How to program a quantum computer

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Let's go for

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super 820.

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Thank you for the introduction.

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And, it's a talk such I want to, show

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how to work on quantum computers
and more concrete.

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First, I want to show what you need.

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What ingredients, how it's,

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mentally realized.

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And one example.

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And then, finally,
how you can run programs and algorithms

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on the quantum computer.

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And there's an especially
the last step is very exciting to me

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because as a theorist, I, most of the time
I'm sitting in the office.

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And so I have at least sometimes elevation
that I can work on an experiment

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and see what comes up.

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Before

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I want to dive into, these topics,
I want to show,

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possible implications
for quantum computers.

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I mean, the most fleshy one,
most of you know, is,

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I have at least heard of is, concerning
prime factorization.

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Using Shor's algorithm, the idea is that
this is an algorithm which,

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factorize prime numbers

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exponentially, faster than any known
classical algorithm.

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And it's, it's the reason why,
for example, the military is interested

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in quantum computers, and the funding
is quite high in this field.

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But, because the quantum

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principle break, public key encryptions.

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But, to be honest, this application is
quite, is quite fine if you take a guess,

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it would take at least 20, one year

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or even longer until you can,

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and make real use cases.

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But this is more exciting
from a physical perspective.

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And this is also like
something mentioned in this talks is,

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this simulation of strongly
interacting quantum systems.

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So in this cases you have of, many,

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competitive terms like

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the kinetic terms and, and, interactions.

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And so you,
you will have not the dominant term

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where you can apply perturbation theory on
and in this cases it's hard to,

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to, to apply classical algorithms.

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And this is, quantum computers
come into play.

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One example are the strongly correlated
systems.

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Took me to mention
before the, the, interesting

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because one of the most, open problems

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in, in physics,
like high temperature superconductivity,

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buried in this models another model,

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as I mentioned, a little bit before, is,

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concerning, quantum chemistry,

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but are also strongly, interacting.

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Let me Tyson in the hot
to simulate classically but but also,

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when you consider high energy physics,

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I mean, you will have in order
to understand

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this,
you'll have to build, large colliders, or,

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or you can do to some very limited

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as stand some classical simulations,

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which goes then it's, let us quickly but,

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but this classical simulations,

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a very hard to realize
you can only consider limited systems

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and so
and have to put much effort into this.

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And it

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turns
out that there are also algorithms, to,

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to simulate the standard models

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and is active work on it
to realize that on quantum computers.

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And it's probably, at the long term
and, and cheaper way

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than building the next largest collider.

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With this in hand, I, I want to show,

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what you need.

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And this was nicely summarized in there
and consensus criteria

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roughly 25 years ago,
the first thing is that you need,

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qubits or

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which are scalable.

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So it's just basically the,
the building block of a quantum computer

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and it's nothing. OS
then you need classical bits.

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Fine. Classical, classical computer.

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The second thing,

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is that you need long enough
coherence times

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this, you need that you,
that you actually can use the loss of,

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quantum mechanics
to, to run algorithms which,

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which are hard to simulate
in classical computers.

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And then it turns out that this is
actually the the most challenging issue

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for, for, for, current realizations.

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And you probably need, quantum
error correction,

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a long term statistical this challenge
that, this, was also mentioned at,

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talked last year, but, by Benedict.

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So I only briefly touched this
at the end of of the talk.

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Then you'll need, universal,
set of quantum gates

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and for quantum computers,
basically the idea is that you will,

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the algorithms,
consists of unitary operations,

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and then you'll need some ingredients
to realize them.

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And then it turns out that, the, the,

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that you basically need one single cubit
gates, which are there other methods and,

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and, for example, a phase
gate at gates here and, in the bottom,

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which I will, trade later.

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And then you need a, two qubit gates
which can entangle,

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qubits, which is in this case a control,

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not operations.

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This universal set, you can, can build
arbitrary unitary operations.

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And finally, to get

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also something out of your,
quantum computer, you will have,

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measurements, to

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get some results and compare
what the, Giving,

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Yeah.

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So in the last 20 years,
there were lots of proposals

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and approaches
to, to satisfy this criteria.

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I just mentioned a few, the few,
probably most promising right now,

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but one, superconducting qubits,
which are,

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which is a strategy, pursued
by, companies like Google, IBM.

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And so here in Oxford.

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And the idea is that, basically use,

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electric,

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particularly as circuit elements involving
Josephson

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junctions and encode the qubits,
in this circuit elements.

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I will show this, explain this later.

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Then you can, another possibility
possibilities using trapped ions,

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values, values like,

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the qubits into energy levels of

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of this ions and then apply,

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policies to manipulate this,

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this, levels

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now, there was, recently
there was some announcement

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that you can use topological quantum
computing by, by Microsoft,

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to not

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want to state
now, that this claims are correct or not.

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But if, this are the case,
this would be also quite a promising,

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realization, which is,

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is it was, to scale up,

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another possibilities.

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It's using ultracold atoms
with neutral atoms in,

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contrast to the ions,
which we have before.

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But, but it emerged, especially in the,

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last five years is,
another competitive, player in the field.

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Now, there are lots of other approaches,

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for example, photonic quantum computers,

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attempts to use silicon, quantum computing
and so on,

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that I cannot, explain all of them,

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because of lack of time and because I

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if you have the lunch served later
and I was hungry.

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So I will focus, now

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on superconducting circuits, qubits.

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So here in this picture, you,

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essentially can see,
for transparent qubits.

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What specifically? This cost state for.

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And when you zoom in a

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little bit, you see the order of micro,

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meter, the hundreds of micrometers,
you see this cross,

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a few zoom in even more,
and then you see what you actually see,

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which has the size of a few hundred
nanometers,

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to, it's basically a Josephson junctions

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and across, the cross shape,
this is basically a large,

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capacitor, c tens.

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And the idea is that,
the Josephson functions,

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is a nonlinear,

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conductivity of your circuit,
which will become later.

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And when you, when you do,

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some elementary physics and,

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for the circuits, you can quantize, say,

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Hamiltonian, corresponding to the system.

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And this has a, has basically this form.

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So the first part, corresponds to the,

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energy.

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And and

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and there's a number of,
Cooper pairs, on the islands.

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And the second term
is, is, is basically a term,

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coming from,

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from the Josephson
current, of, of this junctions.

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But, what is very important is,
when you look at this, point

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that it's not, it's not quadratic,
but it's a cosine, it's a cosine,

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which is basically
almost a harmonic oscillator,

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which is also important
is that, the number

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of Cooper pairs and the Josephson
face, the, the conjugate, the barrier.

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But it's but it's,

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you, so you get almost something as,

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the harmonic oscillator.

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Now, when you look at this model,

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and compared with a harmonic oscillator,
there you have a quadratic potential.

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And as you know, from your,

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first course, as in quantum mechanics,
for a quadratic potential,

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you get equidistant, level spacing.

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Now, the cosine potential looks almost,

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like this,

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harmonic potential, but, but not quite.

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So what what you see is that you have

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a slight distortions of this energy
levels.

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And, the, the qubit itself, corresponds
to the lowest

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two eigenstates, of,
of of the, of your transition qubit.

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So with
this in mind, we can, try to understand

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how you apply quantum operations
on, on this level

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for this.

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I consider a single qubit operations,

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two qubit operations.

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Similar.

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Basically, what you have here is

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a is a, is is a cavity,

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and you, you copied your transplant,

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qubit to, to the, to a resonator.

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But, what happens is basically,
that you get the hybridization

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between the photon and, qubit states,

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which means they are no longer
independent of each other.

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So but you get this light dressing similar
to this quasi particle picture.

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I don't mean to show it before at all.

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Low order approximation.

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The, you can still separate them,

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but what happens is that,

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the, the,
basically by applying a photon pulse,

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you can, you can change this state
as a state of the transition qubit.

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So you basically applying here
microwave pulse, and then,

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introduce,

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transitions in the qubits

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you have between the first
and the second state.

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Yeah.

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This is a point where this, this

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it becomes very important in the sense
that,

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transitions between the lowest
trying states,

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allowed, but,

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transitions to higher states, the,
the slightly off

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resonance, which means that they are
strongly suppressed.

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So you're, you're aware that,
that you excite higher levels and,

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leak information of your qubits?

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And then you want to apply
to qubit operations.

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This is it
can unfortunately, is not visible here

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in this picture, but,
but basically you have, you have cavities.

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Between different, different qubits.

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And then you can, also,

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you can, you can drive one qubit and

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if you,

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if you microwave pies and,

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and the effect depends then on the,
on the state of the other qubit.

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Finally, we have to consider measurements
for this.

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You have,

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here, this, this other resonator

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and also coupled via, via cavity
to this transition qubits.

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And the other concept,
this also provides, similar.

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So, because of this coupling,

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the, the states of the transmission
qubits,

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no longer, completely
separate of the microwave pulse.

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And on the other hand, is also,

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the eight modes of, of this resonator
depend on the qubit states,

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but it explicitly means this when you look
at the transmission frequency,

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of your resonator,
which you can just a measure

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by applying a microwave pulse,
then you see that,

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it has a different resonance, states,

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if the qubit is in state zero,

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but it's, but it's getting shifted
when the qubit is in state one.

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And, basically

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by reading out the transmission frequency,
you can measure the qubit and, infer in

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what state it is.

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So with this in mind, we can

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we, we have basically everything to, to,

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you have to run algorithms and,

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perform a quantum operations
on your quantum computer,

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00:14:34,866 --> 00:14:37,866
the basic operations of which you have,

252
00:14:39,000 --> 00:14:42,766
in this case,
are often illustrated in circuit diagrams.

253
00:14:42,766 --> 00:14:45,766
I want to, briefly sketch
how they look like,

254
00:14:46,800 --> 00:14:48,266
I mean, the.

255
00:14:48,266 --> 00:14:48,566
Yeah.

256
00:14:48,566 --> 00:14:51,566
Easiest case of in your head
when you consider qubits,

257
00:14:51,766 --> 00:14:54,133
they are basically denoted
by a black line.

258
00:14:54,133 --> 00:14:57,133
As you can see here above.

259
00:14:58,300 --> 00:15:00,666
When your, when you consider,

260
00:15:00,666 --> 00:15:03,433
quantum operations, they, illustrated

261
00:15:03,433 --> 00:15:07,833
by, by boxes
and there you, get again the protagonist,

262
00:15:07,833 --> 00:15:10,833
which I have showed
you already before at the beginning.

263
00:15:12,300 --> 00:15:13,800
All of them are unitary gates.

264
00:15:13,800 --> 00:15:16,800
But as you would expect from the laws of,

265
00:15:18,433 --> 00:15:20,333
quantum mechanics,
and then this is basically

266
00:15:20,333 --> 00:15:23,666
the only restrictions
you have, for this operations.

267
00:15:25,733 --> 00:15:27,866
The most illustrative one is,

268
00:15:27,866 --> 00:15:31,166
I think is the,
is the not gate or the X gate.

269
00:15:31,333 --> 00:15:34,666
This is, very similar to, to what your,

270
00:15:35,000 --> 00:15:38,600
expect
on, classical circuits and, basically,

271
00:15:38,766 --> 00:15:41,866
I mean, you're right,
it is a matrix element, but, but this,

272
00:15:43,633 --> 00:15:47,600
operation is, doing a when,
when your qubit is in state zero,

273
00:15:47,800 --> 00:15:52,366
it's, it's, it flips it to a state one
and otherwise it

274
00:15:52,366 --> 00:15:55,366
flips, and vice versa.

275
00:15:56,700 --> 00:15:59,733
Then then you have Hadamard gates.

276
00:16:00,800 --> 00:16:02,900
The idea of this Hadamard gate, this, it

277
00:16:02,900 --> 00:16:07,800
looks, slightly more complicated, but,
basically what it is doing when you start

278
00:16:07,800 --> 00:16:12,000
in the ground state of a qubit,
after applying a gate, your,

279
00:16:12,133 --> 00:16:16,000
your will be in a, superposition
between, state zero and,

280
00:16:16,533 --> 00:16:19,533
state one.

281
00:16:20,500 --> 00:16:23,500
And, what I mentioned before,

282
00:16:23,700 --> 00:16:27,133
you need some additional gates,
which, which can induce

283
00:16:27,600 --> 00:16:30,833
additional phases,
between the states of the qubits.

284
00:16:30,833 --> 00:16:35,233
And this is done by phase gates,
specifically when you have a phase

285
00:16:35,233 --> 00:16:39,666
shift of pi four is done here
and it's, it's called, T gates.

286
00:16:40,166 --> 00:16:42,100
And it turns out when you're basically,

287
00:16:43,433 --> 00:16:43,800
when you

288
00:16:43,800 --> 00:16:47,900
only apply Hadamard, gates, you can,
you can create

289
00:16:47,900 --> 00:16:51,600
arbitrary
one qubit rotations by sticking together,

290
00:16:52,766 --> 00:16:55,966
of, of has
it has been shown roughly 30 years ago

291
00:16:57,433 --> 00:17:00,433
now, one qubit gates,

292
00:17:00,600 --> 00:17:03,600
so one qubit operations.

293
00:17:03,700 --> 00:17:06,233
I mean, the, might be interesting, but,

294
00:17:06,233 --> 00:17:09,666
you cannot do so much useful things
with one qubit.

295
00:17:09,800 --> 00:17:12,466
I do not have to build
a quantum computer for that.

296
00:17:12,466 --> 00:17:15,466
So you need interactions between qubits

297
00:17:15,766 --> 00:17:18,766
and it turns out that when you,

298
00:17:18,966 --> 00:17:21,966
when you have at one another gate,
which is,

299
00:17:22,566 --> 00:17:26,200
a c not gate,
which is shown here, which, basically,

300
00:17:27,566 --> 00:17:30,566
this cNOT gate shifts,

301
00:17:30,933 --> 00:17:33,733
induces a transition of the
of the second qubit only

302
00:17:33,733 --> 00:17:37,566
if when, when the first qubit
is in an excited, state

303
00:17:38,933 --> 00:17:41,433
and it turns out of, in your, at the

304
00:17:41,433 --> 00:17:47,600
si not gate to your, to your second,
then this is already sufficient to, to,

305
00:17:48,566 --> 00:17:51,900
create arbitrary unitary, transformation,

306
00:17:53,000 --> 00:17:55,600
transformations with, with, an arbitrary

307
00:17:55,600 --> 00:17:58,600
number of qubits.

308
00:17:58,733 --> 00:18:01,733
And finally, as mentioned,

309
00:18:01,900 --> 00:18:04,900
you have some of which are basically,

310
00:18:05,466 --> 00:18:07,200
indicate the,

311
00:18:07,200 --> 00:18:10,200
but by this box

312
00:18:10,533 --> 00:18:16,833
now, I do not only want to implement them
classically, but, but I'm also interested

313
00:18:16,833 --> 00:18:22,833
to run them on a real devices
and it turns out that, and the, solution.

314
00:18:22,833 --> 00:18:26,766
So what you can do, is
it it's a illustrates,

315
00:18:28,633 --> 00:18:30,066
in a, a second

316
00:18:30,066 --> 00:18:33,066
is that you can program
your quantum circuits,

317
00:18:34,266 --> 00:18:37,300
with Python library,
which is called Qiskit.

318
00:18:38,900 --> 00:18:42,633
And the idea is basically
you construct your circuit, then,

319
00:18:42,933 --> 00:18:45,766
then you, then you,

320
00:18:45,766 --> 00:18:48,766
submitted to a compiler, which,

321
00:18:49,066 --> 00:18:51,333
translates as your circuit

322
00:18:51,333 --> 00:18:54,333
to a native gate
operations of your quantum computer,

323
00:18:54,333 --> 00:18:59,333
which is very similar as you are
doing for, for classical coding. And,

324
00:19:00,433 --> 00:19:00,700
yeah.

325
00:19:00,700 --> 00:19:04,533
Then, basically you can
analyze this circuit or so with Qiskit,

326
00:19:04,900 --> 00:19:09,266
then you have small scale simulations
with all the ten qubits.

327
00:19:09,266 --> 00:19:13,000
You can simulate it classically,
which is good for debugging to see

328
00:19:13,000 --> 00:19:15,033
whether you are doing the right thing.

329
00:19:15,033 --> 00:19:18,033
But, many of the,

330
00:19:18,266 --> 00:19:21,266
of, companies, they,

331
00:19:21,466 --> 00:19:23,966
they allow access to real hardware via
cloud

332
00:19:23,966 --> 00:19:28,933
services and notably,
there's, a, a, s bracket,

333
00:19:29,400 --> 00:19:33,000
which allows access,
for example, to Google.

334
00:19:33,000 --> 00:19:34,900
It works for,

335
00:19:34,900 --> 00:19:38,666
quantum computers,
but there's less, access, to IBM quantum.

336
00:19:39,200 --> 00:19:44,200
And that's, interesting is that,
you do not have to be a professional.

337
00:19:44,233 --> 00:19:48,266
In fact, everybody can can register
for this service.

338
00:19:48,266 --> 00:19:50,966
And you have also,

339
00:19:50,966 --> 00:19:53,700
limited a number of,

340
00:19:53,700 --> 00:19:57,033
time to, to run operations on this quantum
computers.

341
00:19:57,166 --> 00:20:00,766
So, in fact, I think I know
in the case of IBM quantum, it's,

342
00:20:01,700 --> 00:20:04,666
you'll have ten
minutes time of computation.

343
00:20:05,733 --> 00:20:07,133
Time per month, but,

344
00:20:07,133 --> 00:20:12,166
but this is sufficient to, to run
small operations and also everything.

345
00:20:12,300 --> 00:20:16,000
What I will show
later is done within a few minutes.

346
00:20:19,433 --> 00:20:21,800
When you look at the,

347
00:20:21,800 --> 00:20:24,500
quantum computers,

348
00:20:24,500 --> 00:20:27,700
well, and this is cloud services,
they illustrate,

349
00:20:28,633 --> 00:20:30,266
how the qubits are connected.

350
00:20:30,266 --> 00:20:32,733
This is a this is,

351
00:20:32,733 --> 00:20:34,566
snapshot of IBM. Yes.

352
00:20:34,566 --> 00:20:36,466
Which has,

353
00:20:36,466 --> 00:20:41,033
126 or 27 qubits.

354
00:20:41,033 --> 00:20:43,666
And in principle, you can use all of them.

355
00:20:43,666 --> 00:20:46,466
And it turns out that this is already hard

356
00:20:46,466 --> 00:20:49,466
to simulate on classical devices.

357
00:20:50,600 --> 00:20:51,566
Finally, and

358
00:20:51,566 --> 00:20:54,566
I also want to advocate, you can,

359
00:20:55,733 --> 00:20:56,966
do it on your own.

360
00:20:56,966 --> 00:21:01,200
And it turns out that programing quantum
computers is not that much different

361
00:21:01,433 --> 00:21:04,433
to programing classical computers

362
00:21:05,033 --> 00:21:06,500
too. So this I want to

363
00:21:06,500 --> 00:21:09,800
illustrate
of, first, a very simple example,

364
00:21:11,000 --> 00:21:11,366
which is

365
00:21:11,366 --> 00:21:14,533
creating a base state,
but which is basically,

366
00:21:15,366 --> 00:21:18,033
either both qubits are in state zero

367
00:21:18,033 --> 00:21:21,966
and above states, in, in state one.

368
00:21:22,200 --> 00:21:28,500
So, I mean, so, so it's not very, complex,
but but but in principle,

369
00:21:29,366 --> 00:21:34,033
this, this, like,
creation of such, states,

370
00:21:36,933 --> 00:21:38,100
was very important

371
00:21:38,100 --> 00:21:41,100
also to, to, to, to test

372
00:21:41,133 --> 00:21:44,300
causality of, quantum mechanics
and also respected in

373
00:21:44,333 --> 00:21:47,333
and Nobel Prize a few years ago,
just a few years ago,

374
00:21:48,400 --> 00:21:52,400
it turns out, when you want to run it
on a quantum computer, you first,

375
00:21:52,933 --> 00:21:55,933
import, quantum circuit object.

376
00:21:56,933 --> 00:22:00,900
You, you basically import your, library

377
00:22:02,633 --> 00:22:07,166
and then you apply
your gates, quite straightforward.

378
00:22:07,166 --> 00:22:10,166
So it, in order to create your by state,

379
00:22:10,333 --> 00:22:14,100
first you have to apply a Hadamard gates
to a qubit zero.

380
00:22:14,100 --> 00:22:19,200
So you put it in a, the first qubit
on a superposition of zero and one.

381
00:22:20,933 --> 00:22:24,000
Then you apply a control not operation,

382
00:22:24,466 --> 00:22:29,033
which basically means that the,
the first qubit is then in state zero.

383
00:22:29,033 --> 00:22:32,033
Then when the finished,

384
00:22:32,533 --> 00:22:33,766
zero of qubit is in state

385
00:22:33,766 --> 00:22:36,766
zero and and vice versa.

386
00:22:37,100 --> 00:22:38,900
And then you perform

387
00:22:38,900 --> 00:22:42,933
a few, two measurements to,
read out the qubits.

388
00:22:43,200 --> 00:22:46,200
That's basically it. And then your,

389
00:22:46,200 --> 00:22:49,666
you can test how,
how it looks on the quantum computer.

390
00:22:49,666 --> 00:22:52,666
So it's, five lines of code.

391
00:22:53,766 --> 00:22:55,866
Now, if you want to execute this,

392
00:22:55,866 --> 00:22:58,866
I mean, you can do it
in a classically simulated,

393
00:23:00,333 --> 00:23:03,766
for this,
they provide classical simulators.

394
00:23:05,166 --> 00:23:07,033
If you're,

395
00:23:07,033 --> 00:23:10,333
directly go to a quantum computer,
you do not have to change much.

396
00:23:10,333 --> 00:23:13,500
It's basically it's
basically changing two lines of code.

397
00:23:14,966 --> 00:23:18,266
And then,
the next step is what I mentioned before.

398
00:23:18,266 --> 00:23:22,366
You have to test by, like, compile
your circuit for the, for this, your,

399
00:23:23,400 --> 00:23:25,800
transpile.

400
00:23:25,800 --> 00:23:28,800
Basically that, this, transpile has,

401
00:23:29,333 --> 00:23:32,400
information of, the quantum computer.

402
00:23:32,400 --> 00:23:37,366
You, you want to run your code,
and it's, it translates,

403
00:23:38,133 --> 00:23:41,133
it, it
translates your circuit to the native,

404
00:23:42,166 --> 00:23:45,166
gates of your quantum computer

405
00:23:45,300 --> 00:23:47,233
and then your, afterwards.

406
00:23:47,233 --> 00:23:50,766
And in this case, I have prepared
this, in advance.

407
00:23:53,166 --> 00:23:54,866
This circuit looks like this.

408
00:23:54,866 --> 00:23:57,866
But what you have basically is that,

409
00:23:59,066 --> 00:24:01,400
this is not this,

410
00:24:01,400 --> 00:24:05,300
this is translated
to, such a, two qubit operation,

411
00:24:05,600 --> 00:24:10,366
which is almost a C, not, apart
from some additional, phase shift.

412
00:24:11,633 --> 00:24:15,333
And then this
the single qubit operation is,

413
00:24:16,100 --> 00:24:19,133
is translated in a lot of, of,

414
00:24:19,600 --> 00:24:22,600
rotations and additional face gates.

415
00:24:23,400 --> 00:24:26,433
But it's also interesting
is when you look at the circuit,

416
00:24:26,733 --> 00:24:29,733
there are two numbers, 49 and 50.

417
00:24:30,666 --> 00:24:32,600
And, when you look at,

418
00:24:33,766 --> 00:24:36,766
the quantum
computers, I have, shown before,

419
00:24:36,900 --> 00:24:41,100
it means basically that,
the circuit is run on these two qubits.

420
00:24:41,100 --> 00:24:44,100
You can see here.

421
00:24:45,933 --> 00:24:46,800
And then,

422
00:24:46,800 --> 00:24:49,800
I mean, apart from it,
you basically submit your job.

423
00:24:51,133 --> 00:24:53,866
And in our case,
we want to run this circuit, multiple

424
00:24:53,866 --> 00:24:57,700
times, to, get some statistics
and see what, what comes out.

425
00:24:57,700 --> 00:25:00,933
And then if, retrieve the result,

426
00:25:02,100 --> 00:25:05,000
which encodes some information, what,

427
00:25:05,000 --> 00:25:08,066
what gates you used, but, but,

428
00:25:09,366 --> 00:25:11,133
of properties of the quantum device.

429
00:25:11,133 --> 00:25:11,566
But nice.

430
00:25:11,566 --> 00:25:11,733
Right?

431
00:25:11,733 --> 00:25:15,233
It's it has and also,
of course, the result itself.

432
00:25:15,233 --> 00:25:18,233
And then you can show it in a histogram

433
00:25:18,733 --> 00:25:21,733
in this case, I,

434
00:25:21,900 --> 00:25:24,900
I have prepared it as I mentioned,

435
00:25:25,000 --> 00:25:27,933
when you do the classical simulations,

436
00:25:27,933 --> 00:25:30,600
you get basically this count.

437
00:25:30,600 --> 00:25:34,300
I repeated the,
the simulation a thousand, 24 times.

438
00:25:34,500 --> 00:25:34,833
This,

439
00:25:36,600 --> 00:25:37,000
this is a

440
00:25:37,000 --> 00:25:40,000
basically a matter of seconds
for the circuits.

441
00:25:40,533 --> 00:25:42,233
And, what what,

442
00:25:42,233 --> 00:25:45,533
what you can see
is that you have, basically

443
00:25:45,566 --> 00:25:49,500
of a 520 times here at your
a measured the qubit,

444
00:25:50,433 --> 00:25:54,266
both qubits and state zero
and otherwise you measured in state one.

445
00:25:54,266 --> 00:25:55,566
I mean, it's not not,

446
00:25:55,566 --> 00:25:59,666
perfectly 50%, but this is basically
to statistical fluctuations.

447
00:26:00,466 --> 00:26:03,800
Now, you can,
do the same on, on every other device.

448
00:26:05,166 --> 00:26:07,800
And in this case, you see,

449
00:26:07,800 --> 00:26:11,233
make this observation,
it looks almost the same.

450
00:26:11,233 --> 00:26:14,300
You you get almost 50% on state zero.

451
00:26:14,833 --> 00:26:18,200
Both qubits and state
seal of above qubits on state one.

452
00:26:18,500 --> 00:26:21,700
But what you also see
is that there's, slight deviation.

453
00:26:22,433 --> 00:26:26,333
Basically that only one qubit is in state
one and one qubit,

454
00:26:27,533 --> 00:26:31,733
while the other one and this is
this is basically due

455
00:26:31,733 --> 00:26:35,000
to noise and hardware errors,
which is quite remarkable.

456
00:26:36,133 --> 00:26:37,233
Seen before is,

457
00:26:37,233 --> 00:26:40,666
was a very small circuit,
and we have already 2% error

458
00:26:40,666 --> 00:26:43,800
rates, which gives you an impression how,
how good current

459
00:26:43,800 --> 00:26:46,800
hardware is.

460
00:26:47,133 --> 00:26:50,066
So, I mean, this is basically the reason

461
00:26:50,066 --> 00:26:53,500
why we have to deal with errors,
in a, in the long run.

462
00:26:54,933 --> 00:26:59,566
I mean, as I mentioned,
this was very, simplistic example.

463
00:26:59,900 --> 00:27:03,800
Now, if I want to, show you something
which is,

464
00:27:04,733 --> 00:27:06,866
more connected to real world,

465
00:27:06,866 --> 00:27:09,866
at least from a theorist perspective.

466
00:27:10,366 --> 00:27:13,866
This is namely, this is basically dealing
with quantum dynamics,

467
00:27:15,400 --> 00:27:17,033
which is one of the most,

468
00:27:17,033 --> 00:27:19,800
promising applications,

469
00:27:19,800 --> 00:27:21,733
basically use a quantum computer

470
00:27:21,733 --> 00:27:24,733
to simulate other quantum systems.

471
00:27:24,800 --> 00:27:29,333
And the idea is
that you use the trusted, decomposition.

472
00:27:29,700 --> 00:27:32,933
So you, have, usually you have a very,

473
00:27:33,500 --> 00:27:37,566
complex operator
or a complex system, your molecule or you,

474
00:27:38,733 --> 00:27:41,166
your,

475
00:27:41,166 --> 00:27:44,166
strongly interacting system
to has some before

476
00:27:44,466 --> 00:27:47,633
and what you can, what you can do

477
00:27:47,633 --> 00:27:51,100
is that you decompose this big block
or this from a,

478
00:27:51,666 --> 00:27:56,400
in a bunch of two qubit operations,
and then you have this cubit operations.

479
00:27:56,400 --> 00:27:59,400
It's in state, straightforward.

480
00:28:00,133 --> 00:28:01,400
To practice and compile.

481
00:28:01,400 --> 00:28:04,400
And then you can run this

482
00:28:04,400 --> 00:28:07,200
and this, this looks,

483
00:28:07,200 --> 00:28:08,400
quite simple.

484
00:28:08,400 --> 00:28:11,333
But, the issue is,
from a classical perspective,

485
00:28:11,333 --> 00:28:15,566
the dimension of the Hilbert space scales
exponentially with the number of qubits.

486
00:28:16,033 --> 00:28:20,666
And, when you want to simulate
such systems, classically,

487
00:28:20,700 --> 00:28:23,733
it turns out that, you're basically

488
00:28:23,766 --> 00:28:26,766
at the limits of,

489
00:28:28,000 --> 00:28:31,500
of, state of the art classical computers.

490
00:28:31,500 --> 00:28:34,500
When you go to, to roughly set the qubits,

491
00:28:34,600 --> 00:28:37,600
or a bit more, which is, I would say,

492
00:28:38,333 --> 00:28:39,433
quite far from

493
00:28:39,433 --> 00:28:42,433
complex molecules or, interacting systems.

494
00:28:42,733 --> 00:28:44,600
So that's the reason why, this,

495
00:28:45,566 --> 00:28:46,500
this approach is

496
00:28:46,500 --> 00:28:50,266
actually used also to benchmark
the performance of quantum computers.

497
00:28:50,666 --> 00:28:53,566
And then you do a few, tweaks and tricks.

498
00:28:53,566 --> 00:28:56,866
You can show already that
occurring quantum computers,

499
00:28:59,166 --> 00:29:01,266
can give competitive

500
00:29:01,266 --> 00:29:04,266
results, to, to classical devices.

501
00:29:04,800 --> 00:29:07,800
How is how is this done?

502
00:29:08,033 --> 00:29:10,633
Again, using Qiskit.

503
00:29:10,633 --> 00:29:13,333
I use a very simple toy model.

504
00:29:13,333 --> 00:29:16,333
But it's straightforward to use, some,

505
00:29:16,500 --> 00:29:17,500
something more complex.

506
00:29:17,500 --> 00:29:21,100
And in fact, this case is so simple
that you can solve it.

507
00:29:21,500 --> 00:29:22,733
Exactly.

508
00:29:22,733 --> 00:29:25,233
By hand.

509
00:29:25,233 --> 00:29:28,500
So you have basically you have basically
an interaction between two qubits,

510
00:29:28,900 --> 00:29:32,600
by some interaction and you have
some additional magnetic field,

511
00:29:34,300 --> 00:29:36,200
and then then you want to,

512
00:29:36,200 --> 00:29:39,200
to code that, Trotta evolution,

513
00:29:39,200 --> 00:29:41,833
of what you have to do
is you basically create

514
00:29:41,833 --> 00:29:44,833
a trotter, a trotter gate.

515
00:29:44,866 --> 00:29:48,833
So you, create your Hamiltonian
with online what they took here, but

516
00:29:48,833 --> 00:29:53,833
Hamiltonian
and then this, automatically creates

517
00:29:53,833 --> 00:29:57,600
you an evolution, this, qubit evolution
gate.

518
00:29:58,500 --> 00:30:01,366
And. Yeah,
if you want to multiply it with the times,

519
00:30:02,366 --> 00:30:02,666
you will

520
00:30:02,666 --> 00:30:05,666
have a basically at a few lines of code
which,

521
00:30:06,433 --> 00:30:09,433
apply to, gates, either to the even bonds,

522
00:30:10,200 --> 00:30:12,433
which are the first two lines,

523
00:30:12,433 --> 00:30:15,866
to, to the odd
and that's basically it. So,

524
00:30:17,100 --> 00:30:20,100
I can show again when your,

525
00:30:20,166 --> 00:30:23,266
want to consider
one of these trotter steps for six qubits,

526
00:30:24,300 --> 00:30:26,033
it looks like this.

527
00:30:26,033 --> 00:30:29,933
I mean, it's a it's
a bit more complex than before, but,

528
00:30:30,266 --> 00:30:33,466
but when you look closely at this, then,

529
00:30:35,100 --> 00:30:37,633
this red box corresponds

530
00:30:37,633 --> 00:30:40,600
to one trotter step
which I have implemented.

531
00:30:40,600 --> 00:30:43,800
And and the rest is done,
is done by inference by the.

532
00:30:45,433 --> 00:30:48,433
Now you can again compare

533
00:30:48,500 --> 00:30:51,500
the time evolution,
as I have done by before.

534
00:30:52,000 --> 00:30:53,966
In this case, I'm,

535
00:30:53,966 --> 00:30:56,533
I saw, to not sample

536
00:30:56,533 --> 00:30:59,366
exact strings, but,
but measured in magnetization.

537
00:30:59,366 --> 00:31:03,166
So, so the, the expectation
value of a set on each side.

538
00:31:04,366 --> 00:31:05,900
And you do it classically,

539
00:31:05,900 --> 00:31:08,900
on, the exact simulation
on a classical computer.

540
00:31:09,833 --> 00:31:12,966
I start, with, with,

541
00:31:13,733 --> 00:31:16,733
a staggered initial state, the,

542
00:31:17,300 --> 00:31:21,166
which you,
which is indicated by this pattern.

543
00:31:21,166 --> 00:31:24,666
And then you evolve in time,
you see that, the,

544
00:31:25,566 --> 00:31:27,766
the system equilibria.

545
00:31:27,766 --> 00:31:31,066
But you see also this, this long
term oscillations.

546
00:31:32,200 --> 00:31:35,200
Now, you can compared again
with a quantum computer.

547
00:31:36,133 --> 00:31:40,500
It looks not that bad, in fact, for,
especially when a,

548
00:31:40,500 --> 00:31:44,766
when you have in mind that before
we have a 2% error rate per, packet.

549
00:31:45,000 --> 00:31:47,766
So you,
you see, especially at the beginning,

550
00:31:47,766 --> 00:31:51,766
you, you see this oscillations
there, there's spun qubits.

551
00:31:53,400 --> 00:31:55,833
This, oscillation do not,

552
00:31:55,833 --> 00:31:58,833
decay really,
which indicates that probably this,

553
00:31:59,700 --> 00:32:02,700
Q qubit does not work properly.

554
00:32:02,700 --> 00:32:05,766
And, but additionally, you see that,

555
00:32:07,200 --> 00:32:10,000
that the long time values,

556
00:32:10,000 --> 00:32:13,266
it's, it seems to equilibrate, but,

557
00:32:13,500 --> 00:32:19,033
but you are not able
to, to, to, to capture the oscillations,

558
00:32:19,066 --> 00:32:22,466
at least when we do it
as naively as I did right now.

559
00:32:23,700 --> 00:32:26,266
But, but
still, in comparison to the Bose state

560
00:32:26,266 --> 00:32:29,266
I have shown before, it seems that,
especially when you look at,

561
00:32:30,900 --> 00:32:32,500
look at observables.

562
00:32:32,500 --> 00:32:37,900
So it's, performs
relatively good in comparison

563
00:32:38,066 --> 00:32:40,966
of what you would naively expect from,

564
00:32:40,966 --> 00:32:43,266
from 2% errors per step.

565
00:32:43,266 --> 00:32:46,700
And this is also basically an indication
that when you consider physical systems

566
00:32:46,700 --> 00:32:51,133
also, that they are basically more robust
to errors than you would naively expect.

567
00:32:52,833 --> 00:32:55,800
Now, I showed you

568
00:32:55,800 --> 00:32:58,733
how how valuable
the quantum computers are.

569
00:32:58,733 --> 00:33:01,733
And as you have seen,
you have lots of errors.

570
00:33:01,733 --> 00:33:07,100
So I want to briefly sketch at
the end of my talk how to deal with them.

571
00:33:08,266 --> 00:33:10,866
One thing, and this is

572
00:33:10,866 --> 00:33:13,566
is is basically the path to goal.

573
00:33:13,566 --> 00:33:17,900
And in the long term, then you want to run
more complex algorithms.

574
00:33:17,900 --> 00:33:18,966
That's for example,

575
00:33:18,966 --> 00:33:22,100
Shor's algorithm is that you have to do
phantom error correction.

576
00:33:22,700 --> 00:33:25,700
The idea is basically your,
instead of using,

577
00:33:25,866 --> 00:33:30,766
qubits, your, your encode redundant,
information and basically,

578
00:33:31,366 --> 00:33:35,333
repeat the information of the qubits
in multiple qubits

579
00:33:35,333 --> 00:33:39,700
such, that you can detect
when you have an error incorrect for it.

580
00:33:41,500 --> 00:33:44,100
And this, has, has been done.

581
00:33:44,100 --> 00:33:46,666
Has been, Pope Benedict last time,

582
00:33:46,666 --> 00:33:50,266
but this in order to do this,
you basically,

583
00:33:50,733 --> 00:33:54,700
require quite small error
rates and large number of qubits.

584
00:33:55,333 --> 00:33:58,300
Basically the reason is, when you increase

585
00:33:58,300 --> 00:34:02,100
the number of qubits,
you also increase an error rate.

586
00:34:02,100 --> 00:34:04,800
And so you basically have to balance this.

587
00:34:04,800 --> 00:34:08,000
And, I mean, this
this is an active area of research.

588
00:34:08,000 --> 00:34:11,000
This is for example, a picture of

589
00:34:12,166 --> 00:34:16,933
encoding one qubits
and in terms of roughly,

590
00:34:18,466 --> 00:34:21,466
I think it's for the 50 physical qubits.

591
00:34:21,633 --> 00:34:24,066
And then detecting the errors.

592
00:34:24,066 --> 00:34:28,466
But, the point is,
I think in order to get this work,

593
00:34:28,500 --> 00:34:31,500
you need at least a few more years,

594
00:34:32,733 --> 00:34:36,700
another, promising thing,
which is probably more applicable.

595
00:34:36,933 --> 00:34:41,966
The in this, short term
is, so-called quantum error mitigation.

596
00:34:43,166 --> 00:34:44,100
It's,

597
00:34:44,100 --> 00:34:47,400
as you
will have seen before, for observables,

598
00:34:47,400 --> 00:34:51,500
it seems that we do not need the,
the perfect, quantum computer.

599
00:34:52,700 --> 00:34:55,566
And the idea is that you run experiments

600
00:34:55,566 --> 00:34:58,733
to learn the noise
and then do some interpolation.

601
00:34:59,033 --> 00:35:02,033
This idea is basically quite simple.

602
00:35:02,533 --> 00:35:05,900
And it's also what basically
what you have,

603
00:35:05,900 --> 00:35:08,900
you start with a noise rate one which,

604
00:35:09,200 --> 00:35:12,466
corresponds to the noise you have
from the actual, quantum computer.

605
00:35:12,900 --> 00:35:16,000
And then even, then you know how,

606
00:35:16,200 --> 00:35:21,200
how the errors speed up,
you can basically artificially enhance

607
00:35:21,200 --> 00:35:26,133
your noise rate is done by this, red
dots, red crosses.

608
00:35:26,600 --> 00:35:29,433
And then you can interpolate to zero noise

609
00:35:29,433 --> 00:35:32,433
rate and,

610
00:35:33,500 --> 00:35:35,533
it it's,

611
00:35:35,533 --> 00:35:37,466
looks a bit fishy, but it seems that

612
00:35:37,466 --> 00:35:40,466
it works pretty badly for observables.

613
00:35:40,466 --> 00:35:44,633
And when you want to be competitive
with classical simulations,

614
00:35:44,633 --> 00:35:49,600
and this is the method
which is done to get good results.

615
00:35:49,700 --> 00:35:51,466
Quantum computers already today.

616
00:35:53,900 --> 00:35:56,766
To, to sum up,

617
00:35:56,766 --> 00:35:59,866
well, what I wanted to highlight
is that basically programing

618
00:35:59,866 --> 00:36:03,733
a quantum computer is quite simple,
so everybody can do it.

619
00:36:05,133 --> 00:36:09,300
I mean, this is a kind of trotter step
which is only a few lines of code,

620
00:36:09,300 --> 00:36:13,800
and then you are basically already
at the forefront of research.

621
00:36:16,666 --> 00:36:19,666
The remaining main challenge
you have to do is,

622
00:36:20,466 --> 00:36:24,466
is understanding the error
and is where most efforts are right now.

623
00:36:24,800 --> 00:36:26,100
Thank you for your attention.

624
00:36:26,100 --> 00:36:29,100
And do it yourself.

625
00:36:39,366 --> 00:36:40,800
Okay,

626
00:36:40,800 --> 00:36:44,100
so basically the question
as far as I understand

627
00:36:44,100 --> 00:36:47,166
is a possibility is, better it's

628
00:36:47,200 --> 00:36:51,600
better to think about improving
quantum gates and, how fast you can run.

629
00:36:52,533 --> 00:36:54,433
Yeah. Actually,
that's, that's a good point.

630
00:36:54,433 --> 00:36:58,200
And, I mean, I think that's, that's
the main difference between,

631
00:36:59,400 --> 00:37:02,033
different approaches of quantum computers.

632
00:37:02,033 --> 00:37:06,633
But when you look at the,
the execution times of gates in,

633
00:37:07,066 --> 00:37:11,000
in the case of superconducting qubits,

634
00:37:11,000 --> 00:37:14,000
it's of order one hundreds of nanoseconds.

635
00:37:14,100 --> 00:37:17,100
And when you use trapped ions, it's,

636
00:37:17,433 --> 00:37:20,433
it's basically
three orders of magnitude larger.

637
00:37:20,700 --> 00:37:23,700
And I think one of the,

638
00:37:23,933 --> 00:37:27,333
one of the most important properties,
especially when you have

639
00:37:28,000 --> 00:37:31,200
ions, has
so is finding a, finding approaches

640
00:37:31,200 --> 00:37:34,200
that you can reduce,

641
00:37:34,233 --> 00:37:36,966
the, the execution time of gates.

642
00:37:36,966 --> 00:37:40,833
And this is, this is also
a basically cutting edge of research,

643
00:37:40,833 --> 00:37:43,833
not for the superconducting qubits,
but for other devices.

644
00:37:46,400 --> 00:37:49,400
Okay. The,

645
00:37:49,433 --> 00:37:52,266
basically everyday
you have different like,

646
00:37:52,266 --> 00:37:55,266
language constructs to, to different,

647
00:37:55,666 --> 00:37:58,333
types of quantum computing.

648
00:37:58,333 --> 00:38:01,266
So far as I think

649
00:38:01,266 --> 00:38:05,933
the issue is a little bit the
I mean, the quantum computers are still in

650
00:38:06,166 --> 00:38:10,800
such native stages that,
I think there is so far.

651
00:38:10,833 --> 00:38:14,066
No, no need to think about my infants
cases.

652
00:38:14,066 --> 00:38:17,200
I think it might
be the case. I mean, your,

653
00:38:18,900 --> 00:38:19,933
regard to what

654
00:38:19,933 --> 00:38:23,033
complex algorithms
and how to implement that, for example,

655
00:38:24,100 --> 00:38:26,933
proposals that instead of,

656
00:38:26,933 --> 00:38:29,366
gate operations, you only,

657
00:38:29,366 --> 00:38:31,566
perform measurements.

658
00:38:31,566 --> 00:38:33,866
And and this might be sufficient

659
00:38:33,866 --> 00:38:37,433
to, to, generate
the universal quantum computers.

660
00:38:37,433 --> 00:38:40,566
So in this sense, it is thought about it.

661
00:38:41,700 --> 00:38:45,166
But in principle, it's mostly
that we are only at the single qubit

662
00:38:45,166 --> 00:38:46,100
and two qubit stage.

663
00:38:46,100 --> 00:38:49,300
And so it's a bit early in many cases.

664
00:38:51,900 --> 00:38:53,800
Yeah.

665
00:38:53,800 --> 00:38:57,000
So basically the question is
how does quantum error correction work.

666
00:38:57,000 --> 00:38:57,266
Yeah.

667
00:38:57,266 --> 00:39:00,866
You need physical qubits
to to get the logical qubits.

668
00:39:00,866 --> 00:39:03,866
And then you run in, increasing

669
00:39:05,100 --> 00:39:06,533
required coherence times.

670
00:39:06,533 --> 00:39:07,633
How does it work.

671
00:39:07,633 --> 00:39:08,433
That's a good point.

672
00:39:08,433 --> 00:39:09,466
And that's,

673
00:39:09,466 --> 00:39:10,433
I said the issue of why

674
00:39:10,433 --> 00:39:14,166
we do not have quantum error correction
right now to one point.

675
00:39:15,333 --> 00:39:18,333
The point is that,

676
00:39:18,600 --> 00:39:22,533
the, the way how it works is, when your

677
00:39:23,833 --> 00:39:27,200
have as a sufficient number of qubits,
then,

678
00:39:27,733 --> 00:39:32,400
basically
you can correct a small number of errors.

679
00:39:33,000 --> 00:39:37,200
So, so this helps you,
but at the same time still,

680
00:39:38,533 --> 00:39:42,166
as you mentioned,
you'll have increasing sources of errors.

681
00:39:42,166 --> 00:39:44,533
So you have basically two factors.

682
00:39:44,533 --> 00:39:46,566
What turns out is,

683
00:39:46,566 --> 00:39:51,500
when when your error rate
of physical qubits is, is large, then

684
00:39:51,500 --> 00:39:52,500
you have no chance.

685
00:39:52,500 --> 00:39:55,800
And then trying to do, quantum
error correction,

686
00:39:56,766 --> 00:39:59,200
the Q

687
00:39:59,200 --> 00:40:01,200
however, right now

688
00:40:01,200 --> 00:40:05,000
we are at the stage where basically
quantum error correction of means.

689
00:40:05,000 --> 00:40:09,233
So basically by, by adding security,
by adding qubits,

690
00:40:09,633 --> 00:40:12,966
you, gain as much advantage

691
00:40:13,766 --> 00:40:16,766
that, it basically,

692
00:40:17,766 --> 00:40:21,100
that it basically overtakes
the disadvantage from,

693
00:40:21,966 --> 00:40:27,000
more additional physical cubits
and the as a, as a, concerning

694
00:40:27,000 --> 00:40:32,666
the question how, how many physical qubits
you need to protect, one logical qubit.

695
00:40:33,066 --> 00:40:33,900
So it

696
00:40:35,000 --> 00:40:36,300
basically, if

697
00:40:36,300 --> 00:40:41,500
when you are below this threshold of,
logically a quantum error correction bits,

698
00:40:42,066 --> 00:40:45,533
what you can see
is that, the more physical qubits

699
00:40:45,533 --> 00:40:49,333
you use, the exponentially better, becomes

700
00:40:49,866 --> 00:40:52,466
your, advantage.

701
00:40:52,466 --> 00:40:56,166
And and then it's then it's,
then it's, basically

702
00:40:56,800 --> 00:41:00,366
trying to be as good as possible
with the physical qubits.

703
00:41:00,366 --> 00:41:03,466
And then you
it might be that you need only

704
00:41:03,466 --> 00:41:06,466
a few more,

705
00:41:06,633 --> 00:41:10,466
physical qubits, but it's,
but it's still a work in progress.

706
00:41:10,466 --> 00:41:15,133
In fact, I think the, state of the art
for superconducting qubits

707
00:41:15,133 --> 00:41:18,133
is that you can generate
one logical qubit.

708
00:41:18,900 --> 00:41:19,133
Yeah.

709
00:41:19,133 --> 00:41:20,700
So so the question is,

710
00:41:20,700 --> 00:41:22,766
can you gain the advantage
when instead of,

711
00:41:22,766 --> 00:41:27,066
using qubits with two states,
whether you, can gain advantage with,

712
00:41:27,666 --> 00:41:30,166
three states rights or if more states,

713
00:41:31,766 --> 00:41:33,266
yeah, this

714
00:41:33,266 --> 00:41:37,100
is, is has been explored
and there are some possibilities.

715
00:41:37,100 --> 00:41:40,233
I mean, I think, for,

716
00:41:42,000 --> 00:41:44,100
for most,

717
00:41:44,100 --> 00:41:48,300
long time approaches
when you are sufficiently efficient, it,

718
00:41:48,300 --> 00:41:53,200
it will I mean,
maybe make an difference of a factor.

719
00:41:53,200 --> 00:41:56,200
So, so from a,

720
00:41:56,700 --> 00:41:59,700
teaching and complexity
point of view, it's not change,

721
00:41:59,933 --> 00:42:02,933
but, a is, has been explored.

722
00:42:03,333 --> 00:42:06,966
For example, when you simulate lattice
gauge theory, a bit of it's is,

723
00:42:07,600 --> 00:42:10,433
which is important
to study high energy physics.

724
00:42:10,433 --> 00:42:13,433
So the standard of physics
of the standard models, then,

725
00:42:14,400 --> 00:42:18,500
then especially in, in trapped
ion systems,

726
00:42:20,033 --> 00:42:23,033
it's easy
instead of, controlling two qubits,

727
00:42:24,400 --> 00:42:27,400
to, sorry, two levels,

728
00:42:27,500 --> 00:42:30,500
controlling
multiple levels up to 20 levels.

729
00:42:31,200 --> 00:42:33,533
And it turns out that in this case,

730
00:42:33,533 --> 00:42:38,300
you can gain an advantage
in the length of the, of the circuits.

731
00:42:38,300 --> 00:42:39,933
And and and.

732
00:42:39,933 --> 00:42:42,566
Yeah, and get more efficient computations.

733
00:42:44,333 --> 00:42:46,166
Yeah.

734
00:42:46,166 --> 00:42:46,700
Observation.

735
00:42:46,700 --> 00:42:49,333
So the question is,

736
00:42:49,333 --> 00:42:52,333
but I just quickly pick.

737
00:42:54,666 --> 00:42:57,666
Basically I saw, I saw, results here from.

738
00:42:57,666 --> 00:42:59,233
And what about, time steps.

739
00:42:59,233 --> 00:43:02,233
How does it work
when I, when I, when I measure

740
00:43:02,600 --> 00:43:04,700
the state, I actually destroy it.

741
00:43:04,700 --> 00:43:05,566
And it's a good point.

742
00:43:05,566 --> 00:43:08,733
And, the answer is that I have not run.

743
00:43:08,733 --> 00:43:13,400
You have one experiment, but
30 experiments for each different system

744
00:43:13,400 --> 00:43:16,400
size. So,

745
00:43:17,100 --> 00:43:20,100
so basically, I, I,

746
00:43:20,400 --> 00:43:24,133
in advance,
I state, how many steps do I want,

747
00:43:24,133 --> 00:43:27,133
for example, for, for,

748
00:43:28,033 --> 00:43:30,700
ten steps,
which corresponds to time peak for ten.

749
00:43:30,700 --> 00:43:33,700
And then I run this, this experiment,

750
00:43:34,900 --> 00:43:37,900
in this case,
I run a thousand times to, to,

751
00:43:38,100 --> 00:43:41,100
collect enough statistics
and then to get the measurements.

752
00:43:41,166 --> 00:43:43,366
Of course,
I mean, you get the massive overhead,

753
00:43:44,933 --> 00:43:46,566
but but it's doable.

754
00:43:46,566 --> 00:43:49,566
So in principle, for one two steps,

755
00:43:49,833 --> 00:43:53,733
sorry, for one time
step to, generate a thousand measurements.

756
00:43:53,766 --> 00:43:56,366
It took me,

757
00:43:56,366 --> 00:43:58,100
10s on a quantum computer.

758
00:43:58,100 --> 00:44:02,500
So I think the overall plot on the right
is a matter of five minutes or something.

759
00:44:03,233 --> 00:44:03,966
Yes, exactly.

760
00:44:03,966 --> 00:44:06,500
So I think that this cube.

761
00:44:06,500 --> 00:44:09,300
Yeah, that's, and this,

762
00:44:09,300 --> 00:44:10,600
qubit does not work.

763
00:44:10,600 --> 00:44:13,600
And, actually, even when you're look,

764
00:44:14,133 --> 00:44:18,400
at, at, this IBM, quantum website, you,

765
00:44:18,666 --> 00:44:22,766
you can have access, to,
to the performance of this, qubits.

766
00:44:22,766 --> 00:44:25,766
And the what you see is that, sometimes,

767
00:44:26,633 --> 00:44:31,066
they are some calibrations
and not all of this connections, perfect.

768
00:44:31,233 --> 00:44:34,233
This is what, what happened here?

769
00:44:34,866 --> 00:44:35,700
Yeah. Yeah.

770
00:44:35,700 --> 00:44:39,100
So I think the the point is,
I mean, yeah, it does not work for,

771
00:44:40,166 --> 00:44:42,366
extra classical encryption.

772
00:44:42,366 --> 00:44:46,466
Like, you could,
you can break the as a encryption.

773
00:44:46,900 --> 00:44:49,900
But the reason why
they use it right now is,

774
00:44:50,700 --> 00:44:53,700
it's because it's a relatively cheap
to implement.

775
00:44:54,600 --> 00:44:58,366
Yeah, but but this current research
of quantum cryptography,

776
00:44:58,633 --> 00:45:01,900
which you cannot break
with quantum computers and would be,

777
00:45:03,033 --> 00:45:06,033
secure because of the physical laws
of quantum mechanics.

778
00:45:06,633 --> 00:45:09,766
I mean, nevertheless,
I mean, probably for most cases,

779
00:45:09,766 --> 00:45:13,166
it's too expensive,
and it's like quantum computers.

780
00:45:14,900 --> 00:45:16,766
They might be useful in this field

781
00:45:16,766 --> 00:45:19,766
long time, but, but then you have,

782
00:45:20,466 --> 00:45:22,066
very sensitive information.

783
00:45:22,066 --> 00:45:24,700
You will use a different encryption.

784
00:45:24,700 --> 00:45:26,133
I'll do a certain.

785
00:45:26,133 --> 00:45:29,033
No, I think not. Mine has one.

786
00:45:29,033 --> 00:45:33,700
But I think it's it's,
I think it's a reasonable concern.

787
00:45:33,700 --> 00:45:36,966
And, it's also a
when you look at the research

788
00:45:36,966 --> 00:45:40,733
that it's for example, of classified
and in the US.

789
00:45:40,866 --> 00:45:41,700
So, when you,

790
00:45:42,666 --> 00:45:44,166
when you travel to China and

791
00:45:44,166 --> 00:45:47,166
you are quantum research,
they are very interested in you.

792
00:45:50,700 --> 00:45:51,066
Okay.

793
00:45:51,066 --> 00:45:54,100
I think the question is basically
what is more important

794
00:45:54,100 --> 00:45:57,100
is that understanding,

795
00:45:57,166 --> 00:46:00,533
errors and,
and try to cure them is basically,

796
00:46:01,133 --> 00:46:04,500
getting larger and better quantum
computers, but it's just more important.

797
00:46:06,200 --> 00:46:09,200
The point is, when you're,

798
00:46:09,400 --> 00:46:11,800
when you consider, this error

799
00:46:11,800 --> 00:46:15,100
mitigation techniques I mentioned before,
I think they hope for.

800
00:46:17,400 --> 00:46:19,800
For some cases as observables.

801
00:46:19,800 --> 00:46:24,866
But I think they
they ultimately break down at some point.

802
00:46:24,866 --> 00:46:28,733
And you can it can also show that they,
they will not given any cases.

803
00:46:29,100 --> 00:46:33,033
So I think in the long term run you'll
always need quantum error correction.

804
00:46:33,033 --> 00:46:36,133
And but the quantum computers but

805
00:46:36,466 --> 00:46:39,466
nevertheless when you look at,

806
00:46:39,700 --> 00:46:41,633
amid near-future a

807
00:46:41,633 --> 00:46:45,466
so what what would happen is that you
basically you have an interplay of,

808
00:46:46,366 --> 00:46:50,066
two approaches that error mitigation
that I hope you to be a little bit better

809
00:46:51,033 --> 00:46:53,300
and then you can ever get,

810
00:46:53,300 --> 00:46:56,366
fast improvement
with quantum error correction once is you.

811
00:46:58,500 --> 00:47:00,566
Okay, that's a good question.

812
00:47:00,566 --> 00:47:03,266
The question is basically,

813
00:47:03,266 --> 00:47:07,100
but, I, as a program, responsible
for quantum error correction.

814
00:47:07,200 --> 00:47:10,633
It's done in the compiler
or on a hardware level, I think.

815
00:47:11,400 --> 00:47:14,166
I mean, that's already shown here

816
00:47:14,166 --> 00:47:17,166
a little bit.

817
00:47:18,300 --> 00:47:19,900
But what happens this time

818
00:47:19,900 --> 00:47:22,900
instead of any of the of any of any

819
00:47:23,433 --> 00:47:26,433
if any progress in quantum
computer evolves, is that,

820
00:47:28,366 --> 00:47:32,733
basically one was getting a black box,
I mean, already here, I mean, you see that

821
00:47:32,766 --> 00:47:37,533
a basically creates a poly evolution gate
by calling it, another comment.

822
00:47:38,700 --> 00:47:41,733
So 2 or 3 years ago,
I took coded up a cipher

823
00:47:41,733 --> 00:47:44,733
and it was a bit more complex.

824
00:47:44,966 --> 00:47:47,166
But I think I saw with this, quantum

825
00:47:47,166 --> 00:47:51,100
error correction is basically you, go down

826
00:47:51,100 --> 00:47:55,500
either to the compiler
or is lower to the hardware level.

827
00:47:55,933 --> 00:47:57,533
And what,
whatever. I did not know exactly.

828
00:48:01,500 --> 00:48:02,033
All right.

829
00:48:02,033 --> 00:48:04,800
It looks like it's one of those questions.
So let's think of it again.