diff --git a/crates/circuit/src/dag_circuit.rs b/crates/circuit/src/dag_circuit.rs
index 8ce137bb80d3..15fdf3ea815a 100644
--- a/crates/circuit/src/dag_circuit.rs
+++ b/crates/circuit/src/dag_circuit.rs
@@ -6422,11 +6422,6 @@ impl DAGCircuit {
 
         // Pre-process the instructions
         let qubit_set: Vec<Qubit> = if let Some(qubit_ordering) = &qubit_order {
-            if qubit_ordering.len() != num_qubits {
-                return Err(PyValueError::new_err(
-                    "'qubit_order' does not contain exactly the same qubits as the circuit",
-                ));
-            };
             let mut qubits = vec![];
             for qubit in qubit_ordering {
                 let bound = qubit.bind(py);
@@ -6447,11 +6442,6 @@ impl DAGCircuit {
             (0..num_qubits as u32).map(Qubit).collect()
         };
         let clbit_set: Vec<Clbit> = if let Some(clbit_ordering) = &clbit_order {
-            if clbit_ordering.len() != num_clbits {
-                return Err(PyValueError::new_err(
-                    "'clbit_order' does not contain exactly the same clbits as the circuit",
-                ));
-            };
             let mut clbits = vec![];
             for clbit in clbit_ordering {
                 let bound = clbit.bind(py);
@@ -6509,7 +6499,7 @@ impl DAGCircuit {
             num_clbits,
             Some(num_ops),
             Some(num_vars),
-            Some(num_edges),
+            Some(num_edges + (num_ops / 2) * num_vars),
         )?;
 
         // Assign other necessary data
diff --git a/qiskit/converters/circuit_to_dag.py b/qiskit/converters/circuit_to_dag.py
index f9d1cb3d7fca..39f8a1088d4f 100644
--- a/qiskit/converters/circuit_to_dag.py
+++ b/qiskit/converters/circuit_to_dag.py
@@ -57,6 +57,20 @@ def circuit_to_dag(circuit, copy_operations=True, *, qubit_order=None, clbit_ord
             circ.rz(0.5, q[1]).c_if(c, 2)
             dag = circuit_to_dag(circ)
     """
+    if qubit_order is None:
+        qubits = circuit.qubits
+    elif len(qubit_order) != circuit.num_qubits or set(qubit_order) != set(circuit.qubits):
+        raise ValueError("'qubit_order' does not contain exactly the same qubits as the circuit")
+    else:
+        qubits = qubit_order
+
+    if clbit_order is None:
+        clbits = circuit.clbits
+    elif len(clbit_order) != circuit.num_clbits or set(clbit_order) != set(circuit.clbits):
+        raise ValueError("'clbit_order' does not contain exactly the same clbits as the circuit")
+    else:
+        clbits = clbit_order
+
     dagcircuit = core_circuit_to_dag(circuit, qubit_order, clbit_order)
 
     dagcircuit.duration = circuit.duration