49 lines
1.4 KiB
Markdown
49 lines
1.4 KiB
Markdown
Now we look at circuits constructed with what we looked at.
|
|
These systems will consist of qubits $\in \mathbb{C}^2$ .
|
|
|
|
A very simple example for a quantum circuit, now using pictures instead of formulas:
|
|
|
|
![[Pasted image 20260730091827.png]]
|
|
|
|
Here we have two wires 0 and +.
|
|
First we apply the unitaries X and H to the wires, written as $X \otimes H$.
|
|
Then we apply the unitary U to both qubits (wires) .
|
|
Finally we apply H to the second wire again, because we don't do anything
|
|
with the top wire, we apply the identity to it so $I \otimes H$
|
|
Last but not least we measure the top wire.
|
|
|
|
|
|
## Important gates
|
|
|
|
We distinguish between gates on single qubits and gates on multiple qubits.
|
|
We will introduce some of the more important ones:
|
|
|
|
### Single qubit gates
|
|
|
|
![[Pasted image 20260730092306.png]]
|
|
The Identity matrix to not change a qubit.
|
|
|
|
![[Pasted image 20260730092336.png]]
|
|
Pauli matrices. X is also called Bit-flip.
|
|
|
|
![[Pasted image 20260730092409.png]]
|
|
The Hadamard-gate transforms a classical bit $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ and transforms it into a
|
|
superposition $\begin{pmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}$
|
|
|
|
|
|
### The CNOT Gate
|
|
The controlled-NOT gate operates on two qubits.:
|
|
|
|
![[Pasted image 20260730092639.png]]
|
|
![[Pasted image 20260730092648.png]]
|
|
|
|
|
|
|
|
## Teleportation
|
|
An Example quantum circuit:
|
|
|
|
![[Pasted image 20260730092802.png]]
|
|
![[Pasted image 20260730092809.png]]
|
|
![[Pasted image 20260730092817.png]]
|
|
|