Re-revert "Fix deepcopy/pickle of DAGCircuit variable IO nodes (backport Qiskit#14041) (Qiskit#14043)" (Qiskit#14097)

* Revert "Revert "Fix deepcopy/pickle of `DAGCircuit` variable IO nodes (backport Qiskit#14041) (Qiskit#14043)" (Qiskit#14094)"

This reverts commit 3f094ab.

* Fix: Remove mention of `PyObjectAsKey`

Author: raynelfss

crates/circuit/src/dag_circuit.rs

@@ -5591,7 +5591,7 @@ impl DAGCircuit {
             } else if wire.is_instance(imports::CLBIT.get_bound(py))? {
                 NodeType::ClbitOut(self.clbits.find(wire).unwrap())
             } else {
-                NodeType::VarIn(self.vars.find(wire).unwrap())
+                NodeType::VarOut(self.vars.find(wire).unwrap())
             }
         } else if let Ok(op_node) = b.downcast::<DAGOpNode>() {
             let op_node = op_node.borrow();

releasenotes/notes/fix-dag-var-out-pickle-a7d57e97a330e528.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixed a bug in :class:`~.dagcircuit.DAGCircuit` that would cause
+    output :class:`~.expr.Var` nodes to become input nodes during
+    ``deepcopy`` and pickling.

test/python/dagcircuit/test_dagcircuit.py

@@ -2082,6 +2082,80 @@ def test_present_vars(self):
         right.add_captured_var(a_u8_other)
         self.assertNotEqual(left, right)
 
+    def test_pickle_vars(self):
+        """Test vars preserved through pickle."""
+        a = expr.Var.new("a", types.Bool())
+        b = expr.Var.new("b", types.Uint(8))
+
+        # Check inputs.
+        dag = DAGCircuit()
+        dag.add_input_var(a)
+
+        self.assertEqual(dag.num_vars, 1)
+        self.assertEqual(dag.num_input_vars, 1)
+
+        with io.BytesIO() as buf:
+            pickle.dump(dag, buf)
+            buf.seek(0)
+            output = pickle.load(buf)
+
+        self.assertEqual(output.num_vars, 1)
+        self.assertEqual(output.num_input_vars, 1)
+        self.assertEqual(output, dag)
+
+        # Check captures and declarations.
+        dag = DAGCircuit()
+        dag.add_declared_var(a)
+        dag.add_captured_var(b)
+
+        self.assertEqual(dag.num_vars, 2)
+        self.assertEqual(dag.num_captured_vars, 1)
+        self.assertEqual(dag.num_declared_vars, 1)
+
+        with io.BytesIO() as buf:
+            pickle.dump(dag, buf)
+            buf.seek(0)
+            output = pickle.load(buf)
+
+        self.assertEqual(output.num_vars, 2)
+        self.assertEqual(output.num_captured_vars, 1)
+        self.assertEqual(output.num_declared_vars, 1)
+        self.assertEqual(output, dag)
+
+    def test_deepcopy_vars(self):
+        """Test vars preserved through deepcopy."""
+        a = expr.Var.new("a", types.Bool())
+        b = expr.Var.new("b", types.Uint(8))
+
+        # Check inputs.
+        dag = DAGCircuit()
+        dag.add_input_var(a)
+
+        self.assertEqual(dag.num_vars, 1)
+        self.assertEqual(dag.num_input_vars, 1)
+
+        output = copy.deepcopy(dag)
+
+        self.assertEqual(output.num_vars, 1)
+        self.assertEqual(output.num_input_vars, 1)
+        self.assertEqual(output, dag)
+
+        # Check captures and declarations.
+        dag = DAGCircuit()
+        dag.add_declared_var(a)
+        dag.add_captured_var(b)
+
+        self.assertEqual(dag.num_vars, 2)
+        self.assertEqual(dag.num_captured_vars, 1)
+        self.assertEqual(dag.num_declared_vars, 1)
+
+        output = copy.deepcopy(dag)
+
+        self.assertEqual(output.num_vars, 2)
+        self.assertEqual(output.num_captured_vars, 1)
+        self.assertEqual(output.num_declared_vars, 1)
+        self.assertEqual(output, dag)
+
     def test_wires_added_for_simple_classical_vars(self):
         """Var uses should be represented in the wire structure."""
         a = expr.Var.new("a", types.Bool())