diff --git a/QElephant/QuBit.py b/QElephant/QuBit.py
index 0e4748a..4b0d769 100644
--- a/QElephant/QuBit.py
+++ b/QElephant/QuBit.py
@@ -9,6 +9,11 @@ I = complex(0, 1)
 
 class MuBit:
     def __init__(self, n: int=2) -> None:
+        if type(n) is not int:
+            raise TypeError(f"number of state must be an intergers, not {type(n)}")
+        if not n >= 2:
+            raise ValueError("a MuBit must have at least two intricated QuBit")
+
         self.__n = n
         self.__state: list[complex] = [0]*(2**self.__n)
         self.__state[0] = 1
@@ -34,8 +39,14 @@ class MuBit:
     
     def __set(self, i: int, value: int) -> None:
         """Set the nth QuBit into value"""
-        assert(value in {0, 1})
+        if type(i) is not int:
+            raise TypeError(f"MuBit indices must be integers, not {type(i)}")
+        if i > self.__n:
+            raise IndexError("MuBit index out of range")
+        if not value in {0, 1}:
+            raise ValueError(f"QuBit state must be 0 or 1, not {value}")
 
+        i = i%self.__n
         M = Matrix([[1]])
         for j in range(self.__n):
             if j == i:
@@ -50,12 +61,26 @@ class MuBit:
         return iter([IQuBit(i, self) for i in range(self.__n)])
     
     def __getitem__(self, item: int) -> "QuBit":
+        if type(item) is not int:
+            raise TypeError(f"MuBit indices must be integers, not {type(item)}")
+        if item > self.__n:
+            raise IndexError("MuBit index out of range")
+
+        item = item%self.__n
         return IQuBit(item, self)
 
     def __apply(self, i: int, matrix: Matrix) -> None:
+        if type(i) is not int:
+            raise TypeError(f"MuBit indices must be integers, not {type(i)}")
+        if i > self.__n:
+            raise IndexError("MuBit index out of range")
+        if type(matrix) is not Matrix:
+            raise TypeError(f"can only manipulate MuBit with Matrix, not {type(matrix)}")
+        i = i%self.__n
+
         M = Matrix([[1]])
 
-        for j in range(self.n):
+        for j in range(self.__n):
             if j == i:
                 M *= matrix
             else:
@@ -64,6 +89,14 @@ class MuBit:
         self.__state = M._Matrix__apply(self.__state)
     
     def __mapply(self, matrix: Matrix, i: int) -> None:
+        if type(i) is not int:
+            raise TypeError(f"MuBit indices must be integers, not {type(i)}")
+        if i > self.__n:
+            raise IndexError("MuBit index out of range")
+        if type(matrix) is not Matrix:
+            raise TypeError(f"can only manipulate MuBit with Matrix, not {type(matrix)}")
+        i = i%self.__n
+
         M = Matrix([[1]])
         j = 0
         while j < self.__n:
@@ -77,6 +110,12 @@ class MuBit:
     
     def __getProb(self, i: int) -> float:
         """Probs for i to be zero"""
+        if type(i) is not int:
+            raise TypeError(f"MuBit indices must be integers, not {type(i)}")
+        if i > self.__n:
+            raise IndexError("MuBit index out of range")
+        i = i%self.__n
+
         M = Matrix([[1]])
 
         for j in range(self.__n):
@@ -94,10 +133,33 @@ class MuBit:
             l.append(IQuBit(i, self).observe())
         return l
     
+    @staticmethod
+    def intricateThem(*args: "QuBit") -> "MuBit":
+        for q in args:
+            if type(q) is IQuBit:
+                raise TypeError("cannot intricate QuBit that are already intricated")
+            if type(q) is not QuBit:
+                raise TypeError(f"cannot intricate QuBit and {type(q)}")
+        if len(args) < 2:
+            raise ValueError("cannot intricate less than two QuBits")
+
+        S = Matrix([[1]])
+        for q in args:
+            S *= Matrix([q._QuBit__state])
+
+        mq = MuBit(len(args))
+        mq._MuBit__state = S._Matrix__m[0]
+        return mq
+    
 class QuBit:
     def __init__(self, alpha: complex=1, beta: complex=0):
+        if type(alpha) not in {int, float, complex}:
+            TypeError(f"QuBit state must be int, float or complex, not {type(alpha)}")
+        if type(beta) not in {int, float, complex}:
+            TypeError(f"QuBit state must be int, float or complex, not {type(alpha)}")
         if abs(alpha)**2 + abs(beta)**2 != 1:
-            raise Exception("The initial state must be normalized")
+            raise ValueError(f"the initial state must be normalized. Here, |alpha|**2+|beta|**2={abs(alpha)**2 + abs(beta)**2}")
+        
         self.__state = [alpha, beta]
         self.__intricated = False
     
@@ -111,6 +173,9 @@ class QuBit:
         return f"{round(self.__state[0], 3)} |0> + {round(self.__state[1], 3)} |1>"
     
     def __apply(self, matrix: Matrix) -> None:
+        if type(matrix) is not Matrix:
+            raise TypeError(f"can only manipulate QuBit with Matrix, not {type(matrix)}")
+
         self.__state = matrix._Matrix__apply(self.__state)
     
     def observe(self) -> list[int]:
@@ -123,6 +188,14 @@ class QuBit:
 
 class IQuBit(QuBit):
     def __init__(self, n: int, mb: MuBit) -> None:
+        if type(n) is not int:
+            raise TypeError(f"MuBit indices must be interger, not {type(n)}")
+        if n > mb._MuBit__n:
+            raise ValueError(f"MuBit index out of range")
+        if type(mb) is not MuBit:
+            TypeError(f"an intricate QuBit should be associated with a MuBit, not a {type(mb)}")
+        n = n%mb._MuBit__n
+
         super().__init__()
         self.__n = n
         self.__muBit = mb
@@ -139,6 +212,9 @@ class IQuBit(QuBit):
         return str(QuBit(math.sqrt(p), math.sqrt(1-p)))
     
     def __apply(self, matrix: Matrix) -> None:
+        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)
     
     def observe(self) -> int:
@@ -160,62 +236,98 @@ def H(q: QuBit) -> None:
         q._IQuBit__apply(Matrix.H())
     elif type(q) == QuBit:
         q._QuBit__apply(Matrix.H())
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def X(q: QuBit) -> None:
     if type(q) == IQuBit:
         q._IQuBit__apply(Matrix.X())
     elif type(q) == QuBit:
         q._QuBit__apply(Matrix.X())
+    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())
     elif type(q) == QuBit:
         q._QuBit__apply(Matrix.Y())
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def Z(q: QuBit) -> None:
     if type(q) == IQuBit:
         q._IQuBit__apply(Matrix.Z())
     elif type(q) == QuBit:
         q._QuBit__apply(Matrix.Z())
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def S(q: QuBit) -> None:
     if type(q) == IQuBit:
         q._IQuBit__apply(Matrix.S())
     elif type(q) == QuBit:
         q._QuBit__apply(Matrix.S())
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def T(q: QuBit) -> None:
     if type(q) == IQuBit:
         q._IQuBit__apply(Matrix.T())
     elif type(q) == QuBit:
         q._QuBit__apply(Matrix.T())
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def Rx(q: QuBit, phi: float) -> None:
+    if type(phi) not in {int, float}:
+        TypeError(f"an angle must be integer or float, not {type(phi)}")
+
     if type(q) == QuBit:
         q._QuBit__apply(Matrix.Rx(phi))
     elif type(q) == IQuBit:
         q._IQuBit__apply(Matrix.Rx(phi))
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def Ry(q: QuBit, phi: float) -> None:
+    if type(phi) not in {int, float}:
+        TypeError(f"an angle must be integer or float, not {type(phi)}")
+
     if type(q) == QuBit:
         q._QuBit__apply(Matrix.Ry(phi))
     elif type(q) == IQuBit:
         q._IQuBit__apply(Matrix.Ry(phi))
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def Rz(q: QuBit, phi: float) -> None:
+    if type(phi) not in {int, float}:
+        TypeError(f"an angle must be integer or float, not {type(phi)}")
+
     if type(q) == QuBit:
         q._QuBit__apply(Matrix.Rz(phi))
     elif type(q) == IQuBit:
         q._IQuBit__apply(Matrix.Rz(phi))
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def R1(q: QuBit, phi: float) -> None:
+    if type(phi) not in {int, float}:
+        TypeError(f"an angle must be integer or float, not {type(phi)}")
+
     if type(q) == QuBit:
         q._QuBit__apply(Matrix.R1(phi))
     elif type(q) == IQuBit:
         q._IQuBit__apply(Matrix.R1(phi))
+    else:
+        raise TypeError(f"a QuBit was expected, but a {type(q)} was given")
 
 def CNOT(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()
+
     SWAP(q, 0, n1)
     SWAP(q, 1, n2)
     q._MuBit__mapply(Matrix.CNOT(), 0)
@@ -246,5 +358,6 @@ def test(q: QuBit) -> None:
     print(varName)
 
 if __name__=="__main__":
-    q = MuBit(3)
-    s = q[1].get_Mubit()
\ No newline at end of file
+    q = MuBit(2)
+
+    print(q[0])
\ No newline at end of file
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