diff --git a/lib_q_computer_math.py b/lib_q_computer_math.py
index adb546f..72c90ca 100644
--- a/lib_q_computer_math.py
+++ b/lib_q_computer_math.py
@@ -14,9 +14,20 @@ from load_test import sizeof_fmt
 
 ListOrNdarray = Union[list, np.ndarray]
 
+REPR_TENSOR_OP = "⊗"
+REPR_GREEK_PSI = "ψ"
+REPR_GREEK_PHI = "φ"
+REPR_MATH_KET = "⟩"
+REPR_MATH_BRA = "⟨"
+REPR_MATH_SQRT = "√"
+REPR_MATH_SUBSCRIPT_NUMBERS = "₀₁₂₃₄₅₆₇₈₉"
+
+# Keep a reference to already used states for naming
+UNIVERSE_STATES = []
+
 
 class Matrix(object):
-    """Represents a quantum state as a vector in Hilbert space"""
+    """Wraps a Matrix... it's for my understanding, this could easily probably be np.array"""
 
     def __init__(self, m: ListOrNdarray = None, *args, **kwargs):
         """
@@ -39,7 +50,7 @@ class Matrix(object):
     def __eq__(self, other):
         if isinstance(other, Complex):
             return bool(np.allclose(self.m, other))
-        elif isinstance(other, TwoQubitGate):
+        elif isinstance(other, TwoQubitPartial):
             return False
         return np.allclose(self.m, other.m)
 
@@ -99,7 +110,7 @@ class Matrix(object):
 
 class Vector(Matrix):
     def __init__(self, m: ListOrNdarray = None, *args, **kwargs):
-        super().__init__(m)
+        super().__init__(m, *args, **kwargs)
         if not self._is_vector():
             raise TypeError("Not a vector")
 
@@ -110,7 +121,7 @@ class Vector(Matrix):
 class State(Vector):
     def __init__(self, m: ListOrNdarray = None, name: str = '', *args, **kwargs):
         """State vector representing quantum state"""
-        super().__init__(m)
+        super().__init__(m, *args, **kwargs)
         self.name = name
         if not self._is_normalized():
             raise TypeError("Not a normalized state vector")
@@ -121,7 +132,16 @@ class State(Vector):
     def __repr__(self):
         if self.name:
             return '|{}>'.format(self.name)
-        return str(self.m)
+        for well_known_state in well_known_states:
+            if self == well_known_state:
+                return repr(well_known_state)
+        for used_state in UNIVERSE_STATES:
+            if self.m == used_state:
+                return repr(used_state)
+        next_state_sub = ''.join([REPR_MATH_SUBSCRIPT_NUMBERS[int(d)] for d in str(len(UNIVERSE_STATES))])
+        state_name = '|{}{}>'.format(REPR_GREEK_PSI, next_state_sub)
+        UNIVERSE_STATES.append(self.m)
+        return state_name
 
     def norm(self):
         """Norm/Length of the vector = sqrt(<self|self>)"""
@@ -240,6 +260,16 @@ _1 = State([[0],
             [1]],
            name='1')
 
+_p = State([[1 / np.sqrt(2)],
+            [1 / np.sqrt(2)]],
+           name='+')
+
+_m = State([[1 / np.sqrt(2)],
+            [- 1 / np.sqrt(2)]],
+           name='-')
+
+well_known_states = [_0, _1, _p, _m]
+
 _ = I = UnitaryOperator([[1, 0],
                          [0, 1]],
                         name="-")
@@ -278,7 +308,7 @@ H = UnitaryOperator([[1 / np.sqrt(2), 1 / np.sqrt(2)],
 # np.kron(np.outer(_0.m, _0.m), np.eye(2)) + np.kron(np.outer(_1.m, _1.m), X.m)
 # _0.x(_0) * Matrix(I.m) + _1.x(_1) * Matrix(X.m)
 
-class TwoQubitGate(object):
+class TwoQubitPartial(object):
     def __init__(self, rpr):
         self.rpr = rpr
         self.operator = None
@@ -287,12 +317,12 @@ class TwoQubitGate(object):
         return str("-{}-".format(self.rpr))
 
 
-C_ = TwoQubitGate("C")
-x_ = TwoQubitGate("x")
+C_ = TwoQubitPartial("C")
+x_ = TwoQubitPartial("x")
 
 
 class TwoQubitOperator(UnitaryOperator):
-    def __init__(self, m: ListOrNdarray, A: TwoQubitGate, B: TwoQubitGate,
+    def __init__(self, m: ListOrNdarray, A: TwoQubitPartial, B: TwoQubitPartial,
                  A_p: UnitaryOperator, B_p:UnitaryOperator, *args, **kwargs):
         super().__init__(m, *args, **kwargs)
         A.operator, B.operator = self, self
@@ -327,8 +357,8 @@ CNOT = TwoQubitOperator([[1, 0, 0, 0],
                          [0, 1, 0, 0],
                          [0, 0, 0, 1],
                          [0, 0, 1, 0], ],
-                        TwoQubitGate("C"),
-                        TwoQubitGate("x"),
+                        TwoQubitPartial("C"),
+                        TwoQubitPartial("x"),
                         I,
                         X)
 
@@ -340,8 +370,6 @@ C, x = CNOT.A, CNOT.B
 
 
 def test():
-    _p = State([[1 / np.sqrt(2)], [1 / np.sqrt(2)]], name='+')
-
     # Test properties of Hilbert vector space
     # The four postulates of Quantum Mechanics
     # I: States | Associated to any physical system is a complex vector space
@@ -526,8 +554,8 @@ class QuantumProcessor(object):
             self.add_row(row_data)
 
     def compose_quantum_state(self, step):
-        if any([type(s) is TwoQubitGate for s in step]):
-            two_qubit_gates = filter(lambda s: type(s) is TwoQubitGate, step)
+        if any([type(s) is TwoQubitPartial for s in step]):
+            two_qubit_gates = filter(lambda s: type(s) is TwoQubitPartial, step)
             state = []
             for two_qubit_gate in two_qubit_gates:
                 two_qubit_gate.operator.verify_step(step)