U1L3p.txt

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So we've done qubits.

And you know pretty much how to find single gates on qubits.
But of course, applying single gates
on qubits in a quantum circuit, you know,
you start with K qubits.

This qubit never talks to this qubit.
It really doesn't help very much.
To actually get any kind of quantum computation,
you need to do some gate that links two of these qubits
so that they talk to each other.
So what is a state space?

State space of two qubits.

Well, I mean, if you have two polarizations of a photon
and you want them to be distinguishable,
you're going to have to distinguish them somehow.
And one way of doing that is making sure
they're distinguishable in at least one of the photons.
So you have two photons here.
This is vertical-vertical, vertical-horizontal,
horizontal-vertical, horizontal-horizontal.

So this is four dimensional state space.
So does anybody know what the size of the state space
is for n photons?
Yeah?
2 to the n, yeah.
And this is called a tensor product.

So next time, I'm going to start poking about gates
on two qubits where they can talk
to each other and tensor product spaces.
And on the day--
I guess a week from now, I will start
talking about what the measurement is in quantum
computation, because--
so this lets you-- you know, so unitary operations let
you change the state of a system,
but if you're doing-- if you have a quantum computer,
you need to get the information out somehow.
So how do you do that?
Well, you need to measure it.
And measuring it isn't the same as writing down its state,
because if you've heard of the Heisenberg uncertainty
principle, you cannot measure the complete state of a quantum
particle.
You can't measure the position and the momentum
at the same time, and the same thing
is going to be true for qubits.
You cannot measure the complete state of n qubits.
You can just measure some properties of it.