From de312535e484bbbed5ab11ea8ce9f0dbeb704dbc Mon Sep 17 00:00:00 2001
From: Kevin Krsulich <kevin.krsulich@ibm.com>
Date: Tue, 23 Mar 2021 13:17:15 -0400
Subject: [PATCH 1/2] Set sympy.evaluate(False) on frequent code paths for
 phase tracking.

---
 qiskit/dagcircuit/dagcircuit.py                    | 4 +++-
 qiskit/transpiler/passes/basis/basis_translator.py | 4 +++-
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/qiskit/dagcircuit/dagcircuit.py b/qiskit/dagcircuit/dagcircuit.py
index 499d23fff0eb..3748c48ec80f 100644
--- a/qiskit/dagcircuit/dagcircuit.py
+++ b/qiskit/dagcircuit/dagcircuit.py
@@ -987,7 +987,9 @@ def substitute_node_with_dag(self, node, input_dag, wires=None):
                                             replay_node.cargs)
 
         if in_dag.global_phase:
-            self.global_phase += in_dag.global_phase
+            from sympy import evaluate
+            with evaluate(False):
+                self.global_phase += in_dag.global_phase
 
         if wires is None:
             wires = in_dag.wires
diff --git a/qiskit/transpiler/passes/basis/basis_translator.py b/qiskit/transpiler/passes/basis/basis_translator.py
index d29f4648895f..bd2558956e8a 100644
--- a/qiskit/transpiler/passes/basis/basis_translator.py
+++ b/qiskit/transpiler/passes/basis/basis_translator.py
@@ -158,7 +158,9 @@ def run(self, dag):
                     dag.substitute_node(node, dag_op, inplace=True)
 
                     if bound_target_dag.global_phase:
-                        dag.global_phase += bound_target_dag.global_phase
+                        from sympy import evaluate
+                        with evaluate(False):
+                            dag.global_phase += bound_target_dag.global_phase
                 else:
                     dag.substitute_node_with_dag(node, bound_target_dag)
             else:

From 705e0df944bd5a2fb0222bf9d2341e5c5b3c9c9d Mon Sep 17 00:00:00 2001
From: Kevin Krsulich <kevin.krsulich@ibm.com>
Date: Mon, 29 Mar 2021 15:47:59 -0400
Subject: [PATCH 2/2] Add release note.

---
 ...ExcitationPreserving-297f3afd4a987cac.yaml | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)
 create mode 100644 releasenotes/notes/5405-Slow-transpilation-of-ExcitationPreserving-297f3afd4a987cac.yaml

diff --git a/releasenotes/notes/5405-Slow-transpilation-of-ExcitationPreserving-297f3afd4a987cac.yaml b/releasenotes/notes/5405-Slow-transpilation-of-ExcitationPreserving-297f3afd4a987cac.yaml
new file mode 100644
index 000000000000..7205ea7b6836
--- /dev/null
+++ b/releasenotes/notes/5405-Slow-transpilation-of-ExcitationPreserving-297f3afd4a987cac.yaml
@@ -0,0 +1,19 @@
+---
+upgrade:
+  - |
+    Following transpilation of a parameterized :class:`~qiskit.circuit.QuantumCircuit`,
+    the :attr:`~qiskit.circuit.QuantumCircuit.global_phase` attribute of output circuit
+    may no longer be returned in a simplified form, if the global phase is a
+    :class:`~qiskit.circuit.ParameterExpression`.
+
+    For example,::
+
+      qc = QuantumCircuit(1)
+      theta = Parameter('theta')
+
+      qc.rz(theta, 0)
+      qc.rz(-theta, 0)
+
+      transpile(qc, basis_gates=['p']).global_phase
+
+    previously returned ``0``, but will now return ``-0.5*theta + 0.5*theta``.