---
# System prepended metadata

title: Quantum Gate

---

# Quantum Gate
- Top=|0> Bottom=|1>
- +1 of X axis represents |+>, -1 represents |->
- Hermitian: 共軛
- Phi: 大寫Φ，小寫φ


|gate|matrix|phase operator|bit-flip operator|Operation|
|-|-|-|-|-|
|pauli X|![](https://i.imgur.com/ZlmxpSk.png)|X|O|![](https://i.imgur.com/3gyEkm4.gif)|
|pauli Y|![](https://i.imgur.com/SXhdrOz.png)|O|O|![](https://i.imgur.com/DqNSsgf.gif)|
|pauli Z|![](https://i.imgur.com/t4sah7p.png)|O|X|![](https://i.imgur.com/4eWlKY3.gif)
|
|Hadamard (H) |![](https://i.imgur.com/5Abm2cN.png)|O|N/A|![](https://i.imgur.com/z8QQQtO.gif)|

![](https://i.imgur.com/7SOXLdz.png)
## Rotation on the bloch sphere
![](https://i.imgur.com/uU8zaP8.png)

## Quantum Universality
>[color=#00F964] Any Quantum computation operation can be made by using a combination of: **{CNOT, H, S, T}** , which are made of Rotation

## cnot
![](https://i.imgur.com/sVrQKct.png)

## Bell state
![](https://i.imgur.com/Z3LnN8v.png)




$T^4=S^2=Z$
