QElephant/docs/QuBit/QuBit.md
2023-10-22 18:38:55 +02:00

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## QuBit
QuBit(alpha: complexe, beta: complexe)
- alpha: complexe value for |0>
- beta: complexe value for |1>
### Attributes
- ```__state: list[complexe]```
list of the values for the state |0> and |1>
- ```__intricated: bool```
tells if the qubit is intricated or not
### Methode
- ```__init__(alpha: complexe=1, beta: complexe=0) -> None```
initiates the qubit
- ```is_intricated() -> bool```
returns the value of __intricated
- ```get_MuBit() -> None```
returns the MuBit in wich the QuBit is intricated. If not intricated, rerurns None
- ```__str__() -> str```
returns a string representation of the list of __state
- ```__apply(m: Matrix) -> None```
takes a Matrix and modifies the QuBit according the matrix
- ```observe() -> list[int]```
forces the QuBit in a state, where the probabilities are given throught __state. Returns the new __state obtained.
### Staticmethods
- ```I() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0\\
0 & 1
\end{pmatrix}
```
- ```H() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
\frac {1} {\sqrt 2} & \frac {1} {\sqrt 2}\\
\frac {1} {\sqrt 2} & -\frac{1} {\sqrt 2}
\end{pmatrix}
```
- ```X() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
0 & 1\\
1 & 0
\end{pmatrix}
```
- ```Y() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
0 & -i\\
i & 0
\end{pmatrix}
```
- ```Z() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0\\
0 & -1
\end{pmatrix}
```
- ```S() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0\\
0 & i
\end{pmatrix}
```
- ```T() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0\\
0 & e^{i\frac {\pi} {4}}
\end{pmatrix}
```
- ```Rx(phi: float) -> Matrix```
returns the matrix
```math
\begin{pmatrix}
\cos(\frac \phi 2) & -i\sin(\frac \phi 2)\\
-i\sin(\frac \phi 2) & \cos(\frac \phi 2)
\end{pmatrix}
```
- ```Ry(phi: float) -> Matrix```
returns the matrix
```math
\begin{pmatrix}
\cos(\frac \phi 2) & -\sin(\frac \phi 2)\\
\sin(\frac \phi 2) & \cos(\frac \phi 2)
\end{pmatrix}
```
- ```Rz(phi: float) -> Matrix```
returns the matrix
```math
\begin{pmatrix}
e^{-i\frac \phi 2} & 0\\
0 & e^{i\frac \phi 2}
\end{pmatrix}
```
- ```R1(phi: float) -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & p\\
0 & e^{i\phi}
\end{pmatrix}
```
- ```CNOT() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 0 & 1\\
0 & 0 & 1 & 0
\end{pmatrix}
```
- ```SWAP() -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 0 & 1 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 0 & 0
\end{pmatrix}
```
- ```Cu(u: Matrix) -> Matrix```
returns the matrix
```math
\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & u_{00} & u_{01}\\
0 & 0 & u_{10} & u_{11}
\end{pmatrix}
```