Addressing Julien's and Abby's comments; fixing broken links

releasenotes/notes/conservative-commutation-checking-b728e7b6e1645615.yaml

@@ -5,13 +5,13 @@ fixes:
     :class:`~.circuit.Instruction`\ s with  float-only ``params`` as key to query the relation.
     This could lead to incorrect results if the instruction's definition
     depended on additional information beyond just the :attr:`~.circuit.Instruction.params`
-    attribute, as in the case of :class:`.PauliEvolutionGate`.
-    This behavior is now fixed, and the commutation checker conservatively caches
+    attribute, as, for example, in the case of :class:`.PauliEvolutionGate`.
+    This behavior is now fixed, and the commutation checker eagerly caches
     commutations only for Qiskit-native standard gates.
-    For custom gates, this change may incur a performance cost, however guarantees correct
+    For custom gates, this change might incur a performance cost; however, guarantees correct
     results by avoiding unsafe caching.
   - |
-    Fixed a bug in the :class:`.CommmutationChecker`, where checking commutation relations of
+    Fixed a bug in the :class:`.CommutationChecker`, where checking commutation relations of
     an instruction
     with non-numeric values in the :attr:`~.circuit.Instruction.params` attribute (as in the
     case of :class:`.PauliGate`) could raise an error.

releasenotes/notes/fix-efficient-su2-numqubits-issue-2b2c91c1186f82ac.yaml

@@ -1,7 +1,10 @@
 fixes:
   - |
     Fixed a bug that caused the following circuit library functions to produce errors
-    when called with ``num_qubits=1``: :func:`.efficient_su2`, :func:`.real_amplitudes`,
-    :func:`.excitation_preserving` and :func:`.pauli_two_design` (for a single qubit,
-    these circuits do not contain any 2-qubit gates).
+    when called with ``num_qubits=1``:
+    :func:`~qiskit.circuit.library.efficient_su2`,
+    :func:`~qiskit.circuit.library.real_amplitudes`,
+    :func:`~qiskit.circuit.library.excitation_preserving` and
+    :func:`~qiskit.circuit.library.pauli_two_design`
+    (for a single qubit, these circuits do not contain any 2-qubit gates).
     Fixed `#13480 <https://github.com/Qiskit/qiskit/issues/13480>`__.

releasenotes/notes/fix-mcmt-to-gate-ec84e1c625312444.yaml

@@ -4,13 +4,13 @@ fixes:
     Fixed a bug where any instruction named ``"mcmt"`` was incorrectly passed to the
     high-level synthesis routine for a :class:`.MCMTGate`, leading to a failure or an
     invalid result. This issue could happen, for example, when handling the :class:`.MCMT`
-    _circuit_, named ``"mcmt"``, and implicitly converting it into an instruction
-    (e.g. when appending it to another circuit).
+    *circuit*, named ``"mcmt"``, and implicitly converting it into an instruction
+    (e.g., when appending it to another circuit).
     Fixed `#13563 <https://github.com/Qiskit/qiskit/issues/13563>`__.
 
 upgrade_synthesis:
   - |
-    The high level synthesis plugins for :class:`.LinearFunction` no longer raise an
+    The high-level synthesis plugins for :class:`.LinearFunction` no longer raise an
     error when an object other than :class:`.LinearFunction` is passed into the ``run``
     method. Instead, they now return ``None``, which is consistent with other plugins.
     If you relied on this error being raised, you can manually perform an instance-check.

releasenotes/notes/fix-pauli-evo-all-identity-b129acd854d8c391.yaml

@@ -6,3 +6,5 @@ fixes:
     should introduce a global phase equal to ``-evolution_time``, but was off by a factor
     of 2 and could break for parameterized times.
     Fixed `#13625 <https://github.com/Qiskit/qiskit/issues/13625>`__.
+    Fixed `#13675 <https://github.com/Qiskit/qiskit/issues/13675>`__.
+    Fixed `#13644 <https://github.com/Qiskit/qiskit/issues/13644>`__.

releasenotes/notes/fix-target-instr-supported-900a1caa76e30655.yaml

@@ -2,5 +2,5 @@
 fixes:
   - |
     Fixed a bug in the :meth:`.Target.instruction_supported` method where 
-    targets with ``self.num_qubits=None`` would always return ``False``
+    targets with ``self.num_qubits==None`` would always return ``False``
     independently of the  supported basis set.