Use InverseCancellation in opt level 1 instead of CXCancellation (#11210

)

* Use InverseCancellation in opt level 1 instead of CXCancellation

This commit updates the default optimization stage plugin to use the
InverseCancellation pass instead of CXCancellation for optimization
level 1. The CXCancellation pass was hard coded to only cancel runs of
CX gates on the same qubits. This was fine when CX is the target, but
for other targets which aren't using CX the pass had no value. An
alternative, more general, inverse cancellation pass was added in #6855
that enables defining arbitrary inverse cancellation rules and
simplifying a dag based on it. This commit updates the default
optimization plugin at optimization level 1 to use this with some common
inverse rules for 2q gates from the standard gate library.

Closes: #6576
Closes: #7016
Related-to: #7112

* Add sx sx dagger inverse pair to pass

qiskit/transpiler/preset_passmanagers/builtin_plugins.py

@@ -39,14 +39,31 @@
     CommutativeCancellation,
     Collect2qBlocks,
     ConsolidateBlocks,
-    CXCancellation,
+    InverseCancellation,
 )
 from qiskit.transpiler.passes import Depth, Size, FixedPoint, MinimumPoint
 from qiskit.transpiler.passes.utils.gates_basis import GatesInBasis
 from qiskit.transpiler.passes.synthesis.unitary_synthesis import UnitarySynthesis
 from qiskit.passmanager.flow_controllers import ConditionalController
 from qiskit.transpiler.timing_constraints import TimingConstraints
 from qiskit.transpiler.passes.layout.vf2_layout import VF2LayoutStopReason
+from qiskit.circuit.library.standard_gates import (
+    CXGate,
+    ECRGate,
+    CZGate,
+    XGate,
+    YGate,
+    ZGate,
+    TGate,
+    TdgGate,
+    SwapGate,
+    SGate,
+    SdgGate,
+    HGate,
+    CYGate,
+    SXGate,
+    SXdgGate,
+)
 
 
 class DefaultInitPassManager(PassManagerStagePlugin):
@@ -468,7 +485,22 @@ def _opt_control(property_set):
                     Optimize1qGatesDecomposition(
                         basis=pass_manager_config.basis_gates, target=pass_manager_config.target
                     ),
-                    CXCancellation(),
+                    InverseCancellation(
+                        [
+                            CXGate(),
+                            ECRGate(),
+                            CZGate(),
+                            CYGate(),
+                            XGate(),
+                            YGate(),
+                            ZGate(),
+                            HGate(),
+                            SwapGate(),
+                            (TGate(), TdgGate()),
+                            (SGate(), SdgGate()),
+                            (SXGate(), SXdgGate()),
+                        ]
+                    ),
                 ]
             elif optimization_level == 2:
                 # Steps for optimization level 2