Avoid intermediate DAGCircuit construction in 2q synthesis

This commit builds on #12109 which added a dag output to the two qubit
decomposers that are then used by unitary synthesis to add a mode of
operation in unitary synthesis that avoids intermediate dag creation.
To do this efficiently this requires changing the UnitarySynthesis pass
to rebuild the DAG instead of doing a node substitution.

qiskit/transpiler/passes/synthesis/unitary_synthesis.py

@@ -39,6 +39,7 @@
 from qiskit.synthesis.two_qubit.two_qubit_decompose import (
     TwoQubitBasisDecomposer,
     TwoQubitWeylDecomposition,
+    GATE_NAME_MAP,
 )
 from qiskit.quantum_info import Operator
 from qiskit.circuit import ControlFlowOp, Gate, Parameter
@@ -293,7 +294,7 @@ def __init__(
         natural_direction: bool | None = None,
         synth_gates: list[str] | None = None,
         method: str = "default",
-        min_qubits: int = None,
+        min_qubits: int = 0,
         plugin_config: dict = None,
         target: Target = None,
     ):
@@ -499,27 +500,55 @@ def _run_main_loop(
                 ]
             )
 
-        for node in dag.named_nodes(*self._synth_gates):
-            if self._min_qubits is not None and len(node.qargs) < self._min_qubits:
-                continue
-            synth_dag = None
-            unitary = node.op.to_matrix()
-            n_qubits = len(node.qargs)
-            if (plugin_method.max_qubits is not None and n_qubits > plugin_method.max_qubits) or (
-                plugin_method.min_qubits is not None and n_qubits < plugin_method.min_qubits
-            ):
-                method, kwargs = default_method, default_kwargs
+        out_dag = dag.copy_empty_like()
+        for node in dag.topological_op_nodes():
+            if node.op.name == "unitary" and len(node.qargs) >= self._min_qubits:
+                synth_dag = None
+                unitary = node.op.to_matrix()
+                n_qubits = len(node.qargs)
+                if (
+                    plugin_method.max_qubits is not None and n_qubits > plugin_method.max_qubits
+                ) or (plugin_method.min_qubits is not None and n_qubits < plugin_method.min_qubits):
+                    method, kwargs = default_method, default_kwargs
+                else:
+                    method, kwargs = plugin_method, plugin_kwargs
+                if method.supports_coupling_map:
+                    kwargs["coupling_map"] = (
+                        self._coupling_map,
+                        [qubit_indices[x] for x in node.qargs],
+                    )
+                synth_dag = method.run(unitary, **kwargs)
+                if synth_dag is None:
+                    out_dag.apply_operation_back(node.op, node.qargs, node.cargs, check=False)
+                    continue
+                if isinstance(synth_dag, DAGCircuit):
+                    qubit_map = dict(zip(synth_dag.qubits, node.qargs))
+                    for node in synth_dag.topological_op_nodes():
+                        out_dag.apply_operation_back(
+                            node.op, (qubit_map[x] for x in node.qargs), check=False
+                        )
+                    out_dag.global_phase += synth_dag.global_phase
+                else:
+                    node_list, global_phase, gate = synth_dag
+                    qubits = node.qargs
+                    for (
+                        op_name,
+                        params,
+                        qargs,
+                    ) in node_list:
+                        if op_name == "USER_GATE":
+                            op = gate
+                        else:
+                            op = GATE_NAME_MAP[op_name](*params)
+                        out_dag.apply_operation_back(
+                            op,
+                            (qubits[x] for x in qargs),
+                            check=False,
+                        )
+                    out_dag.global_phase += global_phase
             else:
-                method, kwargs = plugin_method, plugin_kwargs
-            if method.supports_coupling_map:
-                kwargs["coupling_map"] = (
-                    self._coupling_map,
-                    [qubit_indices[x] for x in node.qargs],
-                )
-            synth_dag = method.run(unitary, **kwargs)
-            if synth_dag is not None:
-                dag.substitute_node_with_dag(node, synth_dag)
-        return dag
+                out_dag.apply_operation_back(node.op, node.qargs, node.cargs, check=False)
+        return out_dag
 
 
 def _build_gate_lengths(props=None, target=None):
@@ -893,6 +922,20 @@ def run(self, unitary, **options):
                 decomposers2q = [decomposer2q] if decomposer2q is not None else []
             # choose the cheapest output among synthesized circuits
             synth_circuits = []
+            # If we have a single TwoQubitBasisDecomposer skip dag creation as we don't need to
+            # store and can instead manually create the synthesized gates directly in the output dag
+            if len(decomposers2q) == 1 and isinstance(decomposers2q[0], TwoQubitBasisDecomposer):
+                preferred_direction = _preferred_direction(
+                    decomposers2q[0],
+                    qubits,
+                    natural_direction,
+                    coupling_map,
+                    gate_lengths,
+                    gate_errors,
+                )
+                return self._synth_su4_no_dag(
+                    unitary, decomposers2q[0], preferred_direction, approximation_degree
+                )
             for decomposer2q in decomposers2q:
                 preferred_direction = _preferred_direction(
                     decomposer2q, qubits, natural_direction, coupling_map, gate_lengths, gate_errors
@@ -919,6 +962,24 @@ def run(self, unitary, **options):
             return synth_circuit
         return circuit_to_dag(synth_circuit)
 
+    def _synth_su4_no_dag(self, unitary, decomposer2q, preferred_direction, approximation_degree):
+        approximate = not approximation_degree == 1.0
+        synth_circ = decomposer2q._inner_decomposer(unitary, approximate=approximate)
+        if not preferred_direction:
+            return (synth_circ, synth_circ.global_phase, decomposer2q.gate)
+
+        synth_direction = None
+        # if the gates in synthesis are in the opposite direction of the preferred direction
+        # resynthesize a new operator which is the original conjugated by swaps.
+        # this new operator is doubly mirrored from the original and is locally equivalent.
+        for op_name, _params, qubits in synth_circ:
+            if op_name in {"USER_GATE", "cx"}:
+                synth_direction = qubits
+        if synth_direction is not None and synth_direction != preferred_direction:
+            # TODO: Avoid using a dag to correct the synthesis direction
+            return self._reversed_synth_su4(unitary, decomposer2q, approximation_degree)
+        return (synth_circ, synth_circ.global_phase, decomposer2q.gate)
+
     def _synth_su4(self, su4_mat, decomposer2q, preferred_direction, approximation_degree):
         approximate = not approximation_degree == 1.0
         synth_circ = decomposer2q(su4_mat, approximate=approximate, use_dag=True)
@@ -932,16 +993,20 @@ def _synth_su4(self, su4_mat, decomposer2q, preferred_direction, approximation_d
             if inst.op.num_qubits == 2:
                 synth_direction = [synth_circ.find_bit(q).index for q in inst.qargs]
         if synth_direction is not None and synth_direction != preferred_direction:
-            su4_mat_mm = su4_mat.copy()
-            su4_mat_mm[[1, 2]] = su4_mat_mm[[2, 1]]
-            su4_mat_mm[:, [1, 2]] = su4_mat_mm[:, [2, 1]]
-            synth_circ = decomposer2q(su4_mat_mm, approximate=approximate, use_dag=True)
-            out_dag = DAGCircuit()
-            out_dag.global_phase = synth_circ.global_phase
-            out_dag.add_qubits(list(reversed(synth_circ.qubits)))
-            flip_bits = out_dag.qubits[::-1]
-            for node in synth_circ.topological_op_nodes():
-                qubits = tuple(flip_bits[synth_circ.find_bit(x).index] for x in node.qargs)
-                out_dag.apply_operation_back(node.op, qubits, check=False)
-            return out_dag
+            return self._reversed_synth_su4(su4_mat, decomposer2q, approximation_degree)
         return synth_circ
+
+    def _reversed_synth_su4(self, su4_mat, decomposer2q, approximation_degree):
+        approximate = not approximation_degree == 1.0
+        su4_mat_mm = su4_mat.copy()
+        su4_mat_mm[[1, 2]] = su4_mat_mm[[2, 1]]
+        su4_mat_mm[:, [1, 2]] = su4_mat_mm[:, [2, 1]]
+        synth_circ = decomposer2q(su4_mat_mm, approximate=approximate, use_dag=True)
+        out_dag = DAGCircuit()
+        out_dag.global_phase = synth_circ.global_phase
+        out_dag.add_qubits(list(reversed(synth_circ.qubits)))
+        flip_bits = out_dag.qubits[::-1]
+        for node in synth_circ.topological_op_nodes():
+            qubits = tuple(flip_bits[synth_circ.find_bit(x).index] for x in node.qargs)
+            out_dag.apply_operation_back(node.op, qubits, check=False)
+        return out_dag