OK.

Sorry for the slight delay at the start.

So in today's lecture, I want to continue

the discussion of things that can be

done on so-called NISC hardware.

So in the last lecture, I gave a brief overview

of what so-called NISC hardware can do.

So NISC being an acronym for Noisy Intermediate Scale Quantum

Computers, which is the level of hardware

development that is available at the moment.

And these have sizes of 50 to 100 qubits

and can do up to 40 layers of gates.

And as a main application of those

are so-called variational quantum algorithms.

And one task in this field, which I discussed last time,

is to approximate the ground state of a Hamiltonian.

So basically, the idea is that one generates a quantum state

that depends on a set of parameters, theta 1 to theta

m, via a sequence of gates that depend on these parameters,

starting from, for example, the natural starting state

where all qubits are in their zero state.

And by an iterative procedure, you

want to find the minimum over all the possible values

of these variational parameters of the expectation

value of that Hamiltonian.

And the way this is done, so if I, for example,

consider four qubits, and then so there

is a sequence of gates that depend on parameters

that is applied to these.

Say, for example, in the first layer, I took two qubit gates.

Then there might be a layer of single qubit gates, and so on.

And then at the end of this gate sequence,

all these qubits are measured, and the result

of this measurement is a specific bit string.

So some 0 and 1 sequence.

This result is fed into a classical computer.

So let me sketch.

So there's a classical computer, keyboard, screen.

And whatever you do in an optimization algorithm

on this classical computer spits out

a new proposal for the string of parameters, which then

are fed back to the quantum computer

to execute again the sequence of gate,

but now with a new set of parameters.

Maybe let me call this prime here.

So it's a classical quantum hybrid algorithm,

where this state is always generated on the quantum chip

and then measured, resulting in this bit string.

And from that information, you get a new set of parameters.

And so if this is a good ansatz and the optimization routine