diff --git a/qiskit/qpy/binary_io/circuits.py b/qiskit/qpy/binary_io/circuits.py
index a50f202afa2a..fe7ff5e00b7d 100644
--- a/qiskit/qpy/binary_io/circuits.py
+++ b/qiskit/qpy/binary_io/circuits.py
@@ -296,7 +296,11 @@ def _read_instruction(file_obj, circuit, registers, custom_operations, version,
             "UCRXGate",
             "UCRYGate",
             "UCRZGate",
+<<<<<<< HEAD
+            "diagonal",
+=======
             "DiagonalGate",
+>>>>>>> 982807e5bc8d7b0b7fa130b4cb2b09064b4224d4
         }:
             gate = gate_class(params)
         else:
diff --git a/qiskit/transpiler/passes/scheduling/dynamical_decoupling.py b/qiskit/transpiler/passes/scheduling/dynamical_decoupling.py
index 5b17ca52d190..49e644951075 100644
--- a/qiskit/transpiler/passes/scheduling/dynamical_decoupling.py
+++ b/qiskit/transpiler/passes/scheduling/dynamical_decoupling.py
@@ -257,7 +257,7 @@ def run(self, dag):
                 if gate is not None:
                     new_dag.apply_operation_back(gate, [dag_qubit])
 
-            new_dag.global_phase = _mod_2pi(new_dag.global_phase + sequence_gphase)
+            new_dag.global_phase = new_dag.global_phase + sequence_gphase
 
         return new_dag
 
@@ -268,9 +268,3 @@ def __gate_supported(self, gate: Gate, qarg: int) -> bool:
         return False
 
 
-def _mod_2pi(angle: float, atol: float = 0):
-    """Wrap angle into interval [-π,π). If within atol of the endpoint, clamp to -π"""
-    wrapped = (angle + np.pi) % (2 * np.pi) - np.pi
-    if abs(wrapped - np.pi) < atol:
-        wrapped = -np.pi
-    return wrapped
diff --git a/releasenotes/notes/add-diagonal-to-DiagonalGate-c945e0f8adcd2940.yaml b/releasenotes/notes/add-diagonal-to-DiagonalGate-c945e0f8adcd2940.yaml
new file mode 100644
index 000000000000..2d221e30ad5e
--- /dev/null
+++ b/releasenotes/notes/add-diagonal-to-DiagonalGate-c945e0f8adcd2940.yaml
@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixes initiation of ``DiagonalGate``. Refer to
+    `#10364 <https://github.com/Qiskit/qiskit-terra/issues/10364>` for more
+    details.
\ No newline at end of file
diff --git a/releasenotes/notes/fix-param-global-phase-300dacb389d2f26c.yaml b/releasenotes/notes/fix-param-global-phase-300dacb389d2f26c.yaml
new file mode 100644
index 000000000000..b32966ebd6ea
--- /dev/null
+++ b/releasenotes/notes/fix-param-global-phase-300dacb389d2f26c.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    2pi wrapping cannot be applied on a parameterized global phase.Use the 
+    DAGCircuit global_phase setter to wrap the phase for floats only.Refer to
+    `#10569 <https://github.com/Qiskit/qiskit-terra/issues/10569>` for more
+    details.
\ No newline at end of file
diff --git a/test/qpy_compat/test_qpy.py b/test/qpy_compat/test_qpy.py
index 7eb9b1a6dd99..867cc9141a27 100755
--- a/test/qpy_compat/test_qpy.py
+++ b/test/qpy_compat/test_qpy.py
@@ -575,6 +575,13 @@ def generate_open_controlled_gates():
     return circuits
 
 
+<<<<<<< HEAD
+def generate_diagonal_gate_circuit():
+    """Generate diagonal gate circuit."""
+    diagonal_circuit = QuantumCircuit(2, name="diagonal_circuit")
+    diagonal_circuit.diagonal([1, -1, -1, 1], [0, 1])
+    return diagonal_circuit
+=======
 def generate_acquire_instruction_with_kernel_and_discriminator():
     """Test QPY serialization with Acquire instruction with kernel and discriminator."""
     from qiskit.pulse import builder, AcquireChannel, MemorySlot, Discriminator, Kernel
@@ -707,6 +714,7 @@ def generate_control_flow_expr():
     qc4.rz(np.pi, 0)
 
     return [qc1, qc2, qc3, qc4]
+>>>>>>> 982807e5bc8d7b0b7fa130b4cb2b09064b4224d4
 
 
 def generate_circuits(version_parts):