Fix wrong argument supplied to _identity_op() (Qiskit#9201)

* Fix wrong argument supplied to _identity_op() Qiskit#9197

* Add test case with large qubit gate

This commit adds a test case to ensure we get the correct result with a
large number of qubits. This also implicitly tests that we've fixed the
excessive memory consumption because the memory requirements for an 8
qubit gate with the bug still present would not be runnable on most
current systems.

Co-authored-by: Jake Lishman <jake.lishman@ibm.com>

* Add release note

---------

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>
Co-authored-by: Jake Lishman <jake.lishman@ibm.com>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

qiskit/circuit/commutation_checker.py

@@ -144,7 +144,7 @@ def commute(
             # being the lowest possible indices so the identity can be tensored before it.
             extra_qarg2 = num_qubits - len(qarg1)
             if extra_qarg2:
-                id_op = _identity_op(2**extra_qarg2)
+                id_op = _identity_op(extra_qarg2)
                 operator_1 = id_op.tensor(operator_1)
             op12 = operator_1.compose(operator_2, qargs=qarg2, front=False)
             op21 = operator_1.compose(operator_2, qargs=qarg2, front=True)

releasenotes/notes/fix-memory-commutation-checker-dbb441de68706b6f.yaml

@@ -0,0 +1,9 @@
+---
+fixes:
+  - |
+    Fixed an issue with the :class:`~.CommutationChecker` class where it would
+    attempt to internally allocate an array for :math:`2^{n}` qubits when it
+    only needed an array to represent :math:`n` qubits. This could cause
+    an excessive amount of memory for wide gates, for example a 4 qubit
+    gate would require 32 gigabytes instead of 2 kilobytes.
+    Fixed `#9197 <https://github.com/Qiskit/qiskit-terra/issues/9197>`__

test/python/circuit/test_commutation_checker.py

@@ -18,7 +18,7 @@
 from qiskit import ClassicalRegister
 from qiskit.test import QiskitTestCase
 
-from qiskit.circuit import QuantumRegister, Parameter
+from qiskit.circuit import QuantumRegister, Parameter, Qubit
 from qiskit.circuit import CommutationChecker
 from qiskit.circuit.library import (
     ZGate,
@@ -357,6 +357,12 @@ def test_complex_gates(self):
         res = comm_checker.commute(lf3, [0, 1, 2], [], lf4, [0, 1, 2], [])
         self.assertTrue(res)
 
+    def test_c7x_gate(self):
+        """Test wide gate works correctly."""
+        qargs = [Qubit() for _ in [None] * 8]
+        res = CommutationChecker().commute(XGate(), qargs[:1], [], XGate().control(7), qargs, [])
+        self.assertFalse(res)
+
 
 if __name__ == "__main__":
     unittest.main()