Fixe matrices

docs/Gate.md

@@ -7,90 +7,117 @@ Here is the list of all the main gates in quantum algorithm available in the lib
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 \frac {1} {\sqrt 2} & \frac {1} {\sqrt 2}\\
 \frac {1} {\sqrt 2} & -\frac {1} {\sqrt 2}
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## X(q: QuBit) -> None
 `Pauli-X gate` or `NOT gate`. Inplementes a rotation aroud the x-axis of $\pi$ radians.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 0 & 1\\
 1 & 0
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## Y(q: QuBit) -> None
 `Pauli-Y gate`. Inplementes a rotation aroud the y-axis of $\pi$ radians.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 0 & -i\\
 i & 0
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## Z(q: QuBit) -> None
 `Pauli-Z gate`. Inplementes a rotation aroud z-axis of $\pi$ radians.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0\\
 0 & -1
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## S(q: QuBit) -> None
 `NOT gate`. Invert the state |0> and |1> of the QuiBit q.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0\\
 0 & i
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## T(q: QuBit) -> None
 `NOT gate`. Invert the state |0> and |1> of the QuiBit q.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0\\
 0 & e^{i\frac\pi4}
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## Rx(q: QuBit, phi: float) -> None
 `NOT gate`. Inplementes a rotation aroud x-axis of $\phi$ radians.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 \cos(\frac\phi2) & -\sin(\frac\phi2)\\
 \sin(\frac\phi2) & \cos(\frac\phi2)
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## Ry(q: QuBit, phi: float) -> None
 `NOT gate`. Inplementes a rotation aroud y-axis of $\pi$ radians.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 e^{-i\frac\phi2} & 0\\
 0 & e^{i\frac\phi2}
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## R1(q: QuBit, phi: float) -> None
 `NOT gate`. Invert the state |0> and |1> of the QuiBit q.
 
 - q: the qubit manipulated by the gate. This function is in-place.
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0\\
 0 & e^{i\frac\phi2}
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## CNOT(q: MuBit, n1: int, n2: int) -> None
 `X-controlled gate`. Invert the state |0> and |1> of the QuiBit in n2 if the state of the QuBit in n1 is 1.
@@ -99,12 +126,15 @@ e^{-i\frac\phi2} & 0\\
 - n1: the first QuBit to manipualte.
 - n2: the second QuBit to manipulate
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0 & 0 & 0\\
 0 & 1 & 0 & 0\\
 0 & 0 & 0 & 1\\
 0 & 0 & 1 & 0
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## SWAP(q: MuBit, n1: int, n2: int) -> None
 `NOT gate`. Invert the state |0> and |1> of the QuiBit q.
@@ -113,12 +143,15 @@ e^{-i\frac\phi2} & 0\\
 - n1: the first QuBit to manipualte.
 - n2: the second QuBit to manipulate
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0 & 0 & 0\\
 0 & 0 & 1 & 0\\
 0 & 1 & 0 & 0\\
 0 & 0 & 0 & 1
-\end{pmatrix}$
+\end{pmatrix}
+```
 
 ## Cu(q: MuBit, u: list[list[float]], n1: int, n2: int) -> None
 `controlled-u gate`. Applies the gate u to the QuBit in n2 if the Qubit in n1 is 1.
@@ -128,9 +161,12 @@ e^{-i\frac\phi2} & 0\\
 - n1: the first QuBit to manipualte.
 - n2: the second QuBit to manipulate
 
-- matrix: $\begin{pmatrix}
+- matrix:
+```math
+\begin{pmatrix}
 1 & 0 & 0 & 0\\
 0 & 1 & 0 & 0\\
 0 & 0 & u_{00} & u_{01}\\
 0 & 0 & u_{10} & u_{11}
-\end{pmatrix}$
+\end{pmatrix}
+```