and one if it's in the equator,
but it will be either a C2 or one if it's on the, on the, on the poles.
Note that we also have a complex phase that we can use when we when we actually move around these this direction.
So basically that's how I like to represent them graphically.
I show them to you a couple of times and then the power of superposition entanglement is what allows us to to have more powerful computation.
We have some things that we have to worry about. Of course, we collapse in wave function. We will measure it.
And what is a quantum computer in three lines is a collection of controllable and addressable qubits.
Okay. And if we didn't have the most important result, I think of all the field is the results of error correction.
Okay. The same way that we can correct errors in classical computing, we can correct errors in quantum in quantum information processing.
And I think that is the most important result in the field, because if we didn't have the ability to actually build error correcting devices,
you know, at least theoretically, they're going to be built experimentally, hopefully very soon.
Larger and larger ones then. Then there is no hope of really having a quantum computer because the coherence eventually will take over.
So I won't talk too much about error correction, except for a couple of points about it.
So okay. So now this is our second slide about quantum computation, just the general graphical picture of it.
You will initialise a quantum state, usually in a classical state, but not necessarily in this case.
I initialise this three bits in the zero zero configuration.
For example, imagine that you have speeds and you polarise them along a particular direction or you have molecules and
put them all in the ground state or whatever is going to be a quantum information processing system.
And by the application of these quantum operations, that will tell you in the first slide,
I can prepare different arbitrary superpositions of this system.
Which I'm going to call all the procedure. Quantum algorithms generate superposition, entanglement over all these quantum states.
And then I will apply a measurement that will select the states according to the square of their amplitude.
So hopefully my quantum algorithm is very smart and concentrates my answer around a number so I can do a bunch of measurements,
calculate an expectation value. So repeating the quantum theory many times and you get a classical information out of it.
Hence the reason that I was telling you at the beginning that I am after classical information of molecules.
So my job has been to think about what's the best quantum algorithm, how to implement it for molecules.
Okay. So that is a story. So a little bit more details about how to think about this because I'll be telling you about council gates and stuff.
A gate is nothing more like an operation like in classical computing.
In this particular case, I want to think about operations that rotate along those three different axis of the sphere X, Y and Z.
The policy moment. This is an example of a gate that we talk a lot about in quantum information.
Processing is a or gate. Note that this is kind of like music.
You start on the left and move to the right, passing by the gate.
So if I have a qubit that is represented by this line, I apply this to our operation and what I do.
It would take my block sphere, say you was on zero and take it to the equator.
So that's a gate. I can also talk with gates.
The simplest one is the control gate entangles two cubits.
And if you want to think about the classical truth table of this gate, it says that if this first Q with is one,
then you flip the sign of the second Q rate and if it settle, you do nothing and that is enough.
Turns out to have this set of gates to actually universally compute anything you want.
You can play Mario Brothers on a quantum computer. With this, you can simulate the molecule or you can, I don't know, play Angry Birds.
Okay, but. What is important is that we also have a concept of subroutines or parts of algorithms.
For example, a very powerful one I will be using and is efficient, is important to know.
That is to calculate the future, transform.
You can calculate the full transform or the inverse of it by actually applying this sequence of gates that again read like music.
I apply the same output. You know what it is now I apply controls, which is the particular control rotation.
So it's kind of like a hybrid of one of these. And these guys between these two qubits then apply a controlled T within these two cubits and so on.
And this is a swap. Okay, so I apply this musical scheme to my qubits and then eventually I get a quantum for your transfer.
Right. So you're saying that. So what? Okay. So let's just dispel a myth now that we all know what quantum computation is less this phenomenon.
I know to me that happens always is. All quantum computers will be able to solve all the problems in computers.
And that's not true. Okay. What does this mean?
Quantum I would say always faster and more efficient than classical ones. And that's not true.
There are many causes of problems that you are not going to be able to solve.
But we have a Hall of Fame, for example, quantum search.
Many people know that it's qualitatively faster to search and database on a quantum computer.
You can factor with an exponential speedup, and this is basically the basis of all the interest of NSA.
They really want to build that is emails. So then they they basically need this.
And what we need is basically quantum simulation.
And as many people have shown and we exploit it, you get an exponential speed of in the time evolution of any local Hamiltonian.
Okay. So there are some restrictions. You have to be able to prepare the state that you want.
And for that, we need to actually go and talk about the stages of quantum simulation.
First you need to prepare the state that you want. I told you, that's kind of the piece.
Then you need to time of it, which I already asserted to you is sufficient, and then you'll be able to wait.
You need to be able to measure the properties which will occur to you that is sufficient.
So computer scientist, is there any computer scientist in the room?
Well, they are very imaginative people, computer scientists, and they have these computational classes.
And the one that we're going to talk about involves Marilyn and Arthur.
And I'm not kidding. It's called Quantum Merlin. Arthur. Okay.
And in this in this game Million Arthur game Merlin is ever powerful.
And he can create any quantum state that he wants or she wants.
Maybe it's a female magician prepares any quantum state and can win it over to Arthur.
Which Arthur is powerful, but not so powerful. Arthur only has a quantum computer.
So I guess now I wish we are going to have a real full blown quantum computer.
Well, Merlin goes and gives a quantum state to Arthur. Renato can verify you can play with it, but with a quantum state.
Okay. And it is in that context of dividing.
I don't know what happened with the project or somebody. Thank you.
Me? You were blocking Arthur. Yeah.
You were looking Arthur out for these things. Yeah. So, so?
So. So Merlin transfers the estate to Arthur to. Not to verify. Right.
So in that context, Quantum Million, Arthur is basically any problem that if given the solution to it,
a quantum computer can verify if it's if the solution is true or not.
Okay. What about the quantum polynomial? In some sense is what I can do by himself.
Arthur says, No worry, I don't need Merlin because I can generate my own solutions.
Okay. So if quantum simulation is involved with quantum polynomial, the whole thing preparing, evolving and measuring, we're all set.
I can simulate all my theories in the universe and I'm all set. You will be happy and I'll be happy.
What in your hand? If it belongs to this computational complexity class, there might be a material, most likely a very frustrated system.
For example, a very frustrated, spinning wheel of material that is not really in integral state,
and perhaps a quantum computer will never be able to simulate. And that is still a discussion.
Okay. So including the preparation of molecular instances, we don't know where we are in terms of quantum simulation.
Well, Georgia Times, what we know is it's in BQ P and these are the computational classes.
And you may be familiar of the NP versus B situation, which is very similar.
Basically, the analogue of QM basically needed merely for preparing some states and then modifying them or developing quantum polynomial again.
And if there are computer scientists here or people that know more about quantum algorithms,
remember, this is a colloquium and I'm just explaining things as best as I can.
Hand-waving. But the point here is, I argue being a chemist, that molecules are easy to prepare.
And this is basically like some sort of ontological or philosophical argument.
Think of a biomolecule. It has to be prepared in the lifetime of a human.
Okay, to be useful or think about this work here.
Well, it was prepared in a lifetime.
That is probably reasonable. In other words, if there is a chemical reaction that more or less results in a molecule in a reasonable amount of time,
in principle it should be some level. Okay. So anyway, we are happy to talk to you about more about that.
We're trying to formalise it with computer scientists. So now I'm going to tell you about quantum chemistry.
So what is the task of a quantum chemist? Okay, this is famous.
And the only reason I'm telling this story is because it's a British scientist, someone,
Boyce said once he stood up in front of an audience and printed his computer program,
which is kind of like the grandfather of the Gaussian program, I guess, in a table,
and said that quantum chemistry is a molecular geometry interest here in my program and an energy comes out.
Okay. That was a vision that someone voice has.
And unfortunately, many of my colleagues still believe that the only thing that quantum chemistry is okay.
But what quantum chemistry is then therefore is taking that input geometry for a molecule using the Oppenheimer approximation,
doing a self-consistent solution in the local basis. We like to call them atomic orbitals.
To obtain a solution is the localised or this local basis to obtain the so-called molecular orbitals.
So he does water and heat out of the occupied and on occupied orbitals of water.
Okay. And that will define the Hamiltonian of the problem I want to solve.
So that's the mean field solution, which I'm going to assume is the reference.
Okay. And from that I want to solve the fully correlated Hamiltonian here of these two Pauli fermion operators.
What they do is basically scatter electrons into orbitals to two orbitals due to two Coulomb repulsion and this one
electron terms that are hoping between orbitals due to the electron kinetic energy and electron nuclear attraction.
Okay. So this is a sample with a polynomial number. Okay.
Actually into the 4% square such theorems.
So to a physicist work. Okay, this is a Hamiltonian for our fermions.
And what we, the chemists do is calculate these very exquisite parameters here.
Okay, using a smart basis, that's a lot of the things that we can do is just calculate those numbers.
For all intents and purposes, except some of my more advanced algorithms, that is the input to the quantum computer.
So now if you wonder, how do I program a quantum computer to do chemistry, I use the chemistry program to do efficiently.
This is in polynomial time.
I can do obtain all these numbers into the four of these numbers and in square of these numbers that fully define the computational problem,
that defines a molecular instance. You want to change the geometry of the molecule a little bit, stretch the water molecule.
You have to do all of this and get this different set of parameters for your quantum computer,
which again will enter your quantum simulator as classical input.
Okay. So and we call like we like to call these numbers the integrals.
This is a one electron integral and this is a two electron integral. Okay.
And I think this the same problem in most lights is ten years. So if anybody got it.
So now.
I want to show you I told you all of that, because it's amazing that I can show you the quantum computer simulation algorithm in half us alive.
Here it is. Okay. This is what I do, guys. And I know that many of you.
This is the first time I saw quantum circuits. So don't worry.
These are harder margin. Remember what the Kalamazoo. What I did there is turned all my cubits into superposition.
All those us do that. Okay. This issue is nothing more than the unitary term evolution of the molecular operator.
In other words, time observing the molecule. We'll talk more about how to implement it and all the caveats.
Well, this is the only three time evolution of this operator generated by the Hamiltonian of the molecule,
which, by this relationship is real, is related to the energy of the molecule.
So I choose a time t so that they have the energy t is minus two times this phase, which I will be reading.
And that's what this other one is called, the Quantum Phase Estimation Algorithm, originally proposed by Seth Lloyd.
So what you do is the following you time evolve system and entangle it with this set of ancillary or auxiliary qubits.
Okay. Each one of them is entangled with a successive power of two of a unitary time evolution operator.
And you might say, What the heck are you doing around? It's actually quite intuitive.
I am entangling the time evolution of a system with a bit and then twice its power and the four times its power and eight times and so on.
And what I'm doing is basically writing in binary the face.
So the face is being written in binary. Okay. And I'm hearing the time domain.
What happens when I play if we transform? I go from a time domain to the energy of frequency domain.
Right. So why do I get here? The energy, the frequency of oscillation of this phase.
And if some of you do quantum dynamics. My chemistry colleagues know that sometimes this metal is used.
Also in classical dynamics. You propagate the way pocket-knife will transfer me to reality cycle values.
So that's basically the basic quantum algorithm for simulating chemistry.
And what we did in 2005 is actually proposed to use it using the chemistry integrals and still doing chemistry problems.
Now, the problems that arise are the things that you have to worry about.
The first one is the following. These are fermions. Electrons are fermions, but the qubits are distinguishable to single health particles.
They are not both ones. They are being withheld particles, but they are distinguishable.
Right. So they are also not fermions. So I know this Q with this here and obviously with this here.
So I do have permutation and symmetry. So what do I do?
I need to build it. And I build it with a so-called Jordan beginner transformation.
So I need to actually transform my operators another bunch of different gates to take into account that.
Okay. So, Bree, that probably this was the hardest lie. And I speak first.
I'm a Spanish speaker, so hopefully us still awake or not too annoyed.
So let's go back to a molecule. How do way make up a molecule to the quantum computer?
I want to make this very, very simple mapping. Each qubit is going to be a spin or metre.
In other words, every two cubits is going to be a molecular orbital,
and the first cubit is going to be the spin up and the second cubit is going to be the spindle for the first orbital,
and then the next cubit is going to be spin up for the next door orbital. And then I want spin down for the next orbital and you keep doing that.
There are more other ones mappings, but this is a whole mapping.
So in other words, I have here, for example, one one set of C2 will be the first possible state of the hydrogen molecule.
It will be two electrons and they get other or symmetric state. And then it will have this excited state and this excited state.
And these other states are not valid because they don't have the same particle number.
That's one example of how to map the wave function to liquids. That is very nice because each cubic has a very nice chemical.
Interpretation is basically the fact that every two cubits will represent one of our atomic basis functions.
So with that I can calculate how many QE do I need to stimulate interesting molecules?
And this is from our original paper on the subject.
When I was supposed to look and you can see that, for example, benzene and don't worry about this basis.
If you're a chemist, you know, there are good ways to say it's benzene, for example. You have to go to a.
Here we're required perhaps about 250 or so quantum bits, fully exact.
Again, these are logical quantum bits.
Caffeine, another very important molecule, at least for theoretical chemists, requires about a hundred thousand cubits and cholesterol.
A molecule very close to my heart requires about 3000 cubits.
Okay. And that's very cool because that's the same number of humans you need to factor a number.
So if I were friends of the say you build a factory and a factory molecule, I would be able to simulate the cholesterol molecule.
Exactly. And calculate how it binds to my walls of my of my veins and maybe prevent my own heart attack from eating too many Mexican tacos.
Okay. So my first real student, James, I gave my first to James.
I project this is when I graduated as a puzzle book with back in 2005.
And I told my student, Well, James, please figure out all the details.
That's the first thing to do. A grad student, right? You're going to be figuring out all the details of my potluck.
Okay. And six years later, we publish this paper, okay?
With all the great sequences, all the detail of how to do all this from unique operators on a quantum computer.
And back then not many people were interested. But it got really cool when this was used as a benchmark for computer scientists.
There was the air fire agency decided to make it a benchmark and say a computer.
Scientists write the compiler for Alan's 2011 paper.
Okay. And then both of computer scientist started thinking about chemistry and started reading about I don't do which tool and stuff like that.
Okay. And notice that in our paper there was this figure that says the problem with the lower scheme is that although efficient.
In other words, we can simulate the molecule exactly in a quantum computer.
It would require too many gates. So if I show this to you and the user uses quantum optics and they tell him
that simulating cholesterol will require ten to the 17 effectively 15 gates,
he would just tell me I'm so real and like go home. Like, you know, this is still efficient.
But the very naive first algorithm is quite expensive.
Okay. So that's where we are. I want to tell you how much progress has been done in the last ten years.
One word about that correction. Even with that very, quote unquote expensive algorithm is not unreasonable to do error corrected simulations.
The way you do error correction is very similar. The way you do classical error correction.
You're going to encode your quantum information over many qubits and measure errors on the qubits,
do central measurements, and figure out if they are destroyed or not. And if they are destroyed, you can correct them.
So if you do that, you can actually show that these naive error correcting Skillings were not very naive and
that with improvements that the Yamamoto group did in Stanford in collaboration with us,
we found that, for example, simulating the lithium hydride molecule would require about the Honda,
the physical cubits and, you know, ten to the seven or 10 million gates.
So that's kind of where we were about, you know, three years ago. Okay.
So that was kind of what we're saying. Look if you can build a machine that those larger with similar lighting.
Exactly. Still not very exciting for our colleagues. So we have to go better than that.
And now in the meantime, things like I needed to get in here.
What's going on? Okay, so how can I show people that this is not pie in the sky?
I have to do experiments, and I have to convince others to do experiments.
Some experiments I didn't do. Some of the people did. And some of them, I'm almost like a honorary co-author, like in this one.
But this is a list of all the experiments in all the different quantum information
processing architectures that have simulated the molecule over the years. Notice that the number of qubits is two or three only.
But the algorithm goes better and better. You will see. Okay.
This is for you, scalable.
These ones here in the bottom are fully scalable, which means that whatever we implement the there is the full algorithm with no tricks, so to speak.
And then this paper, for example, was a very stressful paper because it came out a week after my nature chemistry paper.
So this was in the year. So let's talk about the first system that we simulated.
And this is Paul Dirac showing you here the symmetric and anti-Semitic
non-metallic configurations of the hydrogen molecule that we've been mentioning.
So we did that experiment in collaboration with my colleague Andrew White in Australia, and this is how the experiment looks like.
Basically what you do is you take two entangled photons.
One of them represents each one of the two by two matrices that represent the six by six Hamiltonian of the hydrogen molecule.
And you use this device to do the most expensive drive only station of a two way two matrix ever done in history.
Okay. Which is basically this face estimation algorithm to actually read out bit by bit.
This is an old trick that you have to use bit by bit.
You do the one beat and then adjust the machine and read them a little bit and adjust the displacement them a little bit.
And obtain the potential energy surface for the hydrogen molecule.
Points in this particular a simple system,
we can use an error correction method that only works for small systems called majority voting error correction.
So the curves that you see there are actually error corrected up to 20 beats of precision.
So this this is a digital quantum. Computers are digital objects. So this is as digital as MATLAB, up to 20 bits.
So those dots there are not just placed there. They are actually data from the quantum computer.
Okay. Which we find pretty exciting. So that was the first experiment.
Okay. So now can we fast forward to 2014 and go to Twitter?
And many of you might know who is John Preskill? He's one of the top quantum information theoreticians.
And he was addressing in Twitter what was happening that year, which was a very stressful and interesting year for us.
Okay. So we're colleagues.
Basically we're going to Microsoft published a paper that says that it was impossible to do quantum chemistry of quantum computer for the arguments,
I'm telling you. And he says, well, this paper, when it's formed, which is one of the out of date, there are bigger improvements.
And citing another paper of Microsoft. Okay.
But he was outdated because the day before we had published a paper that had better scaling than that paper.
This is baby, the way you're talking about the paper for Mos. That already already was better than this paper.
You know, I hadn't even noticed. Okay, and why is that?
Because, of course, after this paper came out, there was a race between many groups,
but mostly the Microsoft and ours, because this is what came out in Break-Up wasn't 14.
Okay. Based on this paper, that, again, was the first paper of this race when it appeared in the archive.
And then about six months later on their on their on pray that if you read this, I'm not going to read to you,
but it basically says here that we're in trouble, that, you know,
simulating a molecule with with a with a quantum computer is impossible and so on and so on.
Okay. Well, this is a story that was the original paper in the archive in 2014.
Sorry, there's a typo here. Okay. December.
If the people in the article in December 2014, then in March,
the Microsoft team themselves improved on the way to improve the seven from 8 to 11, where they need a number of basis functions.
And remember, this is the bound like analytical found obtained by methods of computer science on our algorithm.
Right is the worst case scenario. June 2014.
This is our group coming back at them and being better than them by a factor of point five and, you know, log jam.
So we were like, yes, we got back to them in this time and then again us collaborating with them because now we're friends.
So we've together collaborated and got a better estimate,
which we actually looked at the scaling respect to the nuclear charge and what is that is the most important problem.
And then we collaborated with Dominic Barry from Australia to use the sparse algorithms
which have similar scaling but super important in terms of the number of gates,
super important and exponential speed up in terms of accuracy.
They gave us log one over at Epsilon instead of one over Epsilon as all this or that algorithm.
So not only we have algorithms that actually are better in terms of scaling formally
this is about but also are better in terms of scaling respect to precision.
So this is incredible result in a year in the cuts.
I'm so glad that Microsoft got into the business and and also woke us up a little bit to do a lot of work too.
And then we all got together and, you know, beat this problem down.
So Microsoft researchers say that calculations are they estimated that they quantities of years in
computers and coding them more or less now take seconds in some sense by improving all these killings.
Okay. So in other words, quantum chemistry is going really rapidly reducing the resources.
But in the meantime, my group and I will not just be being steel.
I want to show you basically we're going to have a guy at the quantum computer simulation that is graphical that in this paper,
people were telling me,
the reviewers were saying, Alan, you've been doing quantum chemistry for ten years and keep publishing and publishing the same subject.
So I said, let's reply to reviewer number one with this graph. That's not true.
We have proposed four different methods that are completely different to each other,
going through all these different paths of different mathematical transformations.
And the one I just told you right now is just this path which is using the one of a hammer approximation,
using a second quantisation and computing integrals, all living at this formation notarisation and using quantum phase estimation.
We propose an idea about the quantum simulation for the about the quantum devices that are universal.
We propose that quantum dynamics method that can do scattering problems in real space.
And the one I want to tell you about today is the one that we and many other groups are super excited about.
It's called the variation like solver. Okay.
And that one, I argue, is going to be probably the thing that is going to do quantum supremacy sooner, small and phase estimation.
I'll show you some experiments, too. So that's the remainder of the talk.
I'll tell you about the variation of like in software and when do I mean by that?
During the course of all of this, one day we were thinking in my group, actually,
my student John MacLean basically and myself were thinking like, what happens?
Okay, this guy Jaro, what happens if we think about a classical computer?
What does a classical computer do? It gets us a wave function, evaluates the energy, gets us again.
And those is iterative system, right? This is how basically all the quantum chemistry packages work,
including the package that is a boys develop like, you know, almost 50 years, more than 50 years ago.
So then the question is, well, can I do the same? Can I actually get the wave function, prepare the wave function?
Even with the energy which basically all of this process is only in a quantum device,
you prepare and measure it and then use a classical computer as a as a co-processor to optimise the wave function in the liberation of subspace.
So that is the meaning of the, of the variation of like in solver. Okay.
So in the present I can solve it. I can write in three lines what's going on? You have a variation of minimisation over the energy of a Hamiltonian.
Very importantly, note that you can write the Hamiltonian as a sum of different terms of the spin operators.
And the only thing I'm asking my quantum computer friends to do is to calculate these
expectation values that I can multiply by the classical parameters I got from my computer.
I told you, which parameters are those? They are the integrals. So, okay, so I calculate my integrals.
Do I join them in a transformation or a similar transformation? Turns out the better one is probability of.
And I use the transformation to write down how the Hamiltonian looks like in terms of the spin operators and now any quantum computer of the world,
the supercomputing device, the quantum optics, etc. all of them can be seen or announced trap.
All of them can be seen as a basically as a quantum console.
And why is this so cool? Because what quantum computers are good at is to do a measurement.
And in the classical computer, they cannot multiply and optimise and all the things that a quantum computer cannot do very well.
Try to write the quantum circuit for multiplication. I do in my PC.
Okay. And that's why I believe that by issuing quantum like it's already so powerful.
And since this has been published in 2014, there has been eight papers that actually use it for something from our group analysts.
So with the idea of this paper, if you're not,
is the first of two recent experimentalists and the last out of two was to publish it with an experiment at hand.
And Jeremy O'Brien in Bristol actually built this chip, which I love is so high tech connected to low tech.
These are heaters that change the faces in these micros microscopic, kind of smaller,
I would say very small, like a couple of centimetres long quantum optics set up.
Okay. And here, here, do the ones that actually do not look like that.
They look much more advanced, by the way. But this is basically the integrated quantum photonic chip.
One of the earlier ones there has these photos that come in from these rails,
and you can adjust the temperature of this of these regions here to actually body the faces and basically a bunch of interferometers.
And you have these detectors at the end. And turns out that this one can do a two by two arbitrary gate.
So with very similar like in software, we were able to to to basically evolve from two one,
two by two matrices to four by four matrices in four years. It's not so bad.
Okay. So now we were able to do four by four. So what can you do?
You can do helium hydrate. Okay. Helium hydrate plot is a four by four Hamiltonian.
And here is the result. This is a potential energy surface as we dissociate the film hydride in physicists units.
Okay, this is in the paper and the headed mega used for more. That's only a physicist can come up with that unit.
Okay, maybe I use thermal. Okay, I know it's. I know it's the unit that you should be using, but you should use cartridge or something.
A chemist like so kilocalories. But anyway, here is basically the potential sort of face.
And notice how we don't use a lot of correction.
And most of the error here comes due to losses and due to the fact that we are doing this this this phase shifting.
We like this. I consider rudimentary the temperature technology.
Well, nevertheless,
we were able to actually use the volition eigen software and optimise the wave function and each one of these points and get the energy.
And again, this is, again, quantum computers simulating helium hydride. Okay.
So so far, so good. So now. Let me just tell you then the latest experiment.
Okay. I notice that I'm wearing it, so I'm not going to be late and maybe even a bit early.
So since then, of course, I told you so far that we have developed many algorithms with no details,
but we can talk later that reduce the scaling of the face estimation algorithm.
And then I told you that we've been developing this variation of quantum and solver mental.
He already has been employed, by the way, in on drops by one of my former group members,
Michael Young, and a collaborator whose last name is Kim at Senor University as well.
Well, we were trying to see how far we can go. And then so we started talking to Google.
Turns out that as many of you probably know, that Google basically Acqui hired John Martinez from the University of California,
Santa Barbara, and his entire team is now building quantum computers for Google.
And this is how the quantum computer looks like right now is basically nine cubits coupled to these oscillators
for readouts and and he don't really control lines and they call this cubits X one because it looks like axis.
Okay. And they're a very phenomenal cubits. This is another diagram of the wiring diagram of this of this cubits and another picture of five of them.
And basically the idea is like, can we use the X months to actually do both for the first time,
a fully scalable version of the evolution of a quantum console.
In other words, writing down all the operators without calculating them or doing any tricks like we did in the quantum optics experiment.
Just a full, really honest simulation and also face estimation,
which involves many more gates and basically look how they look in a superconducting machine.
And this was done over the span of a few months because they are very good at controlling their device.
So it's mostly talking about the problem and interfacing with them.
That led to this paper that was just submitted in December, where we actually have,
in this particular case, two cubits for the controller and three for the face estimation.
In this particular case,
I'm showing you two and actually one of the ball sequences that was used in the superconductors that corresponds to this liquid, okay,
to calculate the energy which we can in a very minimal basis guide as these numbers that come from
a classical PC multiplying these correlations of the qubits and if you do enough experiments,
measure these correlations at the most in your classical computer, optimise initial state again, you know,
suggest that your parameter for these rotations here and this particular case is a single rotation up.
We will get chemical accuracy in this particular case.
For these bases, we got an accuracy of one kilocalories per month, which is extremely good for chemistry.
So I am very excited about this experiment first because we did it very quickly.
Notice also that the small device has more cubits and can do more gates so we can, in principle, do a larger system there, improving the coherence.
And not only that, we could also do the phase estimation algorithm.
Okay. Which involves characterisation over many terms of the Hamiltonian, and therefore you can see there's more error in the phase estimation.
Okay. And you can see that the variation of quantum insoluble is actually, first of all,
more robust to error intrinsically, but also because it employed less gates.
Underwent less decoherence. So.
What I'm trying to say here is that theoretically this is the best possible angle here.
See data for this experiment and the error that we get in the experiment will be
something like this if we place our computer at the basic theoretical angle,
but the machine is more robust and finds an experimental angle that is slightly different and that experimental angle is actually better.
And why is that? Because we're using the variational theorem and the original theorem allows us to compensate for errors.
It's quite cool. So in some sense if you have a noisy quantum device,
the additional leg and a little bit actually helps you do better than, than, than you should naively.
So this is the last resort slide. So now I'm going to talk about a paper that just appeared in Nature Chemistry.
This is only me and editor of of Nature. They wrote this commentary in Nature Chemistry, which is actually arguing that.
That our our our search is chaotic and maybe, yes, I'm Spanish speaking, so maybe I'm like Quixote.
Okay. And what she basically means is that, well, you know, maybe they would be able to do this.
Maybe not. And the second thing that she's talking about is, well, even if they do it,
maybe the classical computing people say the tensor networks people and all these people that are getting better and better methods.
By the time we get our quantum computer, we already have cracked the problem. Okay, let's let's do it.
So I went to Twitter and I bet we had a bottle of champagne that in 20 years, we want to be able to have a quantum computer do this better than her.
So stupid. What I believe is reasonable because I believe in my experimental colleagues and here is basically revolution writing to first.
And then we did this tabletop quantum optics experiment with them, right?
Jeremy Brian did this experiment in an integrated photonic chip and now we're using eight superconducting qubits.
For those of you that follow the field, this is a rapid progress.
So I trust in my experimentalist colleagues that they helped me right on this bandwagon.
And also there's by this time that she predicted show that we can have a quantum computer, achieve quantum supremacy for chemistry applications.
Okay. So now let me end just briefly, briefly with the following question.
Can we beat classical computers? Okay. So for that, we start collaborating with Intel Research, which got recently interested in quantum computing.
And they have a massive effort now in quantum quantum computing at Intel.
And one of the early theoreticians, Mr. Jansky, collaborated with my graduate student,
Nicholas Away and me in building this package that we like to call.
Q Hipster. Okay. The Quantum High Performance software testing environment.
You just happened to be this acronym for sure, right? But Q Hipster is interesting because it was built at the Interparty Computing Lab.
My student went there as an intern and he supposed, you know,
it's basically built to be as far as possible and therefore allows us to to do up to 40 cubits in the in the text of stampede computer.
Actually, although the machine can handle up to 43 and in the largest computer in the world, you probably can simulate 49 cubits.
Okay. So really, to achieve quantum supremacy, I argue, you need to go beyond 50 logical cubits, which in terms is extended to,
you know, perhaps $0.05 or more of physical cubits just to give you a magnitude of the problem.
And so you have the challenge. And obviously, obviously, the classical computers would keep improving slowly in terms of qubits.
So this is the logo for the software that we're considering.
You can send me suggestions because if people used up all 26 of January, what I think this is going to be the logo of quantum hipster.
And with that, I just want to try to have some time for questions and thank my research group here.
Some of the people that it is work are already gone. But the students that are really pushing these nowadays are Yankee Village can here.
And Jonathan Romero, this is a new blog that was doing quantum computing.
And Giacomo Richie, which is sitting somewhere here, is already moved to Intel.
So and also Saddam was stymied. Two of my group members really move to Intel.
Maybe Djindjic was not there anymore. Here he's sat already had left as well.
So. But anyway, so many, many people are also moving to industry.
So I'm one and also with a superposition of my group in the ground in the excited state.
And with that I open for questions. Thank you.