diff --git a/src/qibotn/QiboCircuitConvertor.py b/src/qibotn/QiboCircuitConvertor.py
index dcbf3e7..2ed3ce7 100644
--- a/src/qibotn/QiboCircuitConvertor.py
+++ b/src/qibotn/QiboCircuitConvertor.py
@@ -3,31 +3,50 @@ import numpy as np
 
 
 class QiboCircuitToEinsum:
+    """This class takes a quantum circuit defined in Qibo (i.e. a Circuit object)
+    and convert it to an equivalent Tensor Network (TN) representation that is formatted for
+    cuQuantum' contract method to compute the state vectors.
+    See document for detail: https://docs.nvidia.com/cuda/cuquantum/python/api/generated/cuquantum.contract.html
+
+    When the class is constructed, it first process the circuit to an intermediate form by extracting the gate matrix
+    and grouping each gate with its corresponding qubit it is acting on to a list.
+
+    It is then converted it to an equivalent TN expression following the Einstein
+    summation convention through the class function state_vector_operand().
+    The output is to be used by cuQuantum's contract() for computation of the state vectors of the circuit.
+    """
+
     def __init__(self, circuit, dtype="complex128"):
+        def op_shape_from_qubits(nqubits):
+            """This function is to modify the shape of the tensor to the required format by cuQuantum
+            (qubit_states,) * input_output * qubits_involved
+            """
+            return (2,) * 2 * nqubits
+
         self.backend = cp
         self.dtype = getattr(self.backend, dtype)
 
-        self.input_tensor_counter = np.zeros((circuit.nqubits,))
         self.gate_tensors = []
+        gates_qubits = []
+
         for gate in circuit.queue:
-            for target in gate.target_qubits:
-                self.input_tensor_counter[target] += 1
-            for control in gate.control_qubits:
-                self.input_tensor_counter[control] += 1
             gate_qubits = gate.control_qubits + gate.target_qubits
+            gates_qubits.extend(gate_qubits)
+
             # self.gate_tensors is to extract into a list the gate matrix together with the qubit id that it is acting on
+            # https://github.com/NVIDIA/cuQuantum/blob/6b6339358f859ea930907b79854b90b2db71ab92/python/cuquantum/cutensornet/_internal/circuit_parser_utils_cirq.py#L32
+            required_shape = op_shape_from_qubits(len(gate_qubits))
             self.gate_tensors.append(
                 (
-                    cp.asarray(gate.matrix).reshape((2,) * 2 * len(gate_qubits)),
+                    cp.asarray(gate.matrix).reshape(required_shape),
                     gate_qubits,
                 )
             )
-        # self.active_qubits is to identify qubits with at least 1 gate acting on it in the whole circuit.
-        self.active_qubits = [
-            indx for indx, value in enumerate(self.input_tensor_counter) if value > 0
-        ]
 
-    def state_vector(self):
+        # self.active_qubits is to identify qubits with at least 1 gate acting on it in the whole circuit.
+        self.active_qubits = np.unique(gates_qubits)
+
+    def state_vector_operands(self):
         input_tensor_count = len(self.active_qubits)
 
         input_operands = self._get_bitstring_tensors(