We go from Charles Bennet

from IBM research one of the pioneers

of Quantum Cryptography among other things, who I said was both a physicist

and a computer scientist. We go to Ady Stern, who is younger

and is only a physicist for now; and one of the reasons for inviting him

to this conference is to try also to get him

to be also a computer scientist. He is one of the best speakers

I have ever heard as I think you will see in a few minutes. He is at the Weitzman Institute,

and he is a newly elected member of our Academy here,

I think last year. I am going to ask him to come

and talk to us about physics and quantum cryptography. So thank you very much

for this introduction, I am honored to be speaking

in a computer science conference. I didn’t know it was

a conversion attempt. I am particularly honored to be

speaking after Charlie Bennet one of the pioneers of this interface

of quantum physics and computation. I have kind of an ambitious program; I would like to tell you about topological

physics and quantum computation. So my plan is to explain, first there

is going to be a lot of physics here, but don’t worry. I will talk about what

Topological states of matter are and what is the quantum Hall effect,

I’ll explain this. Then I will go even more complicated

for something known as Non-Abelian states and I will explain how they may be

tools for doing quantum computations that’s relatively

immune to de-coherence. Since I am going to say it

is going to be relatively immune to de-coherence

I will explain what de-coherence is. And I will explain why Non-abelian

states minimize it. And then you know, being

a physicist I have to come to real life, do we actually need a microphone?

-Yes, for the recording. Whatever you say now

will be classical. So I will tell you how Non-abelian states

may help us in avoiding de-coherence which is the main obstacle we have

on the way for quantum computation. And last, as being a physicist

I’ll go down to real life and tell you where we stand now,

in attempts to actually realize in a laboratory the ideas

that I talked about before. Now there is going to be

a very important device that I’m going to use in the entire talk

and I recommend you to use it as well, this is a carpet, a rug and

I am going to sweep under the rug lots and lots and lots of details

and concepts and unimportant parts, but you know it is a limited time. The first thing that I am going to talk

about is the quantum Hall effect. Now in effect you know,

what’s the Hall effect? The Hall effect is a situation where

we have a two dimensional system where a current, an electrical current, is flowing from the left to the right,

lets say, and there is an magnetic field

acting on the current. What is an magnetic field, let me tell you

the only thing you need to know about it this is that if you go straight and you

are under the effect of a magnetic field, the magnetic field is trying

to push you sideways. Now whether it tries to push you

to the left or to the right, that is not important to us,

as you know, left and right are not easy to distinguish

so it’s not really important. But he tries to push you sideways

and when I prepared that slide, I hope I got the slide right,

in any case, because the magnetic field tries

to push the current sideways charges accumulate

on the side of the device, and there is an electric field

or a voltage developing between the two sides. Now that is something you

learn in high school in some cases or in BSc of physics. The point is, a force is applied

by the magnetic field, which is linear in the magnetic

field therefore an electric field develops that cancels this force. So you’d expect it to be linear, you’d expect this electric field to be

linear in the magnetic field as well. Now, we can measure that electric field

we actually measure voltage and we divide it by the current

to get the resistance, the important thing is we expect it

to be linear in the magnetic field. And it was for

quite a few decades from late 19th century to late

20th century it was linear and not only that,

now you see the experiment and what you see is this

voltage or the resistance, the voltage perpendicular to the

direction that the current is flowing, you see this one as a function

of the magnetic field, this is the red line. There is also a green line

but people don’t like to talk about it, that is a political reference but there

is also a quote from Winne the Pooh. I’ll quote it fully if you ask me

in the break. In any case,

the red line is what we’re interested in and you see it starts linear

in the magnetic field but then a few things happen. First of all, steps develop.

You see the steps and in the step instead of the

proportionality that we expect, we get a straight line.

Right, by the way, do I block your sight? So you see it looks like a straight line.

Now, it doesn’t look like a straight line, it is probably the straightest line

you have ever seen. From here to here the magnetic field

changes by about 30 or 40%. The voltage perpendicular to the current

or what is called the Hall resistivity. The Hall resistivity does not change

not by 1% not by a.01% not by a.001% it does not change…

it is kept constant in 1/10 squared 9. It is one of the most precise

henomenon known in physics. You see, it really

doesn’t change, not only that, you repeat the experiment in a different

device using a different material, a different graduate student,

a different measuring, you change everything and indeed

the beginning of the step will change, the end of the step will change, you know what magnetic field

it starts and ends will change, the value of the resistivity on the step will be the same at

every experiment 1/10 squared 9. Not only that, the ratio between

this number and this number will be 2.0000

that’s an amazing observation. Now the value of the steps is always

25,800 something or other dot various other numbers divided by Nu.

Nu is either an integer, a simple integer like

1,2,3 up to 12, something like… a kid the age of 4 or 3 counts,

or a simple fraction, but again 1/3, 2/5, simple.

Those are the values. There are many questions this brings up, but the first and obvious one

is what is this number, this by the way is measured

in units of Ohm. So what is this number

25,000 Ohms whatever? It turns out that it’s the ratio

of the Plancks constant the constant that defines quantum mechanics

divided by the electric charge squared. Now, this is unbelievable,

it’s true but it’s unbelievable. You know this universe has

four universal constants. The Plancks constant,

the electric charge, the speed of light and the constant

of gravity. And you measure the ratio of these fundamental constants

to 1/109 using this device. Using a device that’s as dirty,

as full of details as this one. As I said, you can replace these

wires by maybe better looking wires you can replace this material which

turns out to be gallium arsenide by silicon, by graphene, by silicon germanium

by one of 30 or 40 materials. You can replace the shape from being

that shape to being slightly different and the answer will be the same. The ratio of the Plancks constant

to the electric charge squared. This is about 30 years old

this observation 30 or 40, somewhere around there. So this is again this data and just to focus

on what exactly will be important to us, in fact,

what is going to be important to us is this number

Nu that I mentioned before. And this Nu will frequently

in the interesting cases actually, not in the cases shown in this plot

but in cases that you see in higher magnetic fields,

this will be a fractional number. So it’s always rational no reference

to squares of 2 and stuff, its always rational

and “p and q” of small numbers. And “q” is frequently

an odd number but not always. Now this is an experimental observation, I’m not going to go deep into this because I’d like to relate it to the topic

of the session of Quantum Computation, but I’d like to tell you that if you

use these experimental results which are beyond doubt, they were produced many many times,

no one cheats, you use basic principles of physics

like conservation of energy, conservation of charge

you know things that are not going to give up just

because some experiment came out. And you use just plain

logical reasoning and a piece of paper not more

than one, you can come out with a few revolutionary conclusions

that you simply cannot, without even understanding anything

you just have to accept. And I’d like to mention two of them. That conclusion is basically

a Nobel Prize winning conclusion for Bob Laughliln from Stanford, and that’s the observation

that the fact that you see this fractional number

Nu implies unavoidably that the system that is made, all of it,

is made of single electrons… You know, electrons come in

single units, this system will have, what we call quasi-particles, which

are like particles but quasi-particles, quasi-particles whose charge is

a fraction of the charge of the electron. Somehow having a system

where each component has the same charge somehow

it may mimic behavior of a charge that is a fraction

of that fundamental charge. Not only that but if you look

at the spectrum, and I’ll remind you in a second

what I mean by a spectrum, if you look at the spectrum of what

possible energies can this system can have, this system I showed you, this piece of semi-conductor

with all this dirty stuff or at least something very close to this. If you look at the energies

that this system may have, you will find

that the lowest energy which we call the ground state

energy, will be degenerate. It will be several

ground states with the same energy. I am not going to show you

how this is an unavoidable conclusion, this will take about twice

as long as my talk, not a full course. But I am going to tell you a little bit about

this degeneracy and what it means. First of all how do you get to it this

is a famous argument call TKNN, Thouless-Kohmoto-Nightingale-den Nijs,

and it’s based on a, thinking about the geometry

it’s slightly different from the one I mentioned to you

from the one I showed to you. This is the geometry of a torus,

you put this system on a torus. I am a theorist as you know, many

of my friends are experimentalists and one of them said dryly:

Come back when it’s plainer. This is not something

you can do in a lab, but as a thought experiment,

you can think about it. A torus has two holes you put

magnetic fields in the two holes and you call them Phi 1 and Phi 2

and you can show that the quantity

that you measured this number Nu is some integral of some derivative

of the ground states with respect to the two flat fields. You take a??,

all this is not really important, what is important

is that you can show that this number… This is an exercise that I teach

in about two meetings, you can show that this number

is an integer number. It’s a topological environ, it’s

something that cannot change its value. Does not change it’s value

if you change the system slightly. You need to have the system

go through a major change in order for that integer number

to change its value. Now that’s

good news and bad news. Good news because it tells you that

you have a quantide number and bad news because it is an integer

and I told you that the experiment shows

that this Nu can be a fraction. So you go back to the proof,

I’m telling you how I teach it, you prove that it must be and integer

and you go back to the proof and ask yourself what assumption

did I make that must be violated. And the assumption is the assumption

of the ground state this implies. The ground state

being non-degenerate. So you assume that it is

non-degenerate this assumption is wrong. Now let me explain what’s

this issue of degenerate. So you know in quantum mechanics

a system has a spectrum, it has a set of possible

states at which it can be, the most famous spectrum

is the one that Nils?? used to give birth to quantum theory and this is the spectrum

of the hydro-generator. The hydro-generator has a ground

state and then it has an excited state you may remember from your chemistry

high school classes there are shells and one shell

has two states another has eight

and 18 also appeared there. In any case there are energies

which are loud and then there are the number

of possible states that each of these energies

can have that’s called the degeneracy. At the end of the day it’s a you have

a matrix you diagonalize it the energies are the icon values and

how many degenerate icon values exist that’s the issue of the degeneracy

of the states. Now, in the hydro-generator there

are two 18 or whatever degeneracies, they come out of symmetry, out of the fact that the hydrogen

atom lives, at least in Boe’s mind or lab it lived isolated from

the rest of the world, so there’s

a spherical symmetry of the system. So whatever state you have, if you rotate a little bit you’ll get

another state that is degenerate in energy because nothing changed

because it’s all spherically symmetric. Real life itself is not in Boe’s mind

or thought experiment and the hydrogen atoms

interact with other atoms and therefore lose this degeneracy

they don’t’ have the symmetry and the degenerate states split. The important aspect here

in this topological world is that there is a degeneracy

that is protected by topology. I read it like Hebrew from right to left. There is a degeneracy

that is protected by topology, meaning in a quantum world system, just out of the mere observation

of the fractional value of Nu, we can conclude that the ground state

of the system when you put it on a torus, I’ll get rid of that

requirement in a minute, the ground state will be

degenerate and this degeneracy will be topologically stable,

meaning that if you change

the system a little bit by having your cell phone

operating while you do the experiment or moving one of these wires that you saw in the

experimental sample moving a little bit. Any small changes will not split

the degeneracy it is not a degeneracy that comes out of symmetry and therefore it does not depend

on any symmetry, it is stable. So the spectrum of the

quantum fractional system will have several degenerate

ground states and then an energy gap. The energy gap is also an experimental

finding related to that green line which I swept under the rug with a joke,

and then there is a continuum. So a few degenerate ground states

separated by an energy gap to a continuum of a state

that we don’t want to know about. The idea of topological computation

is let’s use this set of topologically protected ground states

as our computational subspace. Those will be the states

to which we will encode the qubits and which we

will carry out the manipulations, changing the

states of the qubits and all that. The good thing about that clock there

is that is doesn’t work so I don’t know

how much time I have. So how much time do I have? Good. This is the topological environ. Does it have a name?

Yosi, does it have a name? The name I prefer is the?? activity. So that’s the story, we have a set

of degenerate ground states we are going to use them

to encode the information and use something to manipulate.

I have to tell you what this something is. So I have to say that this is a

combination of good news and bad news. The good news is that this degeneracy

is very robust, it does not respond to bad perturbations

that we don’t want. The cell phone in your pocket,

noise in the lab and so on. But that piece of good news

is also bad news in a way, because the way we deal

with a physical system is that we perturb them

as see how they react. If this system will not react

to our perturbation, how are we going to encode

the information into it, extract information from it and so on. So that’s something I will have

to explain to you. But first I promised you

to get rid of this torus, the torus is a nonstarter experimentally. And that’s where the idea of Non-Abelian

quantum whole states comes in. Non-Abelian quantum whole states

are quantum whole states in which the degeneracy does not

come out of being on a compact geometry with no edges like on a torus

but comes out of having in the system these fractionally charged

quasi-particles, these excitations which I mentioned to you which

we have to accept exist and have a fractional charge. So in some cases,

for some quantum whole states, not all of them,

for the Non Abelian ones, I’ll explain the name

by the way in a few minutes, the existence of these

quasi-particles in the plane, will give rise to

the degeneracy of the ground state. The fact that the ground state

is exponential in the number

of these quasi-particles. Now, who encodes this information?

usually if there are states which are degenerate and are

different from one another, there should be some degree of

freedom that encodes that describe them, in Charlie Bennet’s talk it was

the depolarization of the photon it could have been like that

or like that, it was an internal degree

of freedom of the photon. Here also the information is encoded

in internal degrees of freedom. But the internal degree of freedom

and that’s a major difference from the photons and trapped ions

and the super conducting qubits and all the other realizations, here the internal degrees of freedom

to which you encode the information, are non-local, meaning the information

is not here and not here. If you want to measure it

you have to bring the two quasi-particles close one to another. As long as you don’t and they

are far away from one another you cannot measure this information. And if you cannot

also the environment cannot and there’s no de-coherence. So that’s the world of

topological quantum computation. A set of degenerative ground states, separated by an energy gap we assume

the energy gap to be very large, we wish this assumption was correct, but I’ll say a few things about

that at the end. But a set of degenerative ground states

and those are going to be our qubits. Now, I have to say that if you are familiar

with this type of physical systems, this seems to be also a problem because

how are we going to manipulate the qubits. Let’s say we put the system in one

ground state and that ground state we refer to as the bit being zero, or we put it in a super position

this ground state where the bit is zero and this ground state which we

will refer to the ground state being 1. So we have a super position of

the bit being zero and the bit being 1. Now that’s the story of

quantum computation, right? The entire idea is to have

a super position of 0 and 1 where alpha and beta

are complex numbers the sum of modules squared is 1, but there’s a relative phase

between them. Now, we frequently draw or describe

this alpha and beta as coordinates on what’s known as the “Bloch sphere”. It’s a point on the Bloch sphere

and doing quantum computation means you know how to

move your point on the sphere controllably and precisely

from one point to another point. Now, how do you do that usually? How do you do that in any

non-topological system? You have an energy

difference and you use the fact that as time goes by each of these

two states get a different phase, which is linear in its energy. So this one gets a phase,

epsilon zero it’s energy times T and this one gets and energy of epsilon 1

so its gets a phase epsilon 1 times T. Then if you want to change

the relative phase by Pi p over 2, Pi p over 3 or any other number

that you wish, you tune this product of the energy

times the time in a proper way. But here I told you that there is no

energy difference these two phases will be the same because

the energies are the same, so we need

a new way to manipulate bits. And indeed in a topological quantum

computer there is a new way. And that’s what

I’ll describe to you now. So this is our system,

it has these particles, these quasi-particles these excitations

which are so unique to the system and it has a set of ground states. As I said and exponentially

large number of ground states. And those ground states

all depend as parameters, the wave function depend as parameters

on the positions of these quasi-particles. Now, what we want to do is to find

a way without changing energies, because we know that all

the energies are going to be the same. Without changing energies, we want to be able

to go from one ground state to another. It turns out, the way to do that

is to do something called braiding, am I the right person to talk about

braids I’m not sure. This is what this trick is doing, the braiding is the braiding

of the word-lines?? of the positions of the

quasi-particles as time moves on. So I take this quasi-particle and

move it to the position of this one and take this one and move it

to the original position of the first. When I do that,

the system evolves in time in such a way that it stays

in the ground state substrate. So it stays super position

of ground state but which ground state exactly it

gets to depends, it turns out, this trajectory

that I’m doing. So the operation of interchanging

two quasi-particles or braiding two quasi-particles

this operation applies unitary transformation on the system

that takes it from one ground state, from a super position ground

state to another ground state, or another super

position of ground state. Now, a unitary

transformation is a matrix, matrixes do not

commute when you multiply them therefore if you first interchange

1 and 2 and then 2 and 3 or if you first interchange 2 and 3

and then 1 and 2 the answer will be different, the outcome the final state will be

different because you multiply matrixes and that’s the origin of the name

Non-Abelian, non commutative. So the way we manipulate qubits

will be by interchanging quasi-particles but now comes the

great promise of this story. The great promise is that the final

outcome the unitary transformation that you apply does not depend

on the details of this interchange. If I do it like that

or I do it like that, I’m going to get the same final state. The only thing that matters

is topology of the trajectory. So here you see the topology

of this trajectory I had 1,2, and 3. I first interchanged 2 and 3, then I interchanged 1 and 3

then I interchanged, whatever, 2 and 1 and I ended up

with this braiding process and this will determine

the unitary transformation. The details, the geometry and

the dynamics of the way I do that, do I do that with the velocity going

like that or like that doesn’t matter. There are caveats here but that

doesn’t matter you remember the rug. So it’s all in the topology and this for

a quantum computer is a great promise because the main problem

of the quantum computer is the noise

the noise, the de-coherence. This will be avoided here because

you don’t care whether there is noise in the way you perform the unitary

transformation or the manipulation. A quantum computer

need to fight the de-coherence to fight the noise it also needs

to have a universal set of gates, that is probably a statement

that is better understood by every single member

of the audience compared to me. You need the universal set of gates otherwise you

will not be able to carry out all the unitary

transformations that you make, all the algorithms

that you want to carry out. Does this constitute

a universal set of gates? The answer, it depends,

it depends what Non-Abelian state you are looking at

I don’t know if mu’s law is going to help for a long time

but murphy’s law will. And as you can imagine

the more universal a state is the harder it is to actually realize it

in an experiment. So maybe I’ll ask again about time

because this will make me decide. So everything I told you about

Non-Abelian quantum whole states, there are many examples now

for topological states of matter, a smaller subset

which are states which in principle may be used for topological quantum

computation meaning states which have a degenerative ground state. The second example

which I want to mention is that which is known

as Topological superconductors, superconductors are those

that carry current without getting heated, it’s not every day like

but it’s every day knowledge. I won’t get into details,

I’ll just tell you the mathematics of it because it explains what holds it,

what gives it the topological protection, what gives it the topological stability. So for non-physicists,

a super conductor is something that is described

by a matrix. And if you want to know the

energy states of the super conductor you need to diagonalize

that matrix. Now, if you diagonalize it

and you look at the zero eigenvalues, how many zero eigenvalues tell you

how many ground states you have, it’s not a 1 to 1 relation

there’s a power there, but there’s an exponent actually,

but that’s what you need. You need zero energy eigenvalues. Now, that’s the matrix, you

don’t care what all these letters mean. What you care are two things. First it has an even dimension,

that’s easy to see because this and this are

the same matrix used to transport. So this has an even dimension which

means it has an even number of eigenvalues. Then another thing which I could

show you if I have ten more minutes is that the eigenvalues come

in pairs of positive and negative. Now you combine these two observations and you have to conclude that

if the matrix is even dimensional and the eigenvalues come

in pairs of plus and minus, the number of zero energy

eigenvalues must be even. Otherwise I’ll have

to violate on of these two. Now, zero is an even number

but not an interesting one so let’s go to the next one

which is two. So the number of zero energy

eigenvalues with that matrix will be two. The eigen vector corresponding

to each eigenvalue acts in space, an operator, I won’t get into

details but it has a position. So if I have two

zero eigenvalues one localized here and one localized here each one

of them will be stable because if I come to this one

and try to move it away from zero I cannot because if it moves away

from zero the other guy will remain alone will remain a single one and then I’ll

have an odd number of zero eigenvalues and that’s not allowed. So those two, as long as they

are far away from one another are stable. And that’s the source of the stability

at least for the super conductor. Now, to quickly talk

about the phase coherence the crucial point,

actually the privius talk already covered

a bit of this issue of phase coherence. You need the environment not

to measure you and in this case the distribution of the information

over non local degrees of freedom tell you that you cannot measure,

neither you can nor the environment can, measure the information that set of

qubits without getting them close together. So as long as you keep them

far away from one another you are safe. So in my minute and a half,

I’ll skip this. In my minute and a half that are

remaining I’ll tell you about real life. So this idea of topological

quantum computation originated in the early 2000,

you saw names here and there, Alexei Kitaev is the name

I have to mention in this context he was the originator of this idea. About 10 years ago a big

experimental effort started by Microsoft by what’s known as station Q

or project Q. I was part of it for about the last ten years. And that project

tried first the quantum Hall and now more the super conducting

avenue trying to look at wires, super conducting wires and looking

at zero modes along the wire. There are many experimental knobs

that you can use for realizing this – magnetic field, gate voltages,

charging energies and so on and so forth. The first thing you want to see is that

indeed, that there will be signatures, experimental signatures for

the ground state being degenerate, for having many states

which are degenerate. That’s the first thing

you want to see, that was, I shouldn’t say and I am being

recorded, surprisingly easy, it wasn’t easy but it didn’t take

very long it took about a year or two. What you see here

is not the first experiment but a later one and this peak

at zero voltage, what you see here is a super

conducting wire that’s a dola?? gate where you tune density,

various things. In any case the fact that you

see this stable peak at zero voltage is an indication that there

is a ground state degeneracy. Is it the only explanation for this? There may be alternative explanations

I think it is getting safer and safer to say yes we know that this super

conduction wires have a set of ground states. Now we want to

manipulate them we want to break, we want to start in one ground state

and end in a different ground state. That I think I can safely say

is proven to be very difficult. That is something that is being

attempted now in various labs around the world Copenhagen,

Delph, NYU, Santa Barbara

and various other places. It seems that the difficulty associated

basically with materials quality that’s not something to talk about

in a computer science conference so I won’t. I’ll just summarize,

and my summary has two sentences, The first is that topological states of

matter may provide remarkable robustness and that robustness, that stability may be useful for

overcoming de-coherence and noise in quantum computers by using this idea

of topological quantum computation. But point number two is, Topological quantum computation

is quantum computation; it ain’t going to be easy. That’s not a magic way to realize

a quantum computer in five years but still it’s very,

well, I tried to convince you that it’s a very stimulating

field with many new concepts. Thank you very much. So after we get through

the questions and answers I need one more minute of your time. So I think we will consider

forming a committee to vote you into the hall

of computer scientists so you can get an additional title. Questions please: Moshe, what a surprise. There was a national academies

report that came out last year looking at the prospects

of quantum computation. And one of the thing you said,

ok, what are the prospects of being able to break RSA using

quantum computer and you assume that the keys

are 2000 bits long and then ok so you need 4000 qubits

then you need error correction, so it’s actually not unreasonable

to think that we will need something like 100,000 qubits

to be able to break RSA. Is that something we are

going to see in our lifetime? Not young enough. So I’ll tell you first

the optimistic answer, the optimistic answer

which I’m sure you know. Not when I was born

but when my mother was born, my parents were born; there was not

a single transistor on earth. Nowadays there’s more

than one transistor being produced every second for

every human being on the planet. For every aunt,

for every aunt maybe. That’s three generations or two. So it’s very hard to make

this kind of prediction, try to predict what

is going to happen tomorrow. So you know the lesson,

the reason I brought up the transistor is that was an example

of??. Once they figured it out, Bardeen and Shockley

and their successors it went like fire. Will something like that happen

in this context, I don’t know, it’s a very very challenging endeavor

that the physics community, the physics computer

science community are taking here. I don’t know, it’s really hard to say.

I wouldn’t exclude it, I wouldn’t rule it out as completely

impossible but I don’t know. Other questions? Maybe while we look for someone else

I have a question to Charles. You had this sentence that said, you don’t think it’s worthwhile

showing that a useless problem that cannot be done on a classical computer

can be done on a quantum computer. Can I challenge

the word useless there? even if the problem is not a

practical problem I think figuring out that there is a problem provably

impractical in the classical sense but can be done in polynomial time

on the quantum computer would be a major discovery

which is not the case with factoring because we cannot prove it is intractable. It’s really a comment. Well, I don’t want to embarrass

the profession of computer science but actually there are

no provable intractable problems in short of P space so we don’t know

that P is not equal to P space. Yeh, but intractable in expediential

law bound on time for example or on space,

there are such problems. Well, so it’s hard to find people have

different feelings that factoring is hard is less sure than P not equal 10 P

but that’s just kind of a gut feeling. But I’m talking about expediential

law maybe we do this offline. That’s not what I was talking

about in that issue, this was not a computer science group

this was building a quantum computer and showing that it does something

that a classical computer can’t do in the same time is mainly useful,

with current technology, is mainly useful for trying to

convince people that quantum computers couldn’t exist in principle

but they are wrong. Those people will never be convinced

so it’s worthless trying to convince them. Most people believe

that quantum mechanics is sound that there

isn’t a fundamental obstacle, in principle to believe

in quantum computer just terrible engineering problem. Often I compare it to fusion energy,

it’s not problem, we know it can be done but it’s been

impractical for many decades and may continue to be. So that’s why I say the effort to prove,

they call it quantum supremacy which is kind of

an offensive word in itself. I think the point

of all of these experiments, the reason for doing them is to improve

the understanding of de-coherence and prove the understanding

of all of the things that you do need to know how to do

better to make a quantum computer. Not to convince people who think

that there never will be a quantum computer. Thank you, any other questions to Ady? There was over there. Apart from quantum computing are there

any other uses for the?? systems? Yes, actually there’s one that almost

obvious you know 1/109, so you can use this measurement

as a way to standardize the Ohm. So you know the

standard of the kilogram is some piece of iridium something

or other in some museum near Paris and you need to go to Paris every time

you want to know what the kilogram is. With the Ohm you don’t anymore, you even with the kilogram

you don’t anymore, but this allows you to have an

experimental kit in you lab which defines the Ohm

up to 1/109. If precision is something that

is important to you it’s a use. Maybe I should have mentioned

at some point, these are all low temperature experiments. That means that if you want at home

to standardize the Ohm you are not going to use it. It makes it a rather

expensive experiment.