Fix CS/CSdg inverse cancellation with reversed qargs

crates/transpiler/src/passes/inverse_cancellation.rs

@@ -248,6 +248,7 @@ fn std_inverse_pairs(dag: &mut DAGCircuit) {
         {
             continue;
         }
+        let pair_symmetric_2q = matches!([gate_0, gate_1], [StandardGate::CS, StandardGate::CSdg]);
         let filter = |inst: &PackedInstruction| -> bool {
             match inst.op.view() {
                 OperationRef::StandardGate(gate) => gate == gate_0 || gate == gate_1,
@@ -264,12 +265,17 @@ fn std_inverse_pairs(dag: &mut DAGCircuit) {
                 let NodeType::Operation(next_inst) = &dag[nodes[i + 1]] else {
                     unreachable!("Not an op node");
                 };
-                if inst.qubits == next_inst.qubits
-                    && (inst.op.try_standard_gate() == Some(gate_0)
-                        && next_inst.op.try_standard_gate() == Some(gate_1))
-                    || (inst.op.try_standard_gate() == Some(gate_1)
-                        && next_inst.op.try_standard_gate() == Some(gate_0))
-                {
+                let inst_gate = inst.op.try_standard_gate();
+                let next_gate = next_inst.op.try_standard_gate();
+                let pair_match = (inst_gate == Some(gate_0) && next_gate == Some(gate_1))
+                    || (inst_gate == Some(gate_1) && next_gate == Some(gate_0));
+                let qargs_match = inst.qubits == next_inst.qubits
+                    || (pair_symmetric_2q && {
+                        let a = dag.get_qargs(inst.qubits);
+                        let b = dag.get_qargs(next_inst.qubits);
+                        a.len() == 2 && b.len() == 2 && a[0] == b[1] && a[1] == b[0]
+                    });
+                if pair_match && qargs_match {
                     dag.remove_op_node(nodes[i]);
                     dag.remove_op_node(nodes[i + 1]);
                     i += 2;

releasenotes/notes/fix-inverse-cancellation-qubits-15855.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixed :class:`.InverseCancellation` so the default :class:`.CSGate` and
+    :class:`.CSdgGate` inverse pair is cancelled consistently when the two
+    gates act on the same qubits in opposite order.

test/python/transpiler/test_inverse_cancellation.py

@@ -379,6 +379,16 @@ def test_some_inverse_pairs(self, gates_to_cancel):
         self.assertNotIn("t", new_circ.count_ops())
         self.assertNotIn("tdg", new_circ.count_ops())
 
+    def test_cs_csdg_cancel_with_reversed_qargs_in_both_orders(self):
+        """CS/CSdg are symmetric in qubit order, so both inverse orders cancel."""
+        for first, second in (("csdg", "cs"), ("cs", "csdg")):
+            with self.subTest(first=first, second=second):
+                qc = QuantumCircuit(2)
+                getattr(qc, first)(0, 1)
+                getattr(qc, second)(1, 0)
+                new_circ = InverseCancellation()(qc)
+                self.assertEqual(new_circ, QuantumCircuit(2))
+
     @ddt.data([HGate(), CXGate(), CZGate(), (TGate(), TdgGate())], None)
     def test_some_inverse_and_cancelled(self, gates_to_cancel):
         """Test when there are some but not all pairs to cancel."""