diff --git a/QElephant/Matrix.py b/QElephant/Matrix.py
index 3c82d57..68c5730 100644
--- a/QElephant/Matrix.py
+++ b/QElephant/Matrix.py
@@ -64,6 +64,13 @@ class Matrix:
             [0, 1],
             [1, 0]
         ])
+    
+    @staticmethod
+    def SQRTX() -> "Matrix":
+        return Matrix([
+            [(1+I)/2, (1-I)/2],
+            [(1-I)/2, (1+I)/2]
+        ])
 
     @staticmethod
     def Y() -> "Matrix":
@@ -141,7 +148,7 @@ class Matrix:
         ])
 
     @staticmethod
-    def CNOT() -> "Matrix":
+    def CX() -> "Matrix":
         return Matrix([
             [1, 0, 0, 0],
             [0, 1, 0, 0],
@@ -149,6 +156,24 @@ class Matrix:
             [0, 0, 1, 0]
         ])
     
+    @staticmethod
+    def CY() -> "Matrix":
+        return Matrix([
+            [1, 0, 0, 0],
+            [0, 1, 0, 0],
+            [0, 0, 0, -I],
+            [0, 0, I, 0]
+        ])
+    
+    @staticmethod
+    def CZ() -> "Matrix":
+        return Matrix([
+            [1, 0, 0, 0],
+            [0, 1, 0, 0],
+            [0, 0, 1, 0],
+            [0, 0, 0, -1]
+        ])
+    
     @staticmethod
     def SWAP() -> "Matrix":
         return Matrix([
diff --git a/QElephant/QuBit.py b/QElephant/QuBit.py
index 58cac2a..9bea0e6 100644
--- a/QElephant/QuBit.py
+++ b/QElephant/QuBit.py
@@ -256,7 +256,7 @@ class IQuBit(QuBit):
         if type(matrix) is not Matrix:
             raise TypeError(f"can only manipulate QuBit with Matrix, not {type(matrix)}")
 
-        self.__muBit._MuBit__apply(self.__n, matrix)
+        self.__muBit._MuBit__apply(matrix, self.__n)
     
     def observe(self) -> int:
         r = rd.random()
@@ -288,6 +288,14 @@ def X(q: QuBit) -> None:
     else:
         raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
+def SQRTX(q: QuBit) -> None:
+    if type(q) == IQuBit:
+        q._IQuBit__apply(Matrix.SQRTX())
+    elif type(q) == QuBit:
+        q._QuBit__apply(Matrix.SQRTX())
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
+
 def Y(q: QuBit) -> None:
     if type(q) == IQuBit:
         q._IQuBit__apply(Matrix.Y())
@@ -364,7 +372,7 @@ def R1(q: QuBit, phi: float) -> None:
     else:
         raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
-def CNOT(q: MuBit, n1: int, n2: int) -> None:
+def CX(q: MuBit, n1: int, n2: int) -> None:
     if type(q) is not MuBit:
         TypeError(f"a MuBit was expected, but a {type(q)} was given")
     if type(n1) is not int:
@@ -380,7 +388,47 @@ def CNOT(q: MuBit, n1: int, n2: int) -> None:
 
     SWAP(q, 0, n1)
     SWAP(q, 1, n2)
-    q._MuBit__mapply(Matrix.CNOT(), 0)
+    q._MuBit__mapply(Matrix.CX(), 0)
+    SWAP(q, 0, n1)
+    SWAP(q, 1, n2)
+
+def CY(q: MuBit, n1: int, n2: int) -> None:
+    if type(q) is not MuBit:
+        TypeError(f"a MuBit was expected, but a {type(q)} was given")
+    if type(n1) is not int:
+        TypeError(f"MuBit indices must be intergers, not {type(n1)}")
+    if type(n2) is not int:
+        TypeError(f"MuBit indices must be intergers, not {type(n2)}")
+    if n1 > q._MuBit__n or n2 > q._MuBit__n:
+        ValueError("Mubit index out of range")
+    n1 = n1%q._MuBit__n
+    n2 = n2%q._MuBit__n
+    if n1==n2:
+        ValueError("the CNOT gate must be applied on two differents QuBits")
+
+    SWAP(q, 0, n1)
+    SWAP(q, 1, n2)
+    q._MuBit__mapply(Matrix.CY(), 0)
+    SWAP(q, 0, n1)
+    SWAP(q, 1, n2)
+
+def CZ(q: MuBit, n1: int, n2: int) -> None:
+    if type(q) is not MuBit:
+        TypeError(f"a MuBit was expected, but a {type(q)} was given")
+    if type(n1) is not int:
+        TypeError(f"MuBit indices must be intergers, not {type(n1)}")
+    if type(n2) is not int:
+        TypeError(f"MuBit indices must be intergers, not {type(n2)}")
+    if n1 > q._MuBit__n or n2 > q._MuBit__n:
+        ValueError("Mubit index out of range")
+    n1 = n1%q._MuBit__n
+    n2 = n2%q._MuBit__n
+    if n1==n2:
+        ValueError("the CNOT gate must be applied on two differents QuBits")
+
+    SWAP(q, 0, n1)
+    SWAP(q, 1, n2)
+    q._MuBit__mapply(Matrix.CZ(), 0)
     SWAP(q, 0, n1)
     SWAP(q, 1, n2)
 
diff --git a/docs/Gate.md b/docs/Gate.md
index 1b6d363..5ecddf3 100644
--- a/docs/Gate.md
+++ b/docs/Gate.md
@@ -28,6 +28,19 @@ Here is the list of all the main gates in quantum algorithm available in the lib
 \end{pmatrix}
 ```
 
+## SQRTX(q: QuBit) -> None
+`Square-Root of X`. Inplementes the square root of the X-gate.
+
+- q: the qubit manipulated by the gate. This function is in-place.
+
+- matrix:
+```math
+\begin{pmatrix}
+\frac {1+i} {2} & \frac {1-i} {2}\\
+\frac {1-i} {2} & \frac {1+i} {2}
+\end{pmatrix}
+```
+
 ## Y(q: QuBit) -> None
 `Pauli-Y gate`. Inplementes a rotation aroud the y-axis of $\pi$ radians.
 
@@ -119,7 +132,7 @@ e^{-i\frac\phi2} & 0\\
 \end{pmatrix}
 ```
 
-## CNOT(q: MuBit, n1: int, n2: int) -> None
+## CX(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.
 
 - q: the qubit manipulated by the gate. This function is in-place.
@@ -136,6 +149,40 @@ e^{-i\frac\phi2} & 0\\
 \end{pmatrix}
 ```
 
+## CY(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.
+
+- q: the qubit manipulated by the gate. This function is in-place.
+- n1: the first QuBit to manipualte.
+- n2: the second QuBit to manipulate
+
+- matrix:
+```math
+\begin{pmatrix}
+1 & 0 & 0 & 0\\
+0 & 1 & 0 & 0\\
+0 & 0 & 0 & -i\\
+0 & 0 & i & 0
+\end{pmatrix}
+```
+
+## CZ(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.
+
+- q: the qubit manipulated by the gate. This function is in-place.
+- n1: the first QuBit to manipualte.
+- n2: the second QuBit to manipulate
+
+- matrix:
+```math
+\begin{pmatrix}
+1 & 0 & 0 & 0\\
+0 & 1 & 0 & 0\\
+0 & 0 & 1 & 0\\
+0 & 0 & 0 & -1
+\end{pmatrix}
+```
+
 ## SWAP(q: MuBit, n1: int, n2: int) -> None
 `NOT gate`. Invert the state |0> and |1> of the QuiBit q.
 
diff --git a/docs/Matrix.md b/docs/Matrix.md
index 03a1d5d..51863e6 100644
--- a/docs/Matrix.md
+++ b/docs/Matrix.md
@@ -68,6 +68,17 @@ Matrix(l: list[list[complexe]])
 \end{pmatrix}
 ```
 
+- ```SQRTX() -> Matrix```
+
+  returns the matrix
+
+```math
+\begin{pmatrix}
+\frac {1+i} {2} & \frac {1-i} {2}\\
+\frac {1-i} {2} & \frac {1+i} {2}
+\end{pmatrix}
+```
+
 - ```Y() -> Matrix```
 
   returns the matrix
@@ -156,7 +167,7 @@ e^{-i\frac \phi 2} & 0\\
 \end{pmatrix}
 ```
 
-- ```CNOT() -> Matrix```
+- ```CX() -> Matrix```
 
   returns the matrix
 
@@ -169,6 +180,32 @@ e^{-i\frac \phi 2} & 0\\
 \end{pmatrix}
 ```
 
+- ```CY() -> Matrix```
+
+  returns the matrix
+
+```math
+\begin{pmatrix}
+1 & 0 & 0 & 0\\
+0 & 1 & 0 & 0\\
+0 & 0 & 0 & -i\\
+0 & 0 & i & 0
+\end{pmatrix}
+```
+
+- ```CZ() -> Matrix```
+
+  returns the matrix
+
+```math
+\begin{pmatrix}
+1 & 0 & 0 & 0\\
+0 & 1 & 0 & 0\\
+0 & 0 & 1 & 0\\
+0 & 0 & 0 & -1
+\end{pmatrix}
+```
+
 - ```SWAP() -> Matrix```
 
   returns the matrix