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So hi, everyone.
Um, first of all, it's
really great to be here and I mean, I was
a bit shocked and also amazed at
how many people seemed to be interested
in quantum computing.
For me, to stock is actually kind of
special because it closes a circle.
Um, the first time I
was at the CCC was in
2001, and back
then I was still in school and I was
coming here from my small town
in southwest Germany.
Um, and when I arrived here,
this was kind of like Magic Fairyland.
So there were people doing all kinds
of amazing things, like playing with
electronics, picking locks.
And there was one presentation as well on
a Tesla coil, so to say.
So physics student showing around
the Tesla, I recall that he made himself
and like explaining the physics and how
it worked. And this is kind of how
I got very interested in all these kind
of things and physics and finally took
the decision to study that as well.
So today,
I hope that with my talk, I would be able
to to like instill in some of you also
something similar, like like an interest
in like interest in quantum phenomena and
quantum computing in general.
All right.
So as I talk with you about
quantum computers and
some of the results will show you a lot
of research from different groups.
And some of the results are from my
PhD thesis, which I did that basically.
So I want to just thank all of my former
colleagues and my Ph.D.
advisors for their support during
that work.
All right, so
much of it.
So that's kind of the motivation for me
to give this talk, because as you
probably all noticed, there's a lot of
buzz about quantum computers in the
media. So every month there is an article
on Wired or on VentureBeat showing the
latest results from like
groups and quantum computing.
And also now there was this big
announcement that Google invests money in
building superconducting quantum
computers. So there's a lot of
information floating around.
And it all kinds of ranges between
quantum computers were like, change
everything for us or quantum computers
are kind of hokum. They will never work,
probably.
And what I want to do this talk is
actually to to explain
what quantum computing is, what we wanted
and how it works, actually.
So the
outline for us is to.
Yeah, as I said. Sure.
Why we want actually to build quantum
computers then how
to like solve some interesting
problems with them, for example, cracking
passwords.
And afterwards I will show you how to
build a very simple quantum computer
quantum processor using superconductors,
resonators and microwave signals.
And finally, I will show you some of the
recent progress in quantum computing.
All right, let's get started.
So
what is the history of quantum computing?
Well, the beginning can be probably
traced back to the 80s when
physicists were already using
conventional or classical computers to
help them to simulate physical systems.
And back then, people were asking,
they were seeing that it is actually
pretty hard to simulate a quantum
system with a classical computer somehow
as soon as you like it, a little bit of
complexity to your quantum system.
The classical computer is no longer able
to to kind of simulated.
And in a famous conference in
1981, Richard Feynman,
physics Nobel Prize winner, gave a
talk on exactly this subject where we
discussed how to build a computer that
would actually be able to simulate
quantum mechanics.
And this is, so to say, the birth of the
quantum computer as a concept.
From the beginning, it was really devised
to help physicists to simulate
quantum mechanical system.
And if you now go one
step further and you can, of course, see
that quantum computer seems to be more
powerful than a classical computer
because it can simulate quantum systems.
So maybe it can also help us to solve
some other problems which are not of like
physical nature, but some abstract
mathematical things.
And amazingly, the answer to this is
also. Yes. And now I want to show
you how this how this gets done, so to
say so, to understand
quantum computing, we first need
to have a look at the basics of classical
computing.
And this will be very useful because
later on we will use a lot of concepts
that I will introduce to you a year or
so. It will help you to understand how
exactly quantum computers do what they
do.
So, as you probably know,
um,
computers use bits as the basic
unit of information A is a
system that has two states, zero and one,
and it's kind of an abstract mathematical
concept. But nowadays, if you think of
bits, you probably think of a
way a voltage in a wire in a circuit.
So you could say, OK,
stage zero, if you bid, can be defined by
having a zero voltage as zero zero
volt in comparison to like some ground
state. And bit one would have,
for example, Five-fold.
All right.
To do useful things with bits, we need
many of them, so we put them in a
so-called register.
He had a bizarre, um, enumerated
from top to bottom.
So there are bits in this case.
And if you want to write
the state of the whole wheat register,
you can just kind of multiply them.
The individual is together and write them
like this.
And you would see that for an
input. Bitzer You would have two to
the N possible states.
So it's pretty efficient way to store
information. Definitely better than using
Roman literals.
All right, now, you, of course, want to
do something with your boots, so
you need gates and a gate is also
a abstract concept, which
is a function in that sense, which has
one or several inputs
and one or several outputs on the
other side.
Now, for classical computing, there are
some circuits which
are so-called universal gates,
for example, the nannygate, which you see
here, which is two inputs and
returns, one for all the possible
input states, except if the two input
Bitzer one and this
Gateson universal in the sense that you
can construct any other logic
from this by using combinations
and concatenation of the single gate.
All right, so that's basically all we
need to get started solving
problems of our computer.
Now let's have a look at a fictional
problem.
Let's say, for example, that our,
um, beloved leader wants to
launch a missile.
And of course,
not everybody should have the right to
launch missiles. So we need the password.
And if you want to check
now, if the password is correct,
we need somehow function that
the justice for us and this function
which is shown here and which are called
F.J.
looks like this. So it has an input
on the left and one single output
and it returns a zero for all of the
inputs except for the one that
corresponds to the correct passwords.
All right, so this means that we have
to to the end possibilities here, and
if you make the input register large
enough, we can have a pretty secure
system.
All right, now imagine that we want
to to correct first
password and now
there are several possibilities.
We can, of course, try to reverse
engineer the system and find out to try
to find out how the function works.
But now for this dog, let's assume that
the function is secure and that we cannot
do any kind of reverse engineering.
So then the only way to obtain a password
is to actually brute force it, which
means that we have to try all the
possible values of the password and see
if the function returns one.
And if you want a computer
to do this, we have to teach him to do
it. And for this, we use a so-called
algorithm, which is basically a
baking recipe that the computer can
follow to obtain a solution.
All right. So our algorithms, pretty
simple, would start by setting the
register straight to the first volume,
which is zero zero zero zero, etc.
Then calculate F.I.
and check if we return, if the function
returns of one.
And actually for a lot of
cases, when people choose a zero zero
zero zero as their password, it does so.
In this case, our algorithm is terminated
and we can directly return the
password that we found.
And for some other cases, for people that
use a more secure password, we actually
have to to check the other values as
well. So we go as incremental value
by one and we go back to step two and
repeat this until we find a password.
All right. So now you can ask yourself
how efficient this is actually.
Well, it's pretty easy to answer because
if you have an input state,
we will probably have to check the
password at most to function at most
end times.
So in the best case, we would check it
only once and then the average case we
would check it probably another two
times.
So if you plot now the
number of evaluations of the function F
versus the size of the search space
and would get a linear relationship,
so which means that if we doubled
the size of the search space, we also
have to double the number of function
evaluations.
And this is the so called time complexity
of this algorithm.
And the idea behind us is that, um,
the the cost that you have
in cracking this password is in
calling this function F, which can be
really complicated.
So you really want to measure how often
you have to call this function to obtain
the answer you need.
All right. So.
Please keep this in mind for because we
will see the graph again later in the
talk.
OK, so that's all
I wanted to tell you about classical
computing, and now we are going to
have a look at quantum computing.
So, again, I want to go through the
basics of quantum computing first.
So, um, like
for a classical system in a quantum
system, we have also a fundamental unit
of information, which is called the
quantum bit cubed.
And as the name suggests, this
is a quantum mechanical two-level system.
Basically, it is also an abstract
concept. But I find it really helps if
you imagine it as a as an atom with
two states, which I call zero
and the second third one.
And this atom
has, of course, a quantum mechanical
state, which I indicate by putting
this strange vector around the one.
So whenever you see this disembodied
underdog, you know that I'm talking about
a quantum state.
All right, so now one of the
strange things about quantum systems
is that they can not only be
understood zero or one, but kind
of in both states at the same time.
So in this case, we
wouldn't be able to, like, ride the wave
function of the the state as a as
a simple zero
or one. But we would have to write as a
more complex function here,
which I could say and which concert,
which is kind of a sum of the
state zero with some amplitude,
a plus the
state one, which is an amplitude one
minus eight.
And in addition, some phase, which
is a complex number here in which kind of
makes that we can only add the two states
together, but we kind of can also
subtract them or do more complex things
with them.
And now this is probably pretty hard to
get your head around it. So at least for
me and I find it always helps
to imagine this
as a particle wave.
So, for example, here would have
a particle or wave that comes
from the left and this wave would
encounter like
a barrier of two holes in it.
Then you would have like circular waves
going out from these two holes.
And here in this picture, this is
also like a single system, but it kind of
shows like strange interference
effects. And the two waves
here overlap.
And depending on the phase of between
them, they can kind of like
substract or like add
themselves up. So I think this is a
pretty good way to think about it.
Cubit state as well.
All right, the second
difference to classical bits as
concerning some measurement of quantum
bits, so, um,
for classical computers, I didn't even
mention how we measure them because
it's really trivial.
We can just measure the voltage of
our wire and then we get the information
of ground zero on the one side.
But for quantum system, it's a bit more
complicated because in fact,
whenever we measure the system, we also
change the state.
So let's assume that we have a
measurement apparatus here which is shown
on the right, and we want to measure the
state of the quantum system in the state
011 or one.
So what we do is that we switch on some
kind of interaction between the two
systems. And what will now happen
is that we will have a so-called collapse
of the wave function where
the Cuban said we get projected
either in the state zero with a
probability that's proportional to
the amplitude of the state zero and the
wavefunction or into the
state one with the complementary
amplitude.
So this is something that is kind of
unique for quantum systems and
which we will encounter later again when
we try to to measure the results
that we obtain using our quantum
processor.
All right, um, like for Classico, but
we also need many cubits to
perform useful operations, so we
have a quantum register and that's
before we order the individual cubits
from top to bottom and right away
functions like this.
And now if you want to like, um,
right. The function of the whole Cubitt
register, we just multiply the individual
functions together like this.
And so since there are a lot of
vertices there and it's kind of tedious
to read, I will often like just ah
put all the terms in conference and write
it like this. So when you see a state
like this, you know that actually you
have a multi cubitt state where each
individual cubit is in the state
indicated by its letter.
All right,
a key resource in quantum
computing is the
fact that we can have so-called multi
superposition states.
So let's remember, again,
the two slides ago we talked about the
fact that a cubit can be in the state 091
at the same time.
So now let's imagine that we prefer a
Cubitt registered state where
each individual cubit is in an
equal superposition between zero and one
state. So this is show you like here
and you can see the factor of zero point
five of one or two
is just the normalization constant.
So now if you want to obtain the wave
function of the whole register, I can
again just multiply the individual
functions. But now the difference is that
I have kind of like a sum of
products here.
So if I want to, like, obtain the very
function, I have to multiply out these
four entities. And if I do that.
So to the end times, if I do
that, I will get a quantum
state which looks like this, so you can
see that we are fuda states, zero zero
zero zero, etc.
Then you have to state zero zero zero
zero one up to the state one one
one one one. So basically, it means
that in this register
we have all the possible states of the
cubits at the same time.
And now this is pretty, pretty exciting
and it is kind of a key resource that we
can make use of when making when
using quantum computers to solve
problems.
All right, and you often are,
since the terms are a bit
tedious to readers. Well, I will just
admit to normalization
when I write a state.
So you will often see them like this.
OK, last thing we
need to learn about for quantum computing
is Quantum Gate,
like classical gates, quantum gates
take a number of input cubits and produce
a number of output.
Hubert's.
The difference is, though, that now,
since we have a quantum mechanical
system, the Quantum Gate also needs to
perform a quantum mechanical operation.
And this means that some things which are
possible in classical computing are no
longer possible.
And quantum computing, most notably
copying qubits, for example.
But still, like for classical
computers to also exist, the concept of
a universal gait, which
means that we can find a set of keys that
will allow us to to
realize any classical gate operation with
a quantum computer.
OK, now, if you
combine what we have learned about
multi keyboard super positions and
Quantum Gate, we can
see that if we apply
our quantum gate to an input state, which
is a superposition of all the possible
inputs, then we'll get an output state
which contains a product
of the input state multiplied by
the value of the function that we want to
calculate for all these inputs state at
once. So this is kind of magical
because it means that we have evaluated
this quantum function only once, but we
have calculated its value for all the
possible input values.
So when people tell you that quantum
computers harness the power of the
multiverse, then this is what they
usually mean. So so-called quantum
parallelism.
All right, the last thing that we
need to learn about is quantum
entanglement, and this is a concept
which can we understand like this so
soon that we have to cubitt state
where the first cubit is instead zero.
The second Cubitt is in the state one.
And then we take these two cubits and we
apply some function to them, which we
call F here again.
Now, the effect of this function is
to allow for this input state, which we
have to return, and an output
state which looks like this.
So it's a superposition between the
zero one state and the one zero
state.
And now the state looks
pretty innocuous.
But actually it's kind
of weird because as you might notice,
we can no longer write the individual
qubits separately so we can
no longer, like, factor out
to the first Kuban in a second cubed.
So somehow both of them
are kind of kind of intertwined.
And if you would imagine that we can
would make a measurement or the first
Cubitt, as we said before, the
probability of obtaining either the value
zero or one for the first Kupets is 50
percent. So assuming we obtain a one
and what is then
then really bizarre is that we seem
also to have changed the state of the
second Cubitt because now it's in the
state zero.
So.
This is kind of kind of really weird and
means that somehow there is a likely,
like ghostly interactions between the two
cuboid, which makes that when I measure
the first of it or do something with it,
it also affects the state of the second
cubitt.
And now if you think that's weird, then
you're in good company, because
Albert Einstein wrote a famous paper on
this so-called
EPR paradox where he argued
that this must be a reason
why quantum mechanics is incomplete and
in fact, is actually it's
completely valid behavior.
And we can use this also to speed up
computations when we use a quantum
computer to solve problems.
All right, so
this was a lot of a lot of stuff to to
digest, so just
to a small let's do a small recap of what
we learned. So we saw that Hubert's are
quantum mechanical two-level systems,
that it can be in a superposition between
the state zero and one that a
measurement of Cubitt state will either
zero one and project a cube within the
respective state, and the Cubans
can become entangled with other qubits.
All right, so
back to business, we still have to
find the password for
for a missile launch system.
Now,
let's imagine that we have a
blueprint of the function that calculates
the passwords and we are able to
implement the quantum version of it.
If we can do that, then we can, like
before produce a superposition
of input states, calculate
the function operator F.J.
and then obtain the values
of the password hashing function for all
possible input states.
And amazingly, of course,
they will also be the value of the
correct password in there.
So now we have kind of almost
solve our problem because we have
calculated all the possible outcomes
of the consultation function.
We have identified the state which
contains the right password.
Now, the only thing that remains to be
done is to get the state out of there.
And now what we could
do for this is just to try
to measure the values of the cubitt after
applying the operator.
But since I told you that
a measurement were kind of changed
to Cuban state and projected into
one of the an arbitrary state of
the to superposition state, that we have
the probability that we'll actually
measure the correct state here is only
one over. And where is the probability
that we will get some other state, which
is not the solution to our problem is
one minus one over one.
So that's pretty bad news,
actually.
And this is kind of the dilemma
of quantum mechanics or quantum
computing, because you are able to
evaluate a function for all possible
input states as ones, but you are not
able to extract that information
from the quantum state.
So what can we do?
Um, actually, there's a solution for this
and the so-called Grover algorithm, which
was invented or discovered by Grover
in 1996, and it gives us
a way to extract the information
from the quantum system.
And the algorithm does that by applying a
pretty complicated sequence
of gates to the output state that we
obtain after applying it to the function
and then repeating this square root
of end times.
So after doing this, we can then.
A performance measurement and
what the algorithm has done is to
transfer all the amplitude to the state,
which corresponds to the solution of our
search problem. So when we now make a
measurement, we will have a probability
of almost 100 percent to obtain the
correct answer, which, of course, is
great.
All right, now,
if you have a look at the efficiency
of this, we can visualize
this for the case, for example,
of 10 cubits.
So for 10 cubits, the search space of
our passwords is one thousand
twenty four. And we
can now plot the probability of
obtaining the correct solution after
applying the Grover operator a number
of times. And as you can see in the
beginning, the probability is quite
low. So it's less than zero point one
percent. But as we keep applying this
Grover operation operator, the
probability goes up, up, up
until it reaches almost 100 percent at
after 25 iterations.
And that's pretty great because it means
that we have to evaluate a search
function not one thousand twenty four
times, but only 24 times to obtain the
correct solution.
So if we go
back to the graph from before we apply to
the time complexity of our classical
algorithm, we can now compare that to the
quantum algorithm and we can see that
the quantum algorithm is actually much
faster for this kind of problem because
it only needs a square root of N
attempts or evaluations of the function
to to find the correct solution.
And so when people tell you that
quantum computers are faster than
classical computers, what they actually
mean is that for
some problems, quantum
computer exist algorithms on quantum
computers that have a smaller
time complexity than the best known
algorithms for classical computers.
And the difference between the classical
algorithm and quantum.
Isn't this the so-called quantum
speed-up?
In this case, it would be so it would be
a quadratics beat up, as you can see.
And now I use this example
because it's pretty easy to
explain, and it's also something where
we can prove that there is no better
classical algorithm.
But most of you probably know quantum
computing more from code breaking
or from the so-called short algorithm,
because, um, most
classical as a metric
krypto cryptologic methods
are based today on
the fact that it's pretty easy to obtain
a number by multiplying two large numbers
together. But it's pretty difficult, on
the other hand, to obtain the individual
prime factors of that number from
the multiplied one.
So the best classical algorithm
for this problem is kind of exponential
and looks like this, whereas for a
quantum computer we have an algorithm so
called your algorithm, which can which
can solve the problem and logarithmic
and to restore the power of tree time.
And this is actually a pretty big
difference because it can make, um,
it can change the runtime of such an
algorithm from millions of years to a few
hours.
So but contrary
to the to the search problem that I
showed you before, there's actually no or
to my knowledge, there's no proof that
for a classical computer that doesn't
exist, a better algorithm.
So here we cannot really say that quantum
computers will always be faster than
classical computers because we really
don't know if we can find a better,
better algorithm for classical computer
that could solve this problem faster.
OK, so sorry
if this was a bit theoretical, so I
promise no more equations in this talk.
And now I want to, um, to show
you how you can actually build a quantum
processor and
went to actually many different answers
to this question.
And I talked before about
qubits as kind of atoms.
And that's a good analogy, because there
are actually people or research groups
that are using atoms that are trapped
in an electromagnetic trap, which is
shown here and used in as cubits.
So these are two years from the
research group in Innsbruck.
And what they do is that they trip
a number of ions in a so called Paul trap
and they can put these ions
inside there like string pearls
on a string and then manipulate them
using laser light.
And since the atoms are also coupled to
each other, use by the vibration mode
of the whole system, you can perform
quantum gates between individual ions.
And so this is a pretty successful
and pretty nice way to perform quantum
computing and the larger
system that they're able to do with this
kind of approach and compose about
50 to even 100 cubits.
All right, so what I want to talk
about today, though, are superconducting
quantum processors, like the one I showed
here, which is from the University of
Santa Barbara, from the research group,
which just announced a collaboration with
Google to build quantum processors.
So as I said, these,
um, um, these quantum
processors are realized using
thin layers of superconductors on
microchips.
And for those of you who don't know what
a superconductor is, it's basically a
metal on metal that
loses all of its electric resistance
at a very low temperature and which at
that temperature also exhibits quantum
mechanical behavior and
superconducting quantum bits are quite
attractive because the reasoning is
here that if you manage to build a
few of them and you manage to make them
really good, it would be really easy to
scale the number of qubits to a very
large, large amount because
you can just fabricate them like we
fabricate most of the microchips today.
So and
of course, there are many more
technologies that allow us to build
quantum processors, for example, to a
nuclear magnetic resonance, spins their
quantum dots in both Einstein condensates
can be used to realize quantum bits.
So I just want you to
take away that superconducting quantum
processors and I interrupt.
Quantum processors are not the only
approaches to quantum computing.
All right, now I want to briefly
talk about a very simple
answer to Qubit quantum processor
I built during my PhD thesis
and this process of using so-called
transman cubits, which are an
invention of a research group and year
from 2004.
And what I show you here is an electron
microscope image of the whole Kubitschek.
And this is actually a nice system to
discuss the basic blocks of quantum
processors because it contains all the
elements that you would also need for a
larger scale quantum processor.
So you can see that the chip is about 20
millimeters in size and
it's realized in a material called
niobium, which is a metal that also
becomes superconducting about at about
minus two hundred sixty four degrees.
And on a chip you see a lot of Coplin
a waveguide which we can
use to send microwaves to the qubits
and some other signal lines which we can
use to perform other operations with
them. And so if you ask yourself where
the cupboards are actually on the chip,
the answer is here in the center.
So you can see two of them.
And in the zoomin you can actually see
ah, well, you can probably can't
see very well here because the contrast
is not very high, but it's
a large capacitor that is realized in
aluminum, which also is a superconductor
and which are which
basically acts
as a support for a cubit and a cubit
itself is then are
on the top of this capacitor and
so-called Justesen Junction, which
basically is just an
assistant element that consists of two
thin layers of superconductor separated
by an insulating barrier.
And it's what we call a
bed contact because under
normal conditions, there couldn't be any
current flowing to the system.
But when a system becomes
superconducting, we have a
superconducting wave function and the
wavefunction can somehow tunnel through
the barrier and it can be supercurrent
flowing between the two sides of the
structure.
And now the
the cubit itself
is realized as different states of the
system here, which we call also an
artificial atom, because it kind of
has the ground state and a few excited
states that we can can
control using microwaves, actually.
So the difference is here that the
frequency of the is
compared to an atom much lower and in the
range of a few gigahertz.
All right, um, yes, the first
offense and as I said, we can
sorry for the cheesy animation, we can
manipulate the cubits using microwave
signals, which we sent to them through
this, uh, snakelike structure,
which, in fact is a of waveguide
resonator.
And you can think of this probably as a
as a guitar string, which one we
like excited would vibrate at its own
frequency.
And the
function of this resonator here in the
cubit chip is actually twofold.
On one hand, it isolates the Cuban from
the environment and protects it from the
noise that is, for example, coming from
the input line.
And on the other hand, it also allows us
to measure the state of the cubit after
we have performed some operations on it.
All right, now, I talked about
Tacuba decades earlier, so
in order to do that, we need some kind of
interaction between the two cubits.
And what we do for that is that we put a
very small capacitor between them.
Which kind of couples then are
always when they are at the same
frequency. So that means by changing
the frequencies of the qubits, which we
can do by changing the current.
And is these lines here, we can
bring them in and out of resonance and
realize to cubitt
good operations with them.
All right, so that's basically it, um,
now to operate a chip, we
first glued to a special microwave
PCB, which also contains Koechlin
and safeguards that we can hook up to our
equipment.
Then we take this whole thing and
mounted in a sample holder, whose main
function is to also protect the cubits
from any stray electromagnetic fields
and also to anchor it to the dilution
that the delusion cries
that is basically shown here.
So the sample holder gets attached to
the bottom of that.
And what this thing is, is basically
just a very fancy refrigerator
which cools down to Cuba
to about 20 Malicki, which is
at minus 274 a
degree Celsius, just slightly above
absolute zero.
And we have to do this because
on one hand, the superconductors
wouldn't be superconducting if we were at
room temperature.
And on the other hand, if you would
operate our cubits at room temperature,
we would find that the
noise and thermal exploitations of all
the materials that are around cubits
would destroy the quantum state of them
really fast. So we really, really need to
call them down to a very low temperature
to be able to to operate them for a
sufficiently long time.
All right, um, so that's the short
version of how to build a quantum
processor. The long version takes about
two years and lots of, uh, microwave
calibrations and, uh,
chases for a superconducting leaks and so
and stuff.
So what I want to show you here, just
the results of one of the experiments
we ran with this Tsukuba processor.
And what we basically did here is to, um,
to run the global search algorithm, which
I showed to you earlier, for
the case of two cubits.
So it's really not a practical problem
that you want to solve, but it kind of
demonstrates all the abilities that you
need to build a large scale quantum
computer because it contains single
Kubicki. It's here, for example, for
which we use to create input
superposition state, and it also contains
a multi cubed gates.
For example, here we have the so-called
ISO upgrade and to single Cuban
rotations, which together implement
the function F.J.
that we talked about earlier.
And in this case, uh, the function of J
marks the state 008 as the password
or as the solution of our problem.
All right.
Now for the two Cubitt case to the grower
operator has to be applied only once to
the state to obtain a solution.
So these two gate operations there
do this and afterwards we can
just measure the Cuban state
and see if the, uh, the algorithm has
worked, so to say.
Now you can see the sequence of this
gate operation here.
Um, what you see there is actually the
time on the X axis, on the Y axis,
the amplitudes of the microwave signals
that we show that we are sent to the
cubits which we show in green, as well as
the frequency changes
of the cubits, which is shown red.
So you can see here that in the beginning
we have the two microwave pulses that to
create a superposition.
Then we have like an interaction between
the two qubits where we perform all to
give it good.
Then we separate them again, perform some
more face manipulations, then
we bring them in resonance again for
Grover Operator And finally we change the
frequency and we measure out the state.
All right.
So now we want to see how successful
we are actually at doing this.
We can run this great sequence,
which takes about 200 nanoseconds
and ever do that a lot of times, and
then just average the results to obtain
some good statistics.
And we have done this for the case of
this function of zero zero.
And what we see here is the success
probabilities are to see or the
probability to obtain different output
states as a function of the the,
uh, the search function that we are
looking for. And you can see here that
for this case of the functions of zero
zero, the success probability is about
sixty seven percent, which is
less than 100 percent.
What would you expect?
And I will explain to you why
later.
So to be
more scientific, we have to repeat that
not only for this case of the function
of zero zero, but also for the other
possible search functions.
So we do that and we every time we
calculate to success probability
afterwards and we see that for all the
four cases, we are above 52
percent or 50 percent.
Sorry. And this is pretty nice because
50 percent is the so-called classical
benchmark against which we can compare
or quantum processor because of you would
think of an algorithm, a classical one
that gives you a solution to your
two bit search problem.
Then you could think of an algorithm that
like emulates this function once,
which has a probability of 25 percent
of yielding a right answer.
And if it doesn't find the right answer,
just takes a lucky guess and
returns some of the other remaining three
states. And so this is what I call here,
that I'm feeling lucky bonus because the
success probability of this classical
algorithm would then be 50 percent.
And this is what we measure our quantum
processor against.
So we can see that for the simple case,
we can actually achieve quantum speed
up in an experimental quantum processor.
All right, so now you probably ask
yourself, why can't we just scale it up
and build a quantum processor with like
a thousand or ten thousand cubits
and actually have several problems which
keep you keep us from doing that?
And a few of them I listed here.
So the biggest one for the quantum
processor, which I realized I'm doing
my PhD, is so called decoherence
and decoherence means that
basically the cubitt is not only
manipulated and measured by our own
signals, but also by other quantum
systems which are in the vicinity of
decubitus, for example, on the chip
itself or in the solution.
Krogstad and these quantum sys
systems manipulate the Cubitt
state and also performance measurement on
it. And as we've learned before,
a measurement destroys the quantum state.
So what this does is basically it kills
the state of our cubitt in a pretty short
amount of time for the processor, which I
realized this was on the order of a few
hundred nanoseconds.
OK, then the second problem is to get
food allergy and acute cubitt coupling
for a case of Tsukuba, but it's actually
pretty easy to devise a coupling scheme.
We can perform gaits between each
between a different cubitt.
But now, as you would if you would scale
up the number of cubits, you would see
that it's pretty difficult to switch
on and off the interaction between two
individual cubits with high fidelity.
It's kind of like if you have like a
phone line of a certain frequency
bandwidth and you want to have, for
example, 100 or 1000 subscriber
on it. And if every subscriber
takes some amount of the bandwidth of the
line, at some point you will have no
bandwidth left for new subscribers.
And this is kind of what happens with the
Kubicki. Are we?
At a certain point, we have used
all our frequencies that are available
for the Cubans and we can no longer add
new Cubans without kind of interfering
with the other ones.
So the same goes also for measuring
the Cuban state, because in our case
we can perform a measurement of the cubit
and get the correct result
with the probability of about 90 percent.
But this means, of course, that in 10
percent of the cases, we cannot reliably
measure the state of the Cuban, which is
also for this kind of a system, a big
problem.
All right. And of course, there are some
other problems which are one talk in
detail here, which, for example,
concerned the result of the.
So for quantum computers, it's actually
pretty hard to to reset the state of your
machine to zero.
And this is also like a problem which
which has to be solved and which is not
fully solved in practice yet.
OK, um, so I want to
finish this talk with a small
outlook on our small summary
of the recent trends and superconducting
quantum computing.
And now to the several groups
in the world are trying to improve the
state of quantum processors and
help to really build a large scale
quantum quantum computer.
And here to show you an image of the
research group at the University of Santa
Barbara and John Martinus lab,
which recently partnered up with Google
to build quantum processors.
And what they are doing is basically
to devise new types of architectures
that also use transman qubits like the
ones I showed you before and resonators.
But that couple of these elements and
different ways that makes it easier to
produce a large number of qubits on the
same chip and actually get
get a real quantum computer
out of that. So these approaches are, for
example, code rescue or service code
architecture.
OK, then you can as well
think about improving
the Cubans, Cubans themselves and the
resonators and
some groups, for example, in Ireland and
there and in other places around the
world are doing this by replacing
these copely. Now, Waveguide got
resonators that you see here on the left
by actually treaty resonators,
which are boxes of aluminum, that that
can also resonator microwave frequencies.
So here, for example, we see a system
that has a 3D cavity resonator
with two cubits which are placed
on a SSAFA substrate.
And the advantage of this is that you can
control the environment and fabrication
parameters of the Cuba to a much better
degree than you would be able to do with
microchips. So decoherence times and
the lifetime of the resonator, the
quality factor of the resonator in this
case is much better than fodder for
these so-called like to decubitus.
All right, another thing which some
groups are working on is so-called
quantum error correction, because
you cannot only say, OK,
let's put better qubits, but you can also
say let's work with bad qubits,
but devise algorithms that can help us
to correct errors if they occur.
And amazingly, this is actually possible
even with quantum bits.
And there are several approaches where
groups devise quantum
processors that can to some
degree correct errors and like
keep the quantum state of the Cubans
alive for an indefinite amount of time,
although the results which are obtained
here, for example, in the Yale group are
not yet at this point.
All right, the last thing
is then to instead, um,
instead of using non as solid
state or superconducting cubits to use
different quantum systems to to store
or process quantum information.
So here, for example, I show you work
from the group in Suckley,
which is a hybrid quantum system that
uses a diamond with
so-called envy centers, which are
nitrogen vacancy
centers and Diamont, and which actually
are responsible for the color of this
diamond and which amazingly can
store quantum information.
So what you have to system is that we
have a cubitt. And, uh, when
you want to manipulate the state of
Tacuba to keep the state
on the chip, but if you want to store it,
you can transfer it to the to the
NBA center in the diamond and keep it
there for a long time without having an
interference or any decoherence in a
Cuban state.
All right, so
as you can see, there's a lot of research
going on in this domain and,
um, you could actually plot kind
of a Moore's Law for
quantum computers or superconducting
quantum computers.
And if you do that, you would see that
when we when the research started on this
subject in 1999,
decubitus that we had at the time had a
coherence time of less than one
nanoseconds.
So they were really, really primitive by
today's standards.
And, uh, and the reason in the
following years, in 2002 and 2004,
they were new types of cubits devised,
which had a much longer coherence time.
And actually, this trend of increasing
the concern with the Cubans seems to go
on at a similar or like a
pretty fast rate
until today.
So in 2013, we
have actually superconducting Hubert's
that have coherence times in the order of
a few hundred microseconds,
which is large enough to envision
to actually use these qubits for four
real quantum computing.
So the take away here
is probably that quantum computers
are coming, but there's still,
of course, many, many engineering
challenges that we have to overcome.
And maybe to end this talk in a
selected political way.
Uh, the bad news is that probably
the quantum computers will come
to the hands of all the wrong people,
because right now it's mostly the
research and quantum computing is mostly
funded by governments and big
corporations. So this technology,
when it will become available, will
definitely not be available in like
a democratic fashion to everybody.
So.
All right, that's basically all I wanted
to to say, I just wanted to point out
that if you're interested in
quantum computing and hybrid quantum
systems, there's a talk on it tomorrow.
Diamonds are quantum computers.
Best friend, which is at twelve forty
five in Hall six by
Nicholas. Well OK.
So with that I thank you and
question.
Thank you for your talk.
We now have 15 luxurious minutes
of Q&A, so please
line up at the mikes there, six mikes,
one, two, three, four, five and six in
the back.
And we also have the AC and
Twitter. As I said before, if
you're physically unable to move, as in
not just caffeine deprived, but actually
not able to stand up, then please raise
your hands. We have a back up mic for
you.
OK, make one.
Go ahead.
Hello. Thanks for the very interesting
talk. I've learned a lot
today, Mike.
No, sorry.
Well, first of all, thanks for the very
interesting talk. I've learned a lot.
And if I understand this correctly,
quantum computing is at the moment
limited, limited by the amount of
cubits you can have interact with
each other, plus the amount you can
keep to keep it stable.
Um, do you have any idea
at what amount of time and what amount
of Cubitt quantum computing
can
reach a level where it can actually
compete with normal computing
in, say, doing Aerotek
calculations, et cetera?
Mm hmm.
And it's a very good question.
And the answer to
that is a bit complicated.
But in fact, what you want to achieve
with quantum qubits is the so-called,
uh, error threshold, because as I
talked about, there is a positive
possibility to perform error correction
of Cubitt. So if you are below
a certain level of errors for each
individual operation that you perform in
a cupboard, you can basically correct
that away and have a system that works
perfectly under the right conditions.
So and for, um,
classical approaches, like the
traditional approaches to quantum
computing to zero threshold was pretty
low at the order of like a
few fractions of a percent.
But with new approaches like, for
example, the surface surface
coding approach to error thresholds
has actually moved up quite a bit to a
few percent.
So today it would actually be invisible
to 12 cubits that are good
enough to to build real large scale
quantum computers.
Although, as I pointed out, there are
still a lot of other challenges,
challenges which keep us from doing that.
Okay, so that's a question.
Yeah, it does.
Thanks.
Does the Internet have a question?
Yes, there are two questions.
The first question is, in your example,
we got the right answer with a
probability close to one by applying
Grovers algorithm.
Mm hmm. Is this true for other,
uh, quantum algorithms also?
Um, so there's a small probability of
getting wrong results
for most quantum algorithms.
Yes, this is the case because
most of them are so-called probabilistic
algorithms, which give you the right
answer to a problem with a certain
probability that is close to 100 percent,
but not necessarily 100 percent.
So in this case, it could be the case
that we get the wrong answer, in which
case we just have to to like repeat the
process and check again
a couple of times. So, yeah.
And I mean, there are a lot of quantum
algorithms and I don't know then also
there might be some which are more
deterministic in that sense.
But to my knowledge, most of the quantum
algorithms, probabilistic by nature.
Number six, that's you.
Abbi, thank you very much for your child.
I have a pretty lame question,
um, conventional
computing units, in order to make them
better. You either
increase the density, get more bits
right. Or you
make them faster or you eldard,
um, uh, instructions said in some
way. Which of these are, uh,
feasible for quantum computing?
I mean, you answered a bit with,
uh, probably
closer.
So, um, I think today,
um, the biggest challenge in quantum
computing is not like having
higher packing densities of qubits on a
chip. So I think it's really more, um,
having the ability to even,
like, produce a large number of cubits
regardless of the of the size of the
structure. So I think in that sense,
we wouldn't wouldn't be
like a very high priority to optimize to
the packing or like the size of the
individual qubits under the chip.
And, uh, I think it's
more about if you talk about, like the
performance, you can also, of course,
try to decrease the amount of time
you need to, for example, perform quantum
gates. And this can be done by
increasing the frequency of the cubits
and also increasing the coupling between
individual qubits, which will
also increase the errors because
they will also be errors and cured when
you bring decubitus in and out of
coupling. So it's always like a
compromise between speed and
reliability or fidelity.
So to say things that answer your
question, you think
be a question from a camera angle.
Yes, thank you.
What do you think about linear
approaches for quantum computing based on
linear optics?
So in principle, the photon
is a pretty nice unit because it's
basically free from decoherence
and there are a lot of approaches.
In 2002, with freespace optical
Nohria been integrated into one chip.
And what do you think about these
approaches?
Mm hmm. Um, I'm not,
uh, not an expert in optical quantum
computing, so I don't want to comment
on that too much.
But I mean, as I said before, there are
many approaches to quantum computing.
And as of today, the race
is still open.
And whoever built the first working
quantum computers and if I would have to
bet, I would bet on like
quantum computers before or like
superconducting qubits.
But of course, to the optical systems and
photonic cube, it's also very
interesting. And they could prove to be a
viable alternative in case we should meet
like a roadblock with a superconducting
Hubert's or another technology.
So I think it's yeah, every technology
that can realize cubits is worth checking
out and then you have to like, measure it
against like different criteria.
For example, how far how easy is it to
make a large number of qubits?
How easy is it a couple of cubits with
each other and how good is the fidelity
when you realize individual cubitt
operations? So these are really the
criteria that you want to measure
against. I think maybe we can chat about
this later. I'm sure you would love to
have.
Number two, please.
Hi.
When you have your interference problem
with the with the frequencies, isn't this
a question of using a more complicated
probability space?
Maybe you can get around that.
OK, what problem are you referring to
when you have you have a scaling problem
if you add a lot of cowbirds, the
frequencies for them.
Yes.
OK, now, see, I mean, the problem
with our Cubitt processor was that the
coupling scheme was really very simple,
as as I showed, it was just a capacitor
that coupled the cubits to each other
whenever they were at the same
frequencies. And these architectures, for
example, the one here at the University
of Santa Barbara, use more
intricate coupling schemes that rely on
like different qubits being isolated
from each other by multiple resonators.
So the coupling factor, um,
I like the coupling strings and these
approaches goes down much
faster when you change the frequencies of
the cubits than in our case.
So these approaches are kind of more
reliable and better suited
to, like, realize a large number of
cubits, I would say.
So there are definitely lots,
lots and lots of approaches that you can
can, uh, can try to.
Yeah. To do.
Why don't people use better
superconductors?
Because we can do much better than 20 amk
by now. Hmm.
I mean the the temperature is really not
uh not uh the worst
problem that we have.
And yet we operate at low temperatures
mostly because we want to
avoid excitation of the cubitt
and like noise and like changing
the material of the superconductor would
be possible. But it would also be very
complicated because for those
materials I showed you, aluminum and
niobium, they are actually very good
fabrication processes in place which have
been optimized for like 10, 20 years.
And if you would take a new material, it
would be probably quite tricky to get
like a film of the same quality
and, uh.
All right.
OK, OK.
Internet, please.
Um, how many cubits would be necessary
to crack a two thousand forty eight
hours?
Oh, that's
a really good question.
And I
don't want to lie to the uh to
you now that uh I mean to
my knowledge the number of qubits that
you need to solve this problem goes
linear with the problem size.
So you would also need of the order of
two thousand doesn't something.
But there are as many bit at least
as as you have Bedzin, the number that
you want to create. But this could, of
course, vary by a factor, by a constant
factor of two or three, depending on how
many more bits you need for things like
error, correction and other stuff.
So but I would have to really I can look
it up in the shower algorithm
to give you an exact answer on this.
Number five.
Um, hello, um,
I was wondering the, uh,
the talks seemed like the
the direction of the search is
how we can use quantum computers,
how to solve the problems
that we have with normal computers today.
Um, but the but the the
thing that, uh, white crypto
was doing usually is to
create problems that
are hard to solve as they are
research in that direction to
uh.
Yeah, of course. I mean, uh, the basic
thing about quantum computing is that, as
I said, with the quantum computers, we
are able to solve some of the hard
problems that we use for cryptography
today, much faster than with the
classical computers.
So this kind of eliminates the security
we have in these methods. And, uh, there
is some a lot of research, actually, on
quantum cryptography.
I mean, I think there was a talk here on
those as well. But I'm really not an
expert in that subject and I wouldn't
like to comment on that now.
So but yeah, definitely there's a lot
of, uh, a lot of going on also when it
comes to the quantum cryptography itself.
OK, thank you.
Mm hmm. Number four.
Hi, um, I'm curious
to know what your thoughts are
on in the future in a world where
a lot of these hurdles have been removed,
where we have quantum computers that
can work with meaningful numbers of
qubits and relatively widespread
access to this technology.
What do you think?
Um, you know, some of the most promising
applications of this technology would be.
So for me personally, um, I don't think
that cracking passwords or reading
people's email is like the the thing
where we should build quantum computers.
Right. Um, for me, it's mostly the
ability to simulate quantum systems,
because even if you look today at
conventional electronics, um,
for example, a processor, you would see
that the size of individual transistors
comes down really
fast and approaches the limit where we
actually have a transistor that would
consist only of a few atoms.
So such a system would would by
definition have quantum mechanical
behavior. And if you want to understand
and simulate the systems, we would
definitely need quantum computers to do
that. So there are many other
applications and for example, protein
folding and like biology, genetics,
etc., which would require a profit
from this kind of computer.
So it's for me, it's really not about
cracking codes, but about like doing
science with that.
Yeah, thank you.
Number one one one
oh, thank you.
What I would like to know is you
in the popular press, I've always heard
that scaling to a larger number of bits
is hard. And I assumed that this was
because when you get too big, that they
don't interfere with each other anymore.
Today, I'm taking away that
the the arrows,
the noise is a big problem and
that the retention is a big problem.
And in the beginning, you mentioned that
the iron trap has up to 100
cubits already.
Can you say more about this iron trap
thing and what its parameters are
and why you're going in this way if
the other one is already so far?
So, yeah, as I said, I'm not an expert
on quantum computing, but the
qubits, which they have there are
really very good quality because the
coherence time can be in the range of
seconds and the speed
of operation can also be comparable to
that of superconducting qubits.
So you can have gaits which operate in
like nanoseconds on microseconds and
you can also have a readout fidelities.
So to sort of say the success
probability when you reload, given Cubitt
state, which approaches like 100
percent by like several
like six digits or so.
So this systems definitely seem
to be very promising.
Um, what kind of
could be a problem is probably the
scaling, because if you go
to a very large number of qubits, you
would have to somehow accommodate them
inside a trap, inside a magnetic
trap, which would which could be tricky.
But also for this problem, there are
solutions devised today.
For example, you have like R
atom traps, which are on a ship.
So we can really take individual cubits
or atoms or ions, if you like.
They can shuffle them around on a chip
and transport them to to to other other
sides and like that like isolate them
from each other. So as I said, for
me, the rest is completely open.
And right now I am computing
seems to be ahead.
But this could change, of course, if we
keep improving the superconducting qubits
like we did in the last 10 years.
So.
No.
Number six.
Hey, as it all at the moment,
we still use the binary system
with two systems, but we are not,
um, we can use higher level systems.
Are there any thought experiments
to overcome
the binary system with higher level
systems?
Um, yeah. You could, of course, do that.
And in fact, uh,
we did experiments where we used the
second and the third, uh, energy state of
Tacuba to have like a like a higher order
base for our calculations.
Um, but this is usually not done
because, uh, the speed up or
like to to gain information that you
that you achieved there is not
exponential.
So you could say that if you have lower,
for example, a quantum system of three
states, you would have a state
space, which is true to the power of four
and cubits, whereas for the cubic state
it would be two to the power of.
And so it's still a big difference.
But it's not going like like it's not the
number that that we change is not in the
exponent, so to say.
So, um, that's kind of the kind
of way most people don't do it.
OK, thanks.
OK, we are out of time.
I'm very sorry but I'm sure you can find
a dress outside of Nater thinking
like place.