Prepare 0.8.1 release (#1222)

This commit prepares the 0.8.1 release notes for release.

releasenotes/notes/bug-fix-mps-kraus-764cc96854585030.yaml

@@ -2,6 +2,12 @@
 
 fixes:
   - |
-    Fixed bug in MPS::apply_kraus. After applying the kraus matrix to the relevant
-    qubits, we should propagate the changes to the neighboring qubits.
-
+    Fixed an issue with use of the ``matrix_product_state`` method of the
+    :class:`~qiskit.providers.aer.AerSimulator` and
+    :class:`~qiskit.providers.aer.QasmSimulator` simulators when running a
+    noisy simulation with Kraus errors. Previously, the matrix product state
+    simulation method would not propogate changes to neighboring qubits after
+    applying the Kraus matrix. This has been fixed so the output from the
+    simulation is correct.
+    Fixed `#1184 <https://github.com/Qiskit/qiskit-aer/issues/1184>`__ and
+    `#1205 <https://github.com/Qiskit/qiskit-aer/issues/1205>`__

releasenotes/notes/fix-initialize-sampling-b6948e39112f6a46.yaml

@@ -1,7 +1,11 @@
 ---
 fixes:
   - |
-    Fixes bug where the initialize instruction would disable measurement
-    sampling optimization for the statevector and matrix product state
-    simulation methods even when it was the first circuit instruction or
-    applied to all qubits and hence deterministic.
+    Fixed an issue where the :class:`qiskit.extensions.Initialize` instruction
+    would disable measurement sampling optimization for the ``statevector`` and
+    ``matrix_product_state`` simulation methods of the
+    :class:`~qiskit.providers.aer.AerSimulator` and
+    :class:`~qiskit.providers.aer.QasmSimulator` simulators, even when it was
+    the first circuit instruction or applied to all qubits and hence
+    deterministic.
+    Fixed `#1210 <https://github.com/Qiskit/qiskit-aer/issues/1210>`__

releasenotes/notes/fix-normalize-statevector-extended-stabilizer-3811f44e003099f3.yaml

@@ -1,4 +1,10 @@
 ---
 fixes:
   - |
-    Fix issue #1196 by using the inner products with the computational basis states to calculate the norm rather than the norm estimation algorithm.
+    Fix an issue with the :class:`~qiskit.providers.aer.library.SaveStatevector`
+    and :class:`~qiskit.providers.aer.extensions.SnapshotStatevector`
+    instructions when used with the ``extended_stabilizer`` simulation method
+    of the :class:`~qiskit.providers.aer.AerSimulator` and
+    :class:`~qiskit.providers.aer.QasmSimulator` simulators where it would
+    return an unnormalized statevector.
+    Fixed `#1196 <https://github.com/Qiskit/qiskit-aer/issues/1210>`__

releasenotes/notes/set-mps-b0efa4a250c1e8ef.yaml

@@ -1,6 +1,7 @@
 ---
-
-features:
+fixes:
   - |
-    Added support for set_matrix_product_state.
-
+    The ``matrix_product_state`` simulation method now has support for it's
+    previously missing set state instruction,
+    :class:`qiskit.providers.aer.library.SetMatrixProductState`, which enables
+    setting the state of a simulation in a circuit.