Computer Science | D1S1 3/18 Quantum Science & Technology – Part I – Harnessing Topol… – Ady Stern


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.

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